Integrals
∫cos⁡−1x1−x dx\int \frac { \cos^{-1}{\sqrt{x}} } { \sqrt{1 - x} }\ dx

priorities

2025 March 31

∫sin⁡(tan⁡−1x)2 dx\int \sin \left( \tan^{-1}{x} \right)^2\ dx

curse me

2025 March 27

∫1(ex+1)ln⁡(e−x+1) dx\int \frac{1}{\left(e^{x}+1\right)\ln\left(e^{-x}+1\right)}\ dx

futures

2025 March 27

∫x dx\int \sqrt{ \sqrt{ \sqrt{x} } }\ dx

pretend like it’s the first time

2025 March 27

∫1−x9099x dx\int \frac { \sqrt{1 - x^{9099}} } { x }\ dx

MISFITS

2025 March 27

∫xlog⁡10(x) dx\int x \log_{10}(x)\ dx

fissure

2025 March 27

∫cos⁡−1x1−x21−cos⁡−1x dx\int \frac { \cos^{-1}{x} } { \sqrt{1-x^2} \sqrt{1-\cos^{-1}{x}} }\ dx

INVERSION

2025 March 25

∫tan⁡x+x(tan⁡2x+sec⁡2x)cos⁡x−xtan⁡x dx\int \frac { \tan{x} + x \left( \tan^2{x} + \sec^2{x} \right) } { \cos{x} - x\tan{x} }\ dx

vanquish

2025 March 25

∫11−tan⁡x dx\int \frac{1}{1-\tan{x}}\ dx

reminiscence

2025 March 24

∫(x2+2x)(1−2x3)(x3+1)2 dx\int \frac{\left(x^{2}+2x\right)\left(1-2x^{3}\right)}{\left(x^{3}+1\right)^{2}}\ dx

intensity

2025 March 22

∫2ex+2cos⁡xex(ex+2sin⁡x)−(cos⁡2x−2) dx\int \frac { 2e^x + 2\cos{x} } { e^x \left( e^x + 2\sin{x} \right) - \left(\cos^2{x} - 2 \right) }\ dx

STRAIGHT DOWN

2025 March 20

∫1ex+1ex+... dx\int \frac{1}{ e^x + \frac{1}{ e^x + ... } }\ dx

relinquish

2025 March 20

∫2π4π2x2−1exp⁡(tan⁡−1(2πix)−2π22πi) dx\int \frac { 2\pi } { 4\pi^2 x^2 - 1 } \exp\left( \frac { \tan^{-1}(2\pi ix) - 2\pi^2 } { 2\pi i } \right)\ dx

dragonometry

2025 March 18

∫∫∫1ln⁡(xy)ln⁡(yz)ln⁡(zx) dx dy dz\int \int \int \frac { 1 } { \ln(x^y) \ln(y^z) \ln(z^x) } \ dx \ dy\ dz

b(r[a{ck}e]t)s

2025 March 17

∫−∞∞x4e−x2 dx\int_{-\infin}^{\infin} x^4 e^{-x^2}\ dx

akaka

2025 March 17

∫24x4+64x3+9x2+12x+31+3x2+8x4 dx\int \frac { 24x^4 + 64x^3 + 9x^2 + 12x + 3 } { 1 + 3x^2 + 8x^4 }\ dx

welcome to the arena

2025 March 17

∫πx2−x(2πx−1)3 dx\int \frac { \pi x^2 - x } { (2\pi x - 1)^3 }\ dx

partial pain

2025 March 17

∫csch(x)tanh⁡−1(ex) dx\int \text{csch}(x)\tanh^{-1}(e^x)\ dx

perfectus

2025 March 17

∫sinh⁡(ix)cosh⁡(ix)tanh⁡(ix)sech⁡(ix) dx\int \frac { \sinh(ix) \cosh(ix) } { \tanh(ix) \operatorname{sech}(ix) }\ dx

