Question

Solve $\int \frac{x^5}{x^2+9}dx$

Answer 1

$\int \frac{x^5}{x^2+9}dx$

Put $x^2+9=t$

$2xdx=dt$

$=\frac{1}{2}\frac{{\left(t-9\right)}^2}{t}dt$

$\frac{1}{2}\int \left(t+\frac{81}{t}-18\right)dt$

$=\frac{t^2}{4}+81\log t-9t+c$

$=\frac{{\left(x^2+9\right)}^2}{4}+81\log \left(x^2+9\right)-9\left(x^2+9\right)tc$

$=\frac{x^4}{4}-\frac{9x^2}{4}+81\log \left(x^2+9\right)tc$