6
$\begingroup$

Compute $$\int\frac{x^{1/2}}{1+x^2}\,dx.$$

All I can think of is some integration by substitution. But ran into something scary. Anyone have any tricks?

  • 0
    Just a general note: In searching for a substitution $x=f(y)$ for $\int \frac{P(x)}{Q(x)}\mathbb{d}x$, one could try to solve $f'(y)=Q(f(y))$ which then leaves one with the formally simpler $\int P(f(y))\mathbb{d}y$. Here, sadly, $P(x)$ is no polynomial and so the resulting integral $\int\tan{(y)}^{1/2}\mathbb{d}y$ is merely shorter but probably [not](http://www.wolframalpha.com/input/?i=Integrate[Tan[y]^%281%2F2%29%2Cy]) simpler to solve.2013-01-23

2 Answers 2