What is the integral of sec^2 (3x)/1+4tan^3 (x)

Question

please help me with this, thank you so much

Answer 1

Good thing...that correction makes the problem relatively easy whereas before it would have been difficult!

Make the substitution u=tan 3x, the the integrand becomes du/[3(1+4u)]

which integrates as a natural logarithm. I won't do that integration for you, but if you still can't get it, make a comment so that I can get back to you with more help.