\(\begin{align*} \int\frac{x}{1+x^4}dx\end{align*}\) |
Connaissances:
- Reconnaitre la forme \(\frac{2u'}{1+u²}\)
\(\begin{align*} I & = \int \frac{x}{1+x^4}dx \\
& = \int \frac{x}{1+(x²)²}dx \\
& = \frac{1}{2} \int \frac{2x}{1+(x²)²}dx \\
& = \frac{1}{2} tan^{-1}x²+C \end{align*}\)
\[\boxed {\begin{align*} I & =\frac{1}{2} tan^{-1}x²+C(\in \mathbb R) \end{align*}}\]