Question

integration of cosx/xsinx+cosx

Answer 1

Like this?\[\Large \int\limits \frac{\cos x}{x \sin x + \cos x}dx\]+_+

Answer 2

\[\Large \int\limits \frac{\cos x}{x \sin x}+ \cos x\;dx\]Orrr this maybe? +_+

Answer 3

yeah!!..
the earlier one

Answer 4

Hmmmmmm

Answer 5

Seems like a u-sub gets us close, but not close enough D:\[\Large u=x \sin x+\cos x\]\[\Large du=\cancel{\sin x}+x \cos x -\cancel{\sin x} \; dx\]\[\Large \frac{1}{x}du=\cos x\; dx\]

Giving us,\[\large \int\limits \frac{1}{x \sin x+\cos x}(\cos x dx) \quad=\quad \int\limits \frac{1}{u}\left(\frac{1}{x}du\right)\]

Answer 6

Are you sure I wrote the problem out correctly? :o
What types of methods have you learned for solving these?

Answer 7

well..
i'm not good at u-substitution!!..
methods i know are:
ntegration by parts
partial fractions
trig substitution
rationalizing substitutions
and yeah you wrote the problem correct enough :P >_<

Answer 8

hmmm

Answer 9

@amistre64 @hartnn
Bah I'm tired :c gotta get to bed.
Maybe one of these smart fellas can help ya.

Answer 10

hahaha!!..
sure!!..
thanks for your help!!..
sleep well chap!! . .

Answer 11

the denominator is a differential d(x*sin(x))

Answer 12

i think that is a clue.

Answer 13

this is going to have me up all night.