hypertrauma

2025 March 17

∫cos⁡xsec⁡x−tan⁡x−cot⁡xsec⁡x+tan⁡x dx\int \frac { \cos{x} } { \sec{x} - \tan{x} } - \frac { \cot{x} } { \sec{x} + \tan{x} }\ dx

crossnaut

2025 March 17

∫1x21601−x2159 dx\int \frac { 1 } { x^{2160}\sqrt{1 - x^{2159}} }\ dx

heavy is the chain

2025 March 13

∫x(x+1)exx−e−x dx\int \frac { x (x+1) e^x } { x - e^{-x} }\ dx

heads up, incoming

2025 March 13

∫1x1000+x dx\int \frac { 1 } { x^{1000} + x }\ dx

spare parts

2025 March 13

∫01/21−x2(x1/2+x+x3/2+x2+...) dx\int_{0}^{1/2}\frac{1-\sqrt{x}}{2}\left(x^{1/2}+x+x^{3/2}+x^{2}+...\right)\ dx

azimuth

2025 March 9

∫0πx⋅ddx(ex+cos⁡xex+sin⁡x) dx\int_0^{\pi} x \cdot \frac{d}{dx} \left( \frac{e^x+\cos{x}}{e^x+\sin{x}} \right) \ dx

RECONNECTION

2025 March 8

∫cos⁡(0)−sin⁡(x)−cos⁡(π)sin⁡(π)−cos⁡(x)−sin⁡(0) dx\int \frac { \cos(0) - \sin(x) - \cos(\pi) } { \sin(\pi) - \cos(x) - \sin(0) }\ dx

attention is all you need

2025 March 8

∫cos⁡−1x1−x2−sin⁡−1x1−x2 dx\int \frac{\cos^{-1}x}{\sqrt{1-x^{2}}}-\frac{\sin^{-1}x}{\sqrt{1-x^{2}}}\ dx

Integrity’s Finest

2025 March 8

∫(x+x2+1)2x2+1 dx\int \frac { \left( x + \sqrt{x^2 + 1} \right)^2 } { x^2 + 1 }\ dx

foreshadowing

2025 March 8

∫cos⁡x+sin⁡xe−xcos⁡2x dx\int \frac { \cos{x} + \sin{x} } { e^{-x} \cos^2{x} }\ dx

cirrus

2025 March 8

∫1x14/17sec⁡(x1/17)2tan⁡(x1/17) dx\int \frac{1}{x^{14/17}}\sec\left(x^{1/17}\right)^{2}\tan\left(x^{1/17}\right)\ dx

like it or not

2025 February 27

∫1+xxcot⁡(1−2x−ln⁡x) dx\int \frac { 1 + \sqrt{x} } {x} \cot\left( 1 - 2\sqrt{x} - \ln{x} \right)\ dx

closure

2025 February 26

∫12x3/2−2x+x1/2[2tan⁡−1(2x−1)]2 dx\int \frac{1}{ 2x^{3/2} - 2x + x^{1/2} } \left[ 2 \tan^{-1}\left( 2\sqrt{x}-1 \right) \right]^2\ dx

wishes

2025 February 26

∫(x6+π)(x12+π2)(x24+π4)(x29−πx23) dx\int (x^6 + \pi) (x^{12} + \pi^2) (x^{24} + \pi^4) (x^{29} - \pi x^{23})\ dx

end it

2025 February 26

∫ex(sin⁡x+xsin⁡x+xcos⁡x) dx\int e^x \left( \sin{x} + x \sin{x} + x \cos{x} \right)\ dx

shimmer

2025 February 26

∫x4+12x3+54x2+108x+84x+3 dx\int \frac { x^4 + 12x^3 + 54x^2 + 108x + 84 } { x+3 }\ dx

runaway

2025 February 15

∫π+x2x+x dx\int \frac { \sqrt{\pi} + \sqrt{x} } { 2x + \sqrt{x} }\ dx

salient

2025 February 15

∫x3(1x+tan⁡x)(sec⁡3x) dx\int x^3 \left( \frac{1}{x} + \tan{x} \right) \left( \sec^3{x} \right)\ dx

