How do you find the indefinite integral of int 1/(3x^2+3)dx?

Feb 28, 2017

$\int \frac{1}{3 {x}^{2} + 3} \mathrm{dx} = \frac{1}{3} \arctan x + C$

Explanation:

Factor out a $3$ in the denominator.

$\int \frac{1}{3 \left({x}^{2} + 1\right)}$

$\frac{1}{3} \int \frac{1}{{x}^{2} + 1}$

We now have a known integral.

$\frac{1}{3} \arctan x + C$

Hopefully this helps!