Question

anti derivative of x/(1+3x^2)1/2

Answer 1

Use a u-substitution.\[u = 1 + 3x^2\rightarrow du = 3xdx \rightarrow \frac {du}{3} = xdx\]\[\int\limits \frac {xdx}{(1 + 3x^2)^{1/2}} \rightarrow \frac {1}{3} \int\limits \frac {du}{u^{1/2}}\]

Answer 2

Can you do the rest?

Answer 3

\[\frac {1}{6} \int\limits\limits \frac {du}{u^{1/2}} = \frac {2}{6} \sqrt{u} + C \rightarrow \frac {1}{3} \sqrt{1 + 3x^2} + C\]

Answer 4

Sorry about the first post. du should have been 6xdx not 3xdx. And so xdx = du/6