afterthought

2025 February 14

∫xtan⁡x+ln⁡(sec⁡x) dx\int x\tan{x} + \ln(\sec{x})\ dx

exactly what I mean

2025 February 14

∫(x5+1)4x(x(x5+1)5+x)5 dx\int \frac { (x^5 + 1)^4 } { x } \left( x \left( x^5 + 1 \right)^5 + x \right)^5\ dx

fiver

2025 February 14

∫[cos⁡x+xsin⁡xcos⁡x][x5sec⁡(x)62πexp⁡(43πx3∫0∞ln⁡y1+y2 dy)+x3sec⁡(x)4πexp⁡(4πx2∫∞0ln⁡y1+y2 dy)] dx\int \left[ \frac { \cos{x} + x \sin{x} } { \cos{x} } \right] \left[ \frac { x^5 \sec(x)^6 } { 2 \pi } \exp\left( \frac{4}{3} \pi x^3 \int_{0}^{\infin} \frac { \ln{y} } { 1 + y^2 } \ dy \right) + \frac { x^3 \sec(x)^4 } { \pi } \exp\left( 4 \pi x^2 \int_{\infin}^{0} \frac { \ln{y} } { 1 + y^2 } \ dy \right) \right]\ dx

what do you mean you don’t want to integrate

2025 February 14

∫(1+1x)(x+1x)(x2+1x)(1−1x) dx\int \left( 1 + \frac{1}{x} \right) \left( x + \frac{1}{x} \right) \left( \frac{x^2 + 1}{x} \right) \left( 1 - \frac{1}{x} \right)\ dx

evaporation

2025 February 13

∫sin⁡2x+cos⁡2x−cot⁡2x(sin⁡2x+cos⁡2x+tan⁡2x)−1sin⁡(2x) dx\int \frac { \sin^2{x} + \cos^2{x} - \cot^2{x} } { ( \sin^2{x} + \cos^2{x} + \tan^2{x} )^{-1} } \sin(2x)\ dx

fantastically bananas

2025 February 9

∫e6x−e9x dx\int \sqrt{e^{6x}-e^{9x}}\ dx

hydraulic

2025 February 8

∫0∞1xln⁡x dx\int_{0}^{\infin} \frac{1}{x\ln{x}} \ dx

humour

2025 February 6

∫(1x+1x3)3 dx\int \left( \frac{1}{x} + \frac{1}{x^3} \right)^3\ dx

blossom

2025 February 6

∫ex(sin⁡(x)cos⁡(x)3−sin⁡(x)3cos⁡(x)) dx\int e^{x}\left(\sin\left(x\right)\cos\left(x\right)^{3}-\sin\left(x\right)^{3}\cos\left(x\right)\right)\ dx

ember

2025 February 2

∫022x−x2 dx\int_{0}^{2} \sqrt{2x - x^2}\ dx

jelly

2025 February 2

∫11+x1/5 dx\int \frac{1}{1+x^{1/5}}\ dx

cavity

2025 February 1

∫x(x2+5)3ln⁡x dx\int x\left(x^{2}+5\right)^{3}\ln x\ dx

crossfire

2025 February 1

∫1−tan⁡2x dx\int \sqrt{1-\tan^{2}x}\ dx

architechnica

2025 February 1

∫(10−x)10 dx\int \left(10-\sqrt{x}\right)^{10}\ dx

laughable

2025 February 1

∫(x+12x4+38x7+516x10+3564x13+...)2 dx\int \left( x + \frac{1}{2} x^4 + \frac{3}{8} x^7 + \frac{5}{16} x^{10} + \frac{35}{64} x^{13} + ... \right)^2\ dx

acrid

2025 January 31

∫1+xtan⁡xxln⁡(xsec⁡x) dx\int \frac { 1 + x\tan{x} } { x } \ln\left( x \sec{x} \right)\ dx

