Evaluate the indefinite integrals

1) ∫e^(3x)sin(4x)dx

2) ∫(tanx)^8(secx)^2dx

3) ∫(sinx)^3(cosx)^2dx

4)∫(tan(8x))^3sec(8x)dx

1.) Can be solved through 2 successive integrations and then solving for the integral using algebra.

2.) ∫tan^8(x)*sec^2(x) dx

z = tan(x) => dz = sec^2(x) dx

= ∫z^8 dz = (z^9)/9 + C

= tan^9(x)/9 + C