$$\int \tanh(x) - \tanh^3(x)\,dx$$
I get the answer as $\tanh x + c$?
I took out a factor of $\tanh x$, used the identity $1-\tanh^2 x=\text{sech}^2x$, used the substitution of $u=\tanh x$,
and reduced the question to $\int 1 du$.
Is this the way you would normally approach this question?
Cheers.
Gurjinder.B