cope

2025 January 30

∫tan⁡(x)29sec⁡(x)30 dx\int \frac { \tan(x)^{29} } { \sec(x)^{30} }\ dx

relapse

2025 January 30

∫1x∫1x∫1x dx dx dx\int \frac{1}{x} \int \frac{1}{x} \int \frac{1}{x} \ dx \ dx\ dx

intcore

2025 January 30

∫cos⁡−1(π2−cos⁡(π2−sin⁡−1(π2−x))) dx\int \cos^{-1}\left(\frac{\pi}{2}-\cos\left(\frac{\pi}{2}-\sin^{-1}\left(\frac{\pi}{2}-x\right)\right)\right)\ dx

introspection

2025 January 30

∫sec⁡(x)4tan⁡(x) dx\int \sec\left(\sqrt{x}\right)^4 \tan\left(\sqrt{x}\right)\ dx

fallenrect

2025 January 30

∫(sec⁡x)(tan⁡x)(sec⁡xtan⁡x)(sec⁡2x) dx\int (\sec{x})(\tan{x})(\sec{x}\tan{x})(\sec^2{x})\ dx

calling

2025 January 30

∫(cos⁡x−sin⁡x)(cos⁡x+sin⁡x)1+(sin⁡x)(cos⁡x)−1 dx\int \frac { \left(\cos{x} - \sin{x}\right) \left(\cos{x} + \sin{x}\right) } { 1 + \left(\sin{x}\right) \left(\cos{x}\right) - 1 }\ dx

turnover

2025 January 30

∫sin⁡(4x)cos⁡(3x)2+sin⁡(3x)cos⁡(3x)cos⁡(4x)+sin⁡(3x)cos⁡(7x) dx\int \sin(4x)\cos(3x)^2 + \sin(3x)\cos(3x)\cos(4x) + \sin(3x)\cos(7x)\ dx

morphling

2025 January 30

∫exxex(1x+ln⁡x) dx\int e^x x^{e^x} \left( \frac{1}{x} + \ln{x} \right)\ dx

chrome

2025 January 30

∫2+x+sec⁡x+sec⁡xtan⁡x1+x+sec⁡x dx\int \frac { 2 + x + \sec{x} + \sec{x}\tan{x} } { 1 + x + \sec{x} }\ dx

fits

2025 January 29

∫−∞∞exe−x2 dx\int_{-\infty}^{\infty}exe^{-x^{2}}\ dx

abnormal

2025 January 27

∫sin⁡(1+cos⁡−1x) dx\int \sin\left(1+\cos^{-1}{x}\right)\ dx

export

2025 January 26

∫cos⁡(3x)sin⁡(x)cos⁡(2x) dx\int \frac {\cos(3x)} {\sin(x)\cos(2x)}\ dx

kindred

2025 January 25

∫sec⁡(x)csc⁡(x) dx\int \sec(x)\csc(x) \ dx

brittle

2025 January 24

∫sin⁡(sech xcosh⁡x+sinh⁡x)2+cos⁡(1−tanh⁡x)2 dx\int \sin\left( \frac { \text{sech}\, x } { \cosh{x} + \sinh{x} } \right)^2 + \cos\left( 1 - \tanh{x} \right)^2\ dx

drizzle

2025 January 23

∫exex+1+1ex−1 dx\int \sqrt{ \frac { e^x } { e^x+1 } + \frac { 1 } { e^x-1 } }\ dx

anticonjugate

2025 January 23

∫(2+e−x/2)(1−x+e−x/2)x−e−x/2 dx\int \frac { (2+e^{-x/2})(1-x+e^{-x/2}) } { \sqrt{x-e^{-x/2}} }\ dx

hyperformant

2025 January 23

∫sin⁡x(ex+sin⁡x)+(ex+cos⁡x) dx\int \frac {\sin{x}} {\left( e^x+\sin{x} \right) + \left( e^x+\cos{x} \right)}\ dx

unfazed!

