Question

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

Answer 1

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