Exercice 41

\( \begin{align*}  \int sinh(x).dx \end{align*}\)

Connaissances:

  • trigonométrie hyperbolique

\( \begin{align*}I & = \int sinh(x).dx \\
&= \int \frac{e^x-e^{-x}}{2}.dx \\
& = \int \frac{e^x}{2}dx - \int \frac{e^{-x}}{2}dx \\
& = \frac{e^x}{2}- (-\frac{e^{-x}}{2}) +C\\
& = \frac{e^x+e^{-x}}{2}+C \\
& = coshx +C  \end{align*}\)

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