Question

Trigonometric Integrals and Substitutions: Integral of (tan(x))^(4) dx.

Answer 1

Well sin^2 x + cos^2 x = 1
Hence

tan^2 x + 1 = sec^2 x
and
tan^2 x = (sec^2 x - 1)

Thus first I would write

tan^4x = tan^2 x . sec^2 x - tan^2 x
= tan^2 x . sec^2 x - (sec^2 x - 1)

Answer 2

Next you know the derivative of tan x is sec^2 x. Hence you can now integrate the first two of the above three terms.

Answer 3

Make sense?

Answer 4

Thanks. I really appreciate it.