- #1
JulieK
- 50
- 0
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.