Question

Find the following integral.
$\int (x^{\frac{1}{2}}+2e^x-\frac{1}{x})dx$.

Answer 1

$\int \left(x^{\frac{1}{2}}+2e^x-\frac{1}{x}\right)dx\Rightarrow \int x^{\frac{1}{2}}dx+2\int e^{x}dx-\int \frac{1}{x}dx\Rightarrow \frac{x^{\frac{3}{2}}}{\frac{3}{2}}+2e^x-\log x+c\Rightarrow \frac{2}{3}{x}^{\frac{3}{2}}+2e^x-\log x+c$