How do you integrate int cos x / ((sin x)^(1/2))dx?

1 Answer
Jan 2, 2016

int cosx/(sinx)^(1/2) dx=2(sinx)^(1/2)+C

Explanation:

Let's try to guess what was derived.

We could notice, that:
d/dx sinx=cosx and d/dx (f(x)^(1/2))=(d/dx f(x))/(2f(x)^(1/2)) (chain rule)

So we try to substitute u=sinx:
du=cosx dx

int cosx/(sinx)^(1/2) dx=int (du)/u^(1/2)=2int (du)/(2u^(1/2))=2u^(1/2)+C

We need to substitute u=sinx back:

2u^(1/2)+C=2(sinx)^(1/2)+C

Please tell if you need more explanation.