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## Main Question or Discussion Point

I have the following problem

\begin{equation}

\frac{\mathrm{arcsinh}\left(y\right)}{y}\frac{dy}{dx}=B\end{equation}

where B is constant. To solve the problem I separated the

variables and obtained

\begin{equation}

\int\frac{\mathrm{arcsinh}\left(y\right)}{y}dy=B \int dx\end{equation}

I used Wolfram alpha to integrate the LHS and obtained an expression

which did not work for some reason. To check this I tried to do this

from first principles but the attempts led to dead end. I also could

not find such an integral in standard integral tables. Can someone

suggest a solution method to the problem or show me how to integrate

the LHS from first principles or prove Wolfram is right or wrong.

\begin{equation}

\frac{\mathrm{arcsinh}\left(y\right)}{y}\frac{dy}{dx}=B\end{equation}

where B is constant. To solve the problem I separated the

variables and obtained

\begin{equation}

\int\frac{\mathrm{arcsinh}\left(y\right)}{y}dy=B \int dx\end{equation}

I used Wolfram alpha to integrate the LHS and obtained an expression

which did not work for some reason. To check this I tried to do this

from first principles but the attempts led to dead end. I also could

not find such an integral in standard integral tables. Can someone

suggest a solution method to the problem or show me how to integrate

the LHS from first principles or prove Wolfram is right or wrong.