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