# Integration

• Jun 10th 2008, 12:21 PM
JanW
Integration
Can someone help me with the integration of x/sqrt(1+x^5) ?
I just do not get it.
• Jun 10th 2008, 12:24 PM
o_O
Doesn't look like it can be done by elementary means.
• Jun 10th 2008, 12:30 PM
JanW
Thanks for the try. What I actually need to check is if this improper intergral is convergent. As far as I know you have to solve the integral to do this. Or is there another way?
• Jun 10th 2008, 12:32 PM
Mathstud28
Quote:

Originally Posted by JanW
Thanks for the try. What I actually need to check is if this improper intergral is convergent. As far as I know you have to solve the integral to do this. Or is there another way?

Well I assume it is

$\int_0^{\infty}\frac{x}{\sqrt{1+x^5}}dx$

and since $\frac{x}{\sqrt{x^5+1}}\sim\frac{x}{x^{\frac{5}{2}} }=\frac{1}{x^{\frac{3}{2}}}$

therefore this integral is convergent
• Jun 10th 2008, 12:37 PM
JanW
Great thanks a lot! I forgot the boaders, you are right!
• Jun 11th 2008, 02:07 AM
Moo
Quote:

Originally Posted by Mathstud28
Well I assume it is

$\int_0^{\infty}\frac{x}{\sqrt{1+x^5}}dx$

and since $\frac{x}{\sqrt{x^5+1}}\sim\frac{x}{x^{\frac{5}{2}} }=\frac{1}{x^{\frac{3}{2}}}$

therefore this integral is convergent

This is only true if the integral goes from 1 to infinity.

From 0 to 1, the approximation doesn't work (Shake)