A community for students.
Here's the question you clicked on:
 0 viewing
yegiel
 2 years ago
hi, can anyone explain me how to get the integral:
∫((sin^3 x)/sqrt(cos x))dx
yegiel
 2 years ago
hi, can anyone explain me how to get the integral: ∫((sin^3 x)/sqrt(cos x))dx

This Question is Open

ekaknr
 2 years ago
Best ResponseYou've already chosen the best response.0well, 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.

yegiel
 2 years ago
Best ResponseYou've already chosen the best response.0thanks a lot for your reply, but can you explain a little bit more de chain rule part?

rbliss11
 one year ago
Best ResponseYou've already chosen the best response.0You first need to change sin^3x as follows: sin^3x =sin^2x sinx =(1cos^2x)sinx Substitute this form into original integral and distribute cos^(1/2) over (1cos^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.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.