Question

Evaluate the following integral:
$\int \frac{x^3-3x^2+5x-7+x^2{a}^x}{2x^2}dx$

Answer 1

$\int \frac{x^3-3x^2+5x-7+x^2{a}^x}{2x^2}dx$

$=\frac{1}{2}\int \frac{x^3-3x^2+5x-7+x^2{a}^x}{x^2}dx$

$=\frac{1}{2}\int xdx-\frac{3}{2}\int dx+\frac{5}{2}\int \frac{dx}{x}-\frac{7}{2}\int \frac{dx}{x^2}+\frac{1}{2}\int a^{x}dx$

$=\frac{x^2}{4}-\frac{3x}{2}+\frac{5}{2}\log \left|x\right|+\frac{7}{2x}+\frac{a^x}{2\log a}+c$ where $c$ is the constant of integration.