Not sure how to proceed with uv-vdu integral

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SUMMARY

The discussion centers on finding the integral of the function x^3√(1+x^4)dx. The user initially attempted integration by parts using the substitutions u=x^3 and dv=√(1+x^4), leading to a complex expression. However, a more effective approach is suggested: using the substitution u=1+x^4, which simplifies the integral significantly. The expected result of the integral is confirmed to be (1/6)(x^4+1)^(3/2).

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mushroomyo
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hi, I am trying to find the integral of x^3sqrt(1+x^4)dx
i set it up like this:

u=x^3 dv=sqrt(1+x^4)
du = 3x^2dx v=2/3(1+x^4)^(3/2)

and using uv-integralvdu i get

(2/3x^3(1+x^4)^3/2) - 2/3integral((1+x^4)^(3/2)3x^2)dx

i know that in the end, the integral should equal 1/6(x^4+1)^(3/2) but i don't know how to get there from where i stopped...

help?
 
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Integration by parts is not the best way to do this integral. Try a simple u-substitution:

u = 1 + x4.
 

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