Answer
$$\ln |\sec x|+\frac{1}{2}\cos^2 x+C$$
Work Step by Step
\begin{aligned}
\int \sin ^{2} x \cdot \tan x d x &=\int\left(1-\cos ^{2} x\right) \tan x d x \\
&=\int \tan x d x-\int \cos ^{2} x \tan x d x \\
&=\int \tan x d x-\int \cos ^{2} x \frac{\sin x}{\cos x} d x \\
&=\int \tan x d x-\int \cos ^{2} x \frac{\sin x}{\cos x} d x \\
&=\int \tan x d x-\int \cos x \sin x d x\\
&=\ln |\sec x|+\frac{1}{2}\cos^2 x+C
\end{aligned}
