Question

\[\int\left( 2^x + \frac{5}{x} - \frac{1}{x^{1/3}} \right)dx\]

Answer 1

\[\int\left( 2^x + \frac{5}{x} - \frac{1}{x^\frac{1}{3}} \right)dx\]
\[ = \int 2^x dx + 5 \int\frac{dx}{x} - \int\frac{dx}{x^\frac{1}{3}}\]
\[ = \int 2^x dx + 5 \int\frac{dx}{x} - \int x^{- \frac{1}{3}} dx\]
\[ = \frac{2^x}{\ln 2} + 5 \ln x - \left[ \frac{x^{- \frac{1}{3} + 1}}{- \frac{1}{3} + 1} \right] + C\]
\[ = \frac{2^x}{\ln 2} + 5 \ln x - \frac{3}{2} x^\frac{2}{3} + C\]