Question

What is the Integral of (tan(x))4?

Answer 1

=( - ln|cos x| + C.) 4

(integral) tan x dx = (integral) sin x

COs x dx

set

u = COs x.

then we find

du = - sin x dx

substitute du=-sin x, u=COs x

(integral) sin x

COs x dx = - (integral)

(-1) sin x dx

COs x

= - (integral) du

u

Solve the integral

= - ln |u| + C

substitute back u=COs x

= - ln |COs x| + C

=>(- ln |COs x| + C )4