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## Homework Statement

[tex]\int x(3x^2+1)^\frac{3}{2}[/tex]

## Homework Equations

## The Attempt at a Solution

[tex]u=3x^2+1[/tex]

[tex]du=6x dx[/tex]

[tex]\frac{dx}{6}=xdx[/tex]

[tex]\int\frac{du}{6} u^\frac{3}{2}[/tex]

[tex]\frac{1}{6}\int u^\frac{3}{2}du[/tex]

[tex]\frac{1}{6} \frac{u^\frac{5}{2}}{\frac{5}{2}}[/tex]

[tex]\frac{5}{12}u^\frac{5}{2}[/tex]

[tex]\frac{5}{12}(3x^2+1)^\frac{5}{2}[/tex]