Question #897a8

1 Answer

int 2sin^2(t)sec^4(t)dt= 2/3tan^3(t)+C

Explanation:

Given: int 2sin^2(t)sec^4(t)dt=

Use the identity sin(t)sec(t) = sin(t)/cos(t) = tan(t)

2inttan^2(t)sec^2(t)dt=

Let u = tan(t), then du = sec^2(t)dt and the integral becomes:

2intu^2du=

2/3u^3+C =

Reverse the substitution:

2/3tan^3(t)+C