Mathematics - Indefinite Integration Question with Solution | TestHub

If $\begin{array}{rl}\int \left(\frac{1}{x}+\frac{1}{x^3}\right)& \left(\sqrt[23]{3x^{-24}+x^{-26}}\right)dx\\ & =-\frac{\alpha }{3(\alpha +1)}{\left(3x^{\beta }+x^{\gamma }\right)}^{\frac{\alpha +1}{\alpha }}+C,x>0,\end{array}$ $(\alpha ,\beta ,\gamma \in Z)$, where $C$ is the constant of integration, then $\alpha +\beta +\gamma$ is equal to ________ .