Question #7e566

1 Answer
Nov 1, 2017

tan^3x/3+tanx+C

Explanation:

When integrating powers of tanx and secx it makes it easier to use suitable substitutions.

  • Firstly note that:
    tan^2x+1=sec^2x

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

=intsec^4x dx=intsec^2x(tan^2x+1)dx

  • Now we can use a substitution to solve further

Let u=tan(x)

du=sec^2xdx

intsec^2x(tan^2x+1)dx=int(u^2+1)du

=u^3/3+u+C

sub u back in which gives us our answer

tan^3x/3+tanx+C

Hope this helped, good luck :)