2025 January 23

∫sin⁡(x)exp⁡(1sec⁡x−1)cos⁡2x−2cos⁡x+1 dx\int \frac { \sin(x) \exp(\frac{1}{\sec{x}-1}) } { \cos^2{x} - 2\cos{x} + 1 }\ dx

lighthouse

2025 January 21

∫480x5−17x3+16x dx\int \frac {480} {x^5 - 17x^3 + 16x}\ dx

aggregrate

2025 January 21

∫x34(1−x)36 dx\int \frac {x^{34}} {(1 - x)^{36}}\ dx

rewarp

2025 January 21

∫...∫⏟20(20! x) dx ... dx\underbrace{\int ... \int}_{20} ( 20! \, x )\ dx \, ... \, dx

oh look, constants!

2025 January 19

∫2x 4x 8x...256x dx\int 2^x \, 4^x \, 8^x ... 256^x\ dx

target practice

2025 January 19

∫(e2)ln⁡(x2) dx\int \left(e^2\right)^{\ln(x^2)}\ dx

unfazed

2025 January 18

∫x−1+x+1x+1−x−1 dx\int \sqrt{ \frac { \sqrt{x-1}+\sqrt{x+1} } { \sqrt{x+1}-\sqrt{x-1} } }\ dx

gridded

2025 January 18

∫(x+π4)sin⁡(x+π4)sin⁡(x−π4) dx\int \left( \frac{x+\pi}{4} \right) \sin\left( \frac{x+\pi}{4} \right) \sin\left( \frac{x-\pi}{4} \right)\ dx

steamroller

2025 January 18

∫2sec⁡x−2tan⁡x−cos⁡xsin⁡x−1 dx\int \frac{2\sec x-2\tan x-\cos x}{\sin x-1}\ dx

peroxide

2025 January 15

∫(exln⁡e)(ex+1)(x+1ln⁡e) dx\int \left( \frac{e^x}{\ln{e}} \right)^{\left( e^x + 1 \right)} \left( \frac{x+1}{\ln{e}} \right)\ dx

hearth

2025 January 13

∫ln⁡(ln⁡(xe))exln⁡(xe) dx\int \frac {\ln\left(\ln\left(x^e\right)\right)} {ex\ln\left(x^e\right)}\ dx

origami

2025 January 12

∫03π(1+sin⁡4xsin⁡2x+cos⁡2x)3 dx\int_{0}^{3\pi}\left(\frac{1+\sin4x}{\sin2x+\cos2x}\right)^{3}\ dx

masquerade

2025 January 12

∫cos⁡(3x−π/3)+cos⁡(3x+π/3)sinh⁡(x+π/3)+cosh⁡(x−π/3) dx\int \frac { \cos(3^x-\pi/3) + \cos(3^x+\pi/3) } { \sinh(x+\pi/3)+ \cosh(x-\pi/3) }\ dx

dreadnought

2025 January 12

∫(2x(x2+0.5))2(ln⁡x+0.5) dx\int \left( 2x^{\left(x^2 + 0.5\right)} \right)^2 \left( \ln{x} + 0.5 \right)\ dx

blursed

2025 January 12

∫sec⁡xsec⁡x−tan⁡x dx\int \frac{\sec{x}}{\sec{x} - \tan{x}}\ dx

sabotage

2025 January 12

∫sec⁡4x+2tan⁡4x+tan⁡2x+sec⁡2x−1(tan⁡xsec⁡2x+π)2025 dx\int \frac {\sec^4{x} + 2\tan^4{x} + \tan^2{x} + \sec^2{x} - 1} {\left( \tan{x}\sec^2{x} + \pi \right)^{\sqrt{2025}}}\ dx

treasure hunting

2025 January 12

∫x−2x2tan⁡−1x(x2+1)2 dx\int \frac{x-2x^{2}\tan^{-1}{x}}{\left(x^{2}+1\right)^{2}}\ dx

deadlock

2025 January 12

∫sinh⁡x+cosh⁡xcosh⁡x−sinh⁡x dx\int \sqrt{\frac{\sinh x+\cosh x}{\cosh x-\sinh x}}\ dx

