Question

integrate sinx/(1+sinx)^1/2 dx

Answer 1

http://www.wolframalpha.com/input/?i=integrate++sinx%2F%281%2Bsinx%29%5E1%2F2+dx
click show steps.

Answer 2

use\[\sin^2x+\cos^2x=1\]
after rearranging to become
\[\cos^2x=1-\sin^2x\]
\[\cos x=\sqrt{1-\sin^2x}\]

Answer 3

so you are integrating sin x /cos x
which is the same as integrating tanx

Answer 4

A better way would be to substitute \(x = \frac{\pi}2 - 2y\). Then you can use multiple angle formula to get rid of that square-root.

Answer 5

idk. if it's better though

Answer 6

But that's how I do it, generally.

Answer 7

but i can not remember such formulas
i can only remember sin^2x +cos^2x=1

Answer 8

co2x = cos^2x - \sin^2x => 1 + cos2x = 2cos^2x