Question

hi, can anyone explain me how to get the integral:
∫((sin^3 x)/sqrt(cos x))dx

Answer 1

well, you will need to take cos x as a variable, say 't', and then use chain rule to say that dx = dt/-sinx
Then, you substitute for cos x and simplify and then integrate, and finally substitute for 't' to get the answer.

Answer 2

thanks a lot for your reply, but can you explain a little bit more de chain rule part?

Answer 3

You first need to change sin^3x as follows:

sin^3x
=sin^2x sinx
=(1-cos^2x)sinx

Substitute this form into original integral and distribute cos^(-1/2) over (1-cos^2x)
so you now have
integral of (cos^(-1/2)xsin x - cos^(3/2)xsinx )dx

Now you can make the t substitution described earlier and you will have
integral of t^(-1/2) -t^(3/2) dt which can be integrated by power rule.