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