Answer
$\frac{1}{2}tan^{2}x+C$
Work Step by Step
Substitute $u= tan x$ so that $dx=\frac{du}{sec^{2}x}$ in the given integral. Then,
$\int sec^{2}xtanxdx=\int sec^{2}x\, u\frac{du}{sec^{2}x}$
$=\int udu= \frac{u^{2}}{2}+C$
Undoing substitution, we get
$\int sec^{2}x tanxdx= \frac{1}{2}tan^{2}x+C$
