Welcome :: Homework Help and Answers :: Mathskey.com

Recent Visits

    
Welcome to Mathskey.com Question & Answers Community. Ask any math/science homework question and receive answers from other members of the community.

13,435 questions

17,804 answers

1,438 comments

781,107 users

Evaluate the indefinite integral

0 votes

∫tan^3(x)*sec^3(x)dx?

asked May 27, 2013 in CALCULUS by chrisgirl Apprentice

1 Answer

+1 vote
The given equation is ∫tan^3(x)*sec^3(x) dx

                               =>    ∫tan^2(x)*sec^2(x)*(tanx*secx) dx          [Split tan^3(x) = tan^2(x)*tan(x) and tan^3(x) = tan^2(x)*tan(x) ]

                               =>    ∫(sec^2(x) - 1)*sec^2(x)*(tanx*secx) dx   [ Since  tan^2(x) = sec^2(x) - 1]

                               =>    ∫(sec^4(x) - sec^2(x))*(tanx*secx) dx     

                               =>    ∫(sec^4(x)*(tanx*secx) dx - ∫sec^2(x))*(tanx*secx) dx

                               =>    ∫(sec^4(x)*d(secx) - ∫sec^2(x))d(secx)     [ Since d/dx(secx) = tanx*secx ]

                              =>    (1/5)sec^5(x) - (1/3)sec^3(x) + c
answered Jun 8, 2013 by joly Scholar

Related questions

...