Question

Find the indefinite integral of (y+(2/sin^2y))dy

Answer 1

Hint: what's the derivative with respect to y of cot(y) ?

Answer 2

cscx?

Answer 3

No. But it is related to the 1/sin^2 y in your question

Answer 4

I still don't get it?

Answer 5

csc^2x

Answer 6

\[ \frac{d }{dy} \cot y = - \frac{1}{\sin^2 y} = - \csc^2 y \]

Answer 7

Hence
\[ \int \left( y + \frac{2}{\sin^2 y} \right) \ dy = \int y \ dy + 2 \int \csc^2 y \ dy = ... \]

Answer 8

So what's the answer?

Answer 9

You tell me. I've done the first few steps for you. You only have 2 more to do: evaluate each of those integrals above

Answer 10

y^2/2+2cotx+c

Answer 11

Double check your signs!

Answer 12

Negative cotx

Answer 13

yes

Answer 14

Yes, thank you!!!