## anonymous one year ago Any one out there who can give me a hand doing integrals

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1. Empty

$$\int$$ure, I can help probably.

2. anonymous

$\int\limits_{?}^{?} \sin2x/1+\cos^2x$

3. anonymous

In class, my teacher said to make the denominator = to u or p

4. anonymous

so let p= 1+cos^2x

5. anonymous

dp =?

6. anonymous

Yeah, let the bottom be your u. You will need an identity on the numerator to get the proper cancellation, though.

7. anonymous

Take the derivative of p to get dp. Use the identity for the numerator sin 2x = 2 cos x sin x

8. anonymous

where did you find the identity?

9. anonymous

that's a double angle identity

10. anonymous

oh

11. anonymous
12. anonymous

can you give a hint on how to get dp

13. anonymous

It's going to be the derivative of 1 + cos² x. Use the chain rule

14. anonymous

is it -2cosxsinx?

15. anonymous

yes it is

16. anonymous

with dx at the end?

17. anonymous

yes

18. anonymous

cool, but why? this is the stuff the confuses me

19. anonymous

ohhhhhhhhhhhh

20. anonymous

because there isn't an easy rule to integrate the original problem, so we use the substitution to make it simpler

21. anonymous

u r the man

22. anonymous

lol

23. anonymous

The pic of Ernie is right on point too

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