Question

Evaluate the integral sec^6 (2x)dx

Answer 1

\[\int sec^6 2xdx = int (sex^2 2x) ^2 sec^2 2xdx = int (1+tan^2 2x) sec^2 2xdx = tan^4 4x + 2tan^2 2x + 1 * sec^2xdx\]

Answer 2

\[\int (tan^4 4x + 2tan^2 4x + 1) * sec^2xdx = tan^4 4x sec^2x + 2tan^2 4x sec^2 2x + sec^2xdx\]