Solving the integral I'm trying to calculate the following integral :$\int \sqrt x (2-3x^2)^2dx$, but somehow I can't get it right, here's what I did:
First I expanded the expression:
\begin{align}&\int \sqrt x (4-12x^2 + 9x^4)
\\&= \int(4\sqrt x-12x^2\sqrt x + 9x^4\sqrt x) \end{align}
Then I evaluated each term individually:
\begin{align}&4 \int \sqrt x - 12 \int x ^\frac{5}{2} + 9 \int x^\frac{9}{2} \\&
= \frac{4x^\frac{3}{2} \cdot 2}{3} - \frac{12x^\frac{7}{2} \cdot 2}{7} + \frac{9x^\frac{11}{2} \cdot 2}{11}\end{align}
Which gives
$$\frac{8x^\frac{3}{2}}{3} - \frac{24x^\frac{7}{2}}{7} + \frac{18x^\frac{11}{2}}{11}$$
What's wrong with my solution?

You just forget the constant (and the minus sign as commented), other than that, your answer is correct.
We can verify the solution by differentiating the solution.
\begin{align}\frac{d}{dx}\left(\frac{8x^\frac{3}{2}}{3} - \frac{24x^\frac{7}{2}}{7} + \frac{18x^\frac{11}{2}}{11}+c\right) &=\left( \frac32\right)\frac{8x^\frac12}{3}-\left( \frac72\right)\frac{24x^\frac52}{7}+\left(\frac{11}2\right) \frac{18x^\frac92}{11}\\&= 4x^\frac12-12x^\frac52+9x^\frac92\\&= \sqrt x (4-12x^2 + 9x^4) \end{align}
