How can one find upper bound over the term, $\int_{0}^{-\lambda\tanh{(x)}}\tanh^{-1}(\frac{v}{\lambda})dv$?

Question

I am trying to find an upper bound over the term, \begin{equation} A(x)=\int_{0}^{-\lambda\tanh{(x)}}\tanh^{-1}\Big(\frac{v}{\lambda}\Big)dv \end{equation} where $\lambda$ is a constant and $x$ and $v$ are scalars. My main aim is to find an expression of the sort, $|A(x)| \leq \kappa$ or $|A(x)| \leq \kappa(x)$. Please help me find the bound over this quantity!