A community for students.
Here's the question you clicked on:
 0 viewing
sat_chen
 2 years ago
find the integral of cot^3xcsc^3xdx
sat_chen
 2 years ago
find the integral of cot^3xcsc^3xdx

This Question is Closed

sat_chen
 2 years ago
Best ResponseYou've already chosen the best response.0i got csc^5x/5 + csc^3x/3 + C can someone pls tell me if im doing it right pls let me know thanks

mivanov
 2 years ago
Best ResponseYou've already chosen the best response.1you want integral of cot^3(x)*csc^3(x) dx right?

escolas
 2 years ago
Best ResponseYou've already chosen the best response.0is this (cotx)^3*(cscx)^3 dx?

sat_chen
 2 years ago
Best ResponseYou've already chosen the best response.0sorry about that should have made it more clear

mivanov
 2 years ago
Best ResponseYou've already chosen the best response.1Take the integral: integral cot^3(x) csc^3(x) dx For the integrand cot^3(x) csc^3(x), use the trigonometric identity cot^2(x) = csc^2(x)1: = integral cot(x) csc^3(x) (csc^2(x)1) dx For the integrand cot(x) csc^3(x) (csc^2(x)1), substitute u = csc(x) and du = (cot(x) csc(x)) dx: =  integral u^2 (u^21) du Expanding the integrand u^2 (u^21) gives u^4u^2: =  integral (u^4u^2) du Integrate the sum term by term and factor out constants: = integral u^2 du integral u^4 du The integral of u^4 is u^5/5: = integral u^2 duu^5/5 The integral of u^2 is u^3/3: = u^3/3u^5/5+constant Substitute back for u = csc(x): = (csc^3(x))/3(csc^5(x))/5+constant Which is equal to: Answer:   = 1/30 ((5 cos(2 x)+1) csc^5(x))+constant

mivanov
 2 years ago
Best ResponseYou've already chosen the best response.1so it's just a simple substitution
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.