1. ## Definite Integration

Hi,

(1+(x^m))^n

limits of integration are from 0 to 1. Integration is to be done with respect to x and m and n are positive real numbers.

Is it to do with the incomplete beta function, but the upper limit is coming out to be -1, which should lie in the interval 0 to 1.

Thanks in anticipation.

Dekar

2. It appears to be hypergeometric. I ran it through Maple and it gave me.

$\int{(1+x^{m})^{n}}dx=xhypergeom\left([\frac{1}{m},-n],[1+\frac{1}{m}],-x^{m}\right)$.

3. Thanks Galactus,

Thanks

Dekar

4. Originally Posted by dekar
Thanks Galactus,

Thanks

Dekar
See here.

-Dan

5. Originally Posted by dekar
Hi,

(1+(x^m))^n

limits of integration are from 0 to 1. Integration is to be done with respect to x and m and n are positive real numbers.
I think the following works for $n,m>0$.

$\int_0^1 (1+x^m)^n dx$
Let $t=x^m \implies t' = mx^{m-1}$
Thus,
$\frac{1}{m}\int_0^1 (1+t)^n t^{-1 +\frac{1}{m}}dt= \frac{1}{m}\mbox{B}\left( n+1, \frac{1}{m} \right)$

6. Hi,

It won't work because it is (1+t), to have it to get reduced to the beta function we need (1-t),

Thats why I guess, It may go to Incomplete Beta Function if we substitute say p=-t at this stage, but the upper limit then becomes -1.

Dekar

7. Originally Posted by dekar
Hi,

It won't work because it is (1+t), to have it to get reduced to the beta function we need (1-t),

Thats why I guess, It may go to Incomplete Beta Function if we substitute say p=-t at this stage, but the upper limit then becomes -1.

Dekar