OpenStudy (anonymous):

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

4 years ago
OpenStudy (anonymous):

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.

4 years ago
OpenStudy (anonymous):

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

4 years ago
OpenStudy (anonymous):

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.

4 years ago