hyperactive

2025 January 11

∫x1−1x dx\int \sqrt{\frac{x}{1-\frac{1}{x}}}\ dx

folder

2025 January 11

∫137sin⁡2x+111cos⁡2x dx\int \frac{1}{37\sin^{2}x+111\cos^{2}x}\ dx

orders

2025 January 11

∫(cot⁡x)ln⁡((1/e)sin⁡x)log⁡(1/e)(e−cos⁡x) dx\int \frac {\left(\cot{x}\right) \ln\left( \left(1/e\right)^{\sin{x}} \right)} {\log_{(1/e)}\left (e^{-\cos{x}} \right)}\ dx

ascension

2025 January 11

∫x314−x16 dx\int \frac{x^{31}}{\sqrt{4-x^{16}}}\ dx

kurtosis

2025 January 10

∫x5x6−3x4+4x2−2 dx\int \frac{x^{5}}{x^{6}-3x^{4}+4x^{2}-2}\ dx

bureaucracy

2025 January 10

∫cos⁡x+sec⁡2x+tan⁡2xxcos⁡x+tan⁡x dx\int \frac{\cos x+\sec^{2}x+\tan^{2}x}{x\cos x+\tan x}\ dx

catalyst

2025 January 10

∫esec⁡2xsin⁡xcos⁡x−2sec⁡xln⁡(sec⁡4x+tan⁡4x+2sec⁡2xtan⁡2xsech2 x+tanh2 x) dx\int \frac {e \sec^2{x}\sin{x}} {\cos{x} - 2\sec{x}} \ln \left( \frac {\sec^4{x} + \tan^4{x} + 2\sec^2{x}\tan^2{x}} {\text{sech}^2\,{x} + \text{tanh}^2\,{x}} \right)\ dx

neurotic

2025 January 9

∫4x21−x4 dx\int \frac{4x^{2}}{1-x^{4}}\ dx

mechanism

2025 January 9

∫x7x2+1 dx\int \frac{x^{7}}{x^{2}+1}\ dx

slice and dice

2025 January 9

∫tan⁡(x)sec⁡(x)tan⁡(sec⁡x) dx\int \tan\left(x\right)\sec\left(x\right)\tan\left(\sec x\right)\ dx

palisade

2025 January 9

∫1+tan⁡xsec⁡4x+sec⁡xtan⁡x−2sec⁡2xtan⁡2x+sec⁡x+tan⁡x+tan⁡4x dx\int \frac {1 + \tan{x}} { \sec^4{x} + \sec{x}\tan{x} - 2\sec^2{x}\tan^2{x} + \sec{x} + \tan{x} + \tan^4{x} }\ dx

secanthropic

2025 January 9

∫(sin⁡x)ln⁡(sin⁡2x) dx\int \left(\sin x\right)\ln\left(\sin^{2}x\right)\ dx

frigate

2025 January 7

∫sin⁡(ex+π2)sin⁡(ex−π2) dx\int \frac{\sin\left(e^{x}+\frac{\pi}{2}\right)}{\sin\left(e^{x}-\frac{\pi}{2}\right)}\ dx

rejoice

2025 January 7

∫e(1+tan⁡x)cos⁡2xtan⁡x dx\int \frac{e^{\left(1+\sqrt{\tan x}\right)}}{\cos^{2}x\sqrt{\tan x}}\ dx

ammunition

2025 January 4

∫ln⁡(xx2+4x−21) dx\int \ln\left(\sqrt{x\sqrt{x^{2}+4x-21}}\right)\ dx

in my heart

2024 December 28

∫(2x−x)2 dx\int \left(2^{x}-x\right)^{2}\ dx

divide and conquer

2024 December 27

∫11+1x+1x2 dx\int \frac{1}{1+\frac{1}{x}+\frac{1}{x^{2}}}\ dx

tension

2024 December 27

∫x+x2−x3x−x2+x3 dx\int \frac{x+x^{2}-x^{3}}{x-x^{2}+x^{3}}\ dx

polytypical

2024 December 24

∫sin⁡(2x)cos⁡(x−π) dx\int \sin\left(2x\right)\cos\left(x-\pi\right)\ dx

isomorphism

2024 December 24

∫1+x2x5e(1+1x2) dx\int \frac{1+x^{2}}{x^{5}}e^{\left(1+\frac{1}{x^{2}}\right)}\ dx

