Question

Evaluate :$\int {(x+\frac{1}{x})}^{3}dx,x>0$

Answer 1

$\int {(x+\frac{1}{x})}^{3}dx$

$\Rightarrow \int (x^3+\frac{1}{x^3}+3x^2\frac{1}{x}+3x.\frac{1}{x^2})dx$

$\Rightarrow \int (x^3+\frac{1}{x^3}+3x+\frac{3}{x})dx$

$\Rightarrow \frac{x^4}{4}+\frac{x^{-3+1}}{-3+1}+\frac{3x^2}{2}+3\log x$

$\Rightarrow \frac{x^4}{4}-\frac{1}{2x^2}+\frac{3x^2}{2}+3\log x+c$