Answer
$$\tanh x + x + C$$
Work Step by Step
$$\eqalign{
& \int {{{\tanh }^2}xdx} \cr
& {\text{hyperbolic identity 1}} - {\tanh ^2}x = {\operatorname{sech} ^2}x \cr
& = \int {\left( {{{\operatorname{sech} }^2}x + 1} \right)} dx \cr
& {\text{split the integrand}} \cr
& = \int {{{\operatorname{sech} }^2}x} dx + \int {dx} \cr
& {\text{find the antiderivative}} \cr
& = \tanh x + x + C \cr} $$