flyby

2024 December 24

∫sin⁡(x)2cos⁡(x+e)2−sin⁡(x+e)2cos⁡(x)2 dx\int \sin\left(x\right)^{2}\cos\left(x+e\right)^{2}-\sin\left(x+e\right)^{2}\cos\left(x\right)^{2}\ dx

polymorphism

2024 December 23

∫tan⁡−1(3x)1+9x2 dx\int \frac{\tan^{-1}\left(3x\right)}{1+9x^{2}}\ dx

skylight

2024 December 22

∫e3x−e−xex+e−xdx\int \frac{e^{3x}-e^{-x}}{e^{x}+e^{-x}}dx

expletive

2024 December 17

∫(1−2x−1−3x−2)−2 dx\int \left(1-2x^{-1}-3x^{-2}\right)^{-2}\ dx

workable

2024 December 13

∫−x+x2−4ex2π dx\int \frac{-x+\sqrt{x^{2}-4ex}}{2\pi}\ dx

déjà vu

2024 December 13

∫xx−8x−2−6+12x−1 dx\int x\sqrt{x-8x^{-2}-6+12x^{-1}}\ dx

chummy

2024 December 10

∫1+xx2+ln⁡(xx) dx\int \frac{1+x}{x^{2}+\ln\left(x^{x}\right)}\ dx

quotable

2024 December 10

∫ln⁡(sec⁡x)−ln⁡(csc⁡x)csc⁡xcos⁡3x dx\int \frac{\ln\left(\sec x\right)-\ln\left(\csc x\right)}{\csc x\cos^{3}x}\ dx

pathological

2024 December 10

∫1+x−1cot⁡x−1xln⁡(x−1sin⁡(x−1)) dx\int \frac{1+x^{-1}\cot x^{-1}}{x\ln\left(x^{-1}\sin\left(x^{-1}\right)\right)}\ dx

blink

2024 December 9

∫11−x−2ln⁡(x−1) dx+∫11−x−2ln⁡(x+1) dx\int \frac{1}{\sqrt{1-x^{-2}}}\ln\left(x-1\right)\ dx+\int \frac{1}{\sqrt{1-x^{-2}}}\ln\left(x+1\right)\ dx

lawful evil

2024 December 9

(∫π−12π−112(1−cos⁡(π2))sin⁡(x+12) dx)2−12∫π−1−π−1cos⁡(x+12) dx\left(\int_{\pi-1}^{2\pi-1}\frac{1}{2}\left(1-\cos\left(\frac{\pi}{2}\right)\right)\sin\left(\frac{x+1}{2}\right)\ dx\right)^{2}-\frac{1}{2}\int_{\pi-1}^{-\pi-1}\cos\left(\frac{x+1}{2}\right)\ dx

bleugh

2024 December 8

∫x3x4−6x2+5 dx\int \frac{x^{3}}{x^{4}-6x^{2}+5}\ dx

counting

2024 December

∫ln⁡(4x−12+9x−1) dx\int \ln\left(4x-12+9x^{-1}\right)\ dx

abode

2024 December

∫6x2−14x+12−x3x−2 dx\int \frac{6x^{2}-14x+12-x^{3}}{x-2}\ dx

2024 December

∫1+1+ex dx\int \sqrt{1+\sqrt{1+e^{x}}}\ dx

monster

2024 December

∫2 sign⁡(x)2−x2sin⁡−1(−x2−i2)−i2sin⁡−1(x2−i2)−i2 dx\int \frac {2\ \operatorname{sign}(x)} {\sqrt{2-x^2}} \sqrt{\frac { \sin^{-1}\left(-x^2 - i^2 \right) - i^2 } { \sin^{-1}\left(x^2 - i^2 \right) - i^2 } }\ dx

machina