Determine the indefinite integral. (Hint: Use an Identity.) \[ \int \tanh ^{2} x d x \] \[ \int \tanh ^{2} x d x= \]

Step 1 ：Given the integral \(\int \tanh^{2} x dx\)

Step 2 ：We use the identity \(\tanh^{2} x = 1 - \text{sech}^{2} x\)

Step 3 ：Substitute \(\tanh^{2} x\) with \(1 - \text{sech}^{2} x\) in the integral

Step 4 ：The integral becomes \(\int (1 - \text{sech}^{2} x) dx\)

Step 5 ：Separate the integral into two parts: \(-\int dx - \int \text{sech}^{2} x dx\)

Step 6 ：The integral of 1 with respect to x is x, and the integral of \(\text{sech}^{2} x\) with respect to x is \(\tanh x\)

Step 7 ：So, the integral becomes \(-x - \tanh x + C\), where C is the constant of integration

Step 8 ：\(\boxed{\int \tanh^{2} x dx = -x - \tanh x + C}\)