Question

$\int \left(\frac{m}{x}+\frac{x}{m}+m^x+x^m+mx\right)dx$

Answer 1

$$\begin{gathered} \int \left(\frac{m}{x}+\frac{x}{m}+m^x+x^m+mx\right)dx \\ =m\int \frac{1}{x}dx+\frac{1}{m}\int xdx+\int m^{x}dx+\int x^{m}dx+m\int xdx \\ =m\ln \left|x\right|+\frac{1}{m}\left[\frac{x^{1+1}}{1+1}\right]+\left[\frac{m^x}{\ln m}\right]+\left[\frac{x^{m+1}}{m+1}\right]+m\left[\frac{x^{1+1}}{1+1}\right] \\ =m\ln \left|x\right|+\frac{x^2}{2m}+\frac{m^x}{\ln m}+\frac{x^{m+1}}{m+1}+\frac{m{x}^2}{2}+C \end{gathered}$$