## anonymous 3 years ago Find the indefinite integral of (y+(2/sin^2y))dy

1. JamesJ

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

2. anonymous

cscx?

3. JamesJ

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

4. anonymous

I still don't get it?

5. anonymous

csc^2x

6. JamesJ

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

7. JamesJ

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

8. anonymous

9. JamesJ

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

10. anonymous

y^2/2+2cotx+c

11. JamesJ

12. anonymous

Negative cotx

13. JamesJ

yes

14. anonymous

Yes, thank you!!!