∫eˣ cot²(eˣ+1) dx. So far, I’ve put u = eˣ + 1 and du = eˣdx and substituted them in, so now I have ∫cot²u du. I’m not sure what to do next, since I can’t figure out the antiderivative for this!

Question

abb0t · Answer

$$\cot^2(u) = \csc^2(u)-1$$
Both of which are easily integrable.

anonymous · Answer

so then i have ∫ (csc²u – 1) du?

abb0t · Answer

Correct.

anonymous · Answer

the antiderivative of csc^2 u -1 = -cot u - u?

abb0t · Answer

Correct again.

anonymous · Answer

yes

anonymous · Answer

thank you! is there some kind of thing on here where i give you points or something for helpuing me :D

abb0t · Answer

Remember to plug u back in to the final answer and add the constant.

anonymous · Answer

@ctmusicgirl7 click "Best Response"