Evaluate the integral

Question

∫tan⁴xsec⁴xdx

Answer 1

indefinite integral of tan^4(x)sec^4(x)dx

= [tan^7(x)]/7 + [tan^5]/5 + C

solve by substituting

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

u = tan(x)

integral of u^4(u^2+1)du

= integral of (u^6 + u^4)du

= u^7 + u^5 + C