Question

How to integrate 1/sin^2(x)

Do I take u to be equal to sin^2(x)?

Answer 1

\[\Large\rm \frac{1}{\sin x}=\csc x\]

Answer 2

\[\Large\rm \int\limits \csc^2x ~dx\]So you can write it like this, yes?

Answer 3

Do you remember your derivatives involving cosecant and cotangent and all those? :)

Answer 4

Yes

Answer 5

If I had to use integration by substitution what would u be? Will is be csc^2(x)

Answer 6

I don't think you can do substitution. Hmm.

Answer 7

You just need to remember that the derivative of \(\Large\rm -\cot x\) is \(\Large\rm \csc^2 x\).

Answer 8

So the answer is -cot(x) +c?

Answer 9

Mmmm yah that sounds right!