Epic Errors · Integrity

Top $n$ most common errors, slips and faults in integration, where $n \in \mathbb{Z}$ and $\log(n) > 0$ . Based off my personal experience, my experience with other students around me, and internal hypothesisation.¹

Forgetting +c

Nuff said.

Integration is not distributive over multiplication

int f(x) , g(x) dx , eq, int f(x) dx cdot int g(x) dx

Forgetting to distribute the integral coefficient

egin{align*} k int f(x) + g(x) dx & eq k F(x) + G(x) + c \ k int f(x) + g(x) dx &= k F(x) + extcolor{#f07d1c}{k} G(x) + c end{align*}

Looks unlikely with $f(x)$ and $g(x)$ , but when your functions are fractions and exponents and trigonometric functions, plus you’re worrying about S-I+G-N errors, it’s way too easy to neglect properly multiplying out the leading coefficient.

Memorise your standard derivatives and antiderivatives

Losing track of parts

Derivative coefficients missing in action

Inverse chain rule

Dubious exponential algebra

Phantom division

Not fully dividing through

Divisive fraction splitting

SIGN

Forgetting to substitute the limits

Try sketching graphs

It’s a life skill.

S-I+G-N errors

Need I say any more?

Caring about the answer more than the method

Jumping straight to the answer when reading a solution

Trying to integrate $f(x) / x$

It’s unfortunately not possible with elementary functions.

int rac{e^x}{x} dx quad int rac{ln{x}}{x} dx quad int rac{operatorname{trig}(x)}{x} dx

Not using Desmos

Not using Wolfram Alpha

Not finding integration fun

Not practising enough

I’m not joking tho.

The best way to become cracked at integration is to just do loads of them.

Where can you find questions? I mean, we’ve got 300 here on Integrity ;)

Seriously, what’s the noun form of “hypothesise”??↩