\(\begin{align*}\int(x+\frac{1}{x})²dx \end{align*}\)

Connaissances:

  • primitive de fonctions polynomes

\(\begin{align*}I &= \int(x+\frac{1}{x})²dx \end{align*}\)

Distibuons:


\(\begin{align*}I& = \int (x²+2+x^{- 2})dx \end{align*}\)

\[\boxed{I=\frac{1}{3}x^3 + 2x - \frac{1}{x} + C(\in \mathbb R)}\]