Hi everyone,
Could someone please tell me how I would solve the integral 1 to infinity x/sq.1+x^6?
I did separation by parts?
u=sq. 1+x^6
dv=xdx
du=1/2(1+x^6)(6x^5)dx
v=x^2/2
Would this work?
Thank you very much
Hi everyone,
Could someone please tell me how I would solve the integral 1 to infinity x/sq.1+x^6?
I did separation by parts?
u=sq. 1+x^6
dv=xdx
du=1/2(1+x^6)(6x^5)dx
v=x^2/2
Would this work?
Thank you very much
Just for your benefit, I don't believe this is integrable by elementary means.
Therefore, parts will not work too well.
$\displaystyle \int_{1}^{\infty}\frac{x}{\sqrt{1+x^{6}}}dx$
I ran it through Maple and got 0.9473799840
For the indefinite, I got: $\displaystyle \frac{x^{2}}{2}hypergeom\left([\frac{1}{3},\frac{1}{2}],[\frac{4}{3}],-x^{6}\right)$
Just a thought to throw out there.
Well, seeing as the indefinite integral has a solution the definite integral ought to as well. The hypergeometric function is a series solution so I wonder if chocolatelover should just derive a Taylor series for the integrand and integrate term by term? Of course then you have to worry about series convergence, etc, so it wouldn't be a walk in the park.
-Dan
As I stated previously, the solution is 0.9473799840.
Of course, I arrived at this via Maple 10.
Here's a graph using Simpson's rule and 100 partitions. I couldn't use 1 to infinity, so I just used 1 to 100. The graph gets infinitely close to the x-axis, so it's not that bad of an estimate