Integration of (3x^2+1)^(3/2) - Step-by-Step Solution

[duki]

Homework Statement

\int x(3x^2+1)^\frac{3}{2}

Homework Equations

The Attempt at a Solution

u=3x^2+1

du=6x dx

\frac{dx}{6}=xdx

\int\frac{du}{6} u^\frac{3}{2}

\frac{1}{6}\int u^\frac{3}{2}du

\frac{1}{6} \frac{u^\frac{5}{2}}{\frac{5}{2}}

\frac{5}{12}u^\frac{5}{2}

\frac{5}{12}(3x^2+1)^\frac{5}{2}

 

[Feldoh]

\frac{1}{6} \frac{u^\frac{5}{2}}{\frac{5}{2}} =/= \frac{5}{12}u^\frac{5}{2}

 

[duki]

\frac{2}{30}u^\frac{5}{2} ?

 

[Feldoh]

Yeah looks right