`int tan^2(theta) sec^4(theta) d theta` Evaluate the integral

`inttan^2(theta)sec^4(theta)d theta`

Rewrite the integrand as,

`=intsec^2(theta)sec^2(theta)tan^2(theta)d theta`

Now use the identity: `sec^2(x)=1+tan^2(x)`

`=int(1+tan^2(theta))sec^2(theta)tan^2(theta)d theta`

Now apply integral substitution,

Let `u=tan(theta)`

`du=sec^2(theta)d theta`

`=int(1+u^2)u^2du`

`=int(u^2+u^4)du`

`=u^3/3+u^5/5`

Substitute back `u=tan(theta)`

`=(tan^3(theta))/3+(tan^5(theta))/5`

add a constant C to the solution,

`=(tan^3(theta))/3+(tan^5(theta))/5+C`