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## Homework Statement

find the definite integral [itex]\int\frac{x^3}{\sqrt{x^2 + 1}}[/itex] dx from 0 to 1

## Homework Equations

## The Attempt at a Solution

This problem is in the integration by parts section .. I chose u = x^3 , and dv=[itex]\frac{1}{\sqrt{x^2 + 1}}[/itex] so v = [itex]\frac{x^4}{4}[/itex] and du = -(x^2 + 1)^([itex]\frac{-3}{2}[/itex]) , so the integral is equal to [itex]\frac{x^4}{4}[/itex] . [itex]\frac{1}{√x^2 + 1}[/itex] - [itex]\int\frac{x^4}{4}[/itex] . -(x^2 + 1)^([itex]\frac{-3}{2}[/itex]) .. and my problem is the integral on the right hand side of the equation; I don't know how to integrate it and I don't know whether if I've chosen the parts correctly or there is a better way of choosing the parts

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