\(\begin{align*} \int \sqrt{1+cos(2x)}.dx \end{align*}\) |
Connaissances:
- Trigonométrie
- Primitive de \(cosx\)
\(\begin{align*} I & = \int \sqrt{1+cos(2x)}.dx \\
& = \int \sqrt{1+(2cos²x-1)}.dx \\
& = \int \sqrt{2cos²x}.dx \\
& = \sqrt{2} \int cosx.dx \\
& = \sqrt{2} \times sinx+C \\
\end{align*}\)
\[\boxed {\begin{align*} I = \sqrt{2} \times sinx+C(\in \mathbb R) \end{align*}}\]