MHB Can Integration by Parts Solve This Tricky Question?

jaychay
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Can you help me with this question ?
I am really struck with this question.
Thank you in advance.
 
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Using integration by parts, I would let

$u = x^3$ and $dv=x^2\sqrt{x^3+1}$Alternatively, one could use the same setup for the method of substitution letting $t= x^3+1$
 

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