Evaluate \[ \int\frac{x}{1+x^4}\,dx. \]
Solution
Let \(u=x^2\), so \(du=2x\,dx\). Then \[ \boxed{\int\frac{x}{1+x^4}\,dx=\frac12\arctan(x^2)+C.} \]
$\int\frac{x}{1+x^4}\,dx$
P-JIAQR
- Area
- Prelim
- Topics
- Integrals, u-Substitution
- Status
- draft
P-JIAQR
Evaluate \[ \int\frac{x}{1+x^4}\,dx. \]
Let \(u=x^2\), so \(du=2x\,dx\). Then \[ \boxed{\int\frac{x}{1+x^4}\,dx=\frac12\arctan(x^2)+C.} \]