Question

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

Answer 1

\[\int\left( \frac{m}{x} + \frac{x}{m} + m^x + x^m + mx \right)dx\]
`= m ∫  1/x dx + 1/m ∫  x dx +∫  m^x dx + ∫  x^m dx + m ∫     x  dx `
\[ = m\ln\left| x \right| + \frac{1}{m}\left[ \frac{x^{1 + 1}}{1 + 1} \right] + \left[ \frac{m^x}{\ln m} \right] + \left[ \frac{x^{m + 1}}{m + 1} \right] + m\left[ \frac{x^{1 + 1}}{1 + 1} \right]\]
\[ = m \ln \left| x \right| + \frac{x^2}{2m} + \frac{m^x}{\ln m} + \frac{x^{m + 1}}{m + 1} + \frac{m x^2}{2} + C\]