\(\begin{align*} \int \frac{e^{tanx}}{1-sin²x}dx \end{align*}\) |
Connaissances:
- Trigonométrie
- Trigonométrie notation anglosaxonne
\(\begin{align*} I & = \int \frac{e^{tanx}}{1-sin²x}dx \\
& = \int \frac{e^{tanx}}{cos²x}dx \\
& = \int sec²x.e^{tanx}dx \\
& = \int u'e^udu \\
& = e^{tanx}+C \end{align*}\)
\[\boxed {\begin{align*} I = e^{tanx}+C(\in \mathbb R) \end{align*}}\]