TITLE: isn&#39;t this wikipedia Definite integrals involving rational or irrational expression wrong!?
QUESTION [9 upvotes]: isn't this wikipedia Definite integrals involving rational or irrational expression wrong!?
According to my calculations:
$\sin[\frac{(m+1)\pi}{n}]$ while in wiki it is 
$\sin[\frac{(m+1)}{n}]$
seems $\pi$ missed.
here is result of my work:
$\int_0^\infty \frac{x^m \, dx}{({x^n+a^n)}^r}=\frac{(-1)^{r-1}\pi a^{m+1-nr}\Gamma [(m+1)/n]}{n\sin[\pi (m+1)/n](r-1)!\Gamma[(m+1)/n-r+1]} \ \ , 0<m+1<nr$
ref:List of definite integrals
Remark:
@icurays1 in your link there is another wrong  $\Gamma [\frac {(m+1)}{(n-p+1)}]$ while it could be $\Gamma [(\frac {m+1}{n})-p+1]$

REPLY [8 votes]: It is definitely wrong.  Take $a=1, m=0, n=2, r=1$.  Then it reads
$$\int_0^\infty \frac{1}{x^2+1}\,dx = \frac{\pi}{2 \sin(1/2)}$$
which is false.  The correct value is $\pi/2$, which agrees with your proposed $\sin\left[\frac{(m+1)\pi}{n}\right]$.
Taking the sine of a rational number is definitely a red flag.