Exercice 33

\(\begin{align*} \int e^{2lnx}dx \end{align*}\)

Connaissances:

  • exponentielle
  • logarithme
  • primitive de fonction polynome

\(\begin{align*} I & = \int e^{2lnx}dx \\
& = \int e^{ln(x²)}dx \\
& = \int x²dx \\
& = \frac{x^3}{3}+C
\end{align*}\)

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