Answer
$7 \ln ( \cosh \dfrac{x}{7}) +C$
Work Step by Step
As we are given that $\int \tanh (\dfrac{x}{7}) dx$
Now, Plug $\dfrac{x}{7}=a$ and $dx= 7 da$
Thus, $\int \tanh (\dfrac{x}{7}) dx= 7 \int \tanh a da =7 \int \dfrac{\sinh a}{\cosh a} da $
Now, again plug $\cosh a =u \implies \sinh a da =du$
This implies
$7 \int \dfrac{\sinh a}{\cosh a} da=7 \int \dfrac{dt}{t}= 7 [\ln |u|] +C= 7 \ln ( \cosh \dfrac{x}{7}) +C$
