Integration question

Hi, I'm doing some integration questions and I need help - how should I go about doing this question? Is it integration by partial fractions? I can do all of the integration methods quite well it's just a case of choosing which one to use thanks

Its not partial fractions because the denominator, ignoring the 3 because it can be moved outside the integral, does not factorise.

To integrate 1/(1+x^2) you need a trigonometric substitution.

For the most part integration (and practically all math problems) is a case of "if the technique works, good job; if not, try something else". Key word is try (then probably try to recognize the "shape" of the integrand, so next time you know what to try first).
So say you want to try partial fractions. We want the denominator to be nicely factored, right? Well... can we do it here?

This integral, without the 1/3, is actually common enough that remembering by heart is worth it (that is, if you happen to know it).
Otherwise, as RDK suggests, it's a trig sub.