Evaluate \[ \int\frac{dx}{9+x^2}. \]
Solution
With \(u=x/3\), \(dx=3\,du\), \[ \int\frac{dx}{9+x^2} =\frac13\int\frac{du}{1+u^2} =\boxed{\frac13\arctan\!\left(\frac x3\right)+C.} \]
$\int\frac{1}{9+x^2}\,dx$
P-UGR7G
- Area
- Prelim
- Topics
- Integrals
- Status
- draft