Question

Any one out there who can give me a hand doing integrals

Answer 1

\(\int\)ure, I can help probably.

Answer 2

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

Answer 3

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

Answer 4

so let p= 1+cos^2x

Answer 5

dp =?

Answer 6

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

Answer 7

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

Answer 8

where did you find the identity?

Answer 9

that's a double angle identity

Answer 10

oh

Answer 11

http://en.wikipedia.org/wiki/List_of_trigonometric_identities#Double-angle.2C_triple-angle.2C_and_half-angle_formulae

Answer 12

can you give a hint on how to get dp

Answer 13

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

Answer 14

is it -2cosxsinx?

Answer 15

yes it is

Answer 16

with dx at the end?

Answer 17

yes

Answer 18

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

Answer 19

ohhhhhhhhhhhh

Answer 20

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

Answer 21

u r the man

Answer 22

lol

Answer 23

The pic of Ernie is right on point too