Question

How do you integrate this
∫tanxsec^2xdx

Answer 1

u have options

Answer 2

Let u = tanx,
du / dx = sec²x
du = sec²x dx
∫ tanxsec²x dx = ∫ u du
∫ tanxsec²x dx = u² / 2 + C
Since u = tanx,
∫ tanxsec²x dx = tan²x / 2 + C

Answer 3

choose a substitution u = tanx. then use the integral substitution rule from there because the derivative of tanx is sec^2x.