How should I approach this integral? int[2,infinity] [(x^2)/(sqrt[x^7 - 1])] dx

[mathymathmathmathmathguy]

I have been struggling with this problem for a while now, any advice is greatly appreciated!

 

[BigBeachBanana]

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I have been struggling with this problem for a while now, any advice is greatly appreciated!

Can you tell us more about the integral? Where did it come from?

 

[mmm4444bot]

CAS gives antiderivative in terms of the hypergeometric function ₂F₁(a,b; c; z). ?

??[imath]\text{AND}[/imath]
[imath]\;[/imath]

 

[Steven G]

Did you bother to check if the integrand is non-decreasing? In this case the integral would diverge.

 

[Steven G]

View attachment 35273
I have been struggling with this problem for a while now, any advice is greatly appreciated!

Can we see what you have tried? That way we may be able to help you continue.

 

[skeeter]

Did you bother to check if the integrand is non-decreasing? In this case the integral would diverge.

relative power of the integral overall is [imath]\dfrac{1}{x^{3/2}}[/imath] … it will converge.

 

[Steven G]

relative power of the integral overall is [imath]\dfrac{1}{x^{3/2}}[/imath] … it will converge.

Yes, I know that. However, I think that the student should at least think about it just in case it does diverge.