Integral de (9*x)^1/3/((9-x^2)1/3) dx

  /                         /           /  ___     6 ___ 3 ___\                                                                                                                                                            /    ___     6 ___ 3 ___\\
 |                          |   5/6     |\/ 3    2*\/ 3 *\/ x |                                                                                                                                                    5/6     |  \/ 3    2*\/ 3 *\/ x ||
 | 3 _____                  |  3   *atan|----- + -------------|   3 ___    /   2/3      2/3     3 ___ 3 ___\   3 ___    /   2/3      2/3     3 ___ 3 ___\   3 ___    /3 ___   3 ___\   3 ___    /3 ___   3 ___\   3   *atan|- ----- + -------------||
 | \/ 9*x               2/3 |           \  3           3      /   \/ 3 *log\4*3    + 4*x    - 4*\/ 3 *\/ x /   \/ 3 *log\4*3    + 4*x    + 4*\/ 3 *\/ x /   \/ 3 *log\\/ 3  + \/ x /   \/ 3 *log\\/ x  - \/ 3 /            \    3           3      /|
 | -------- dx = C - 3*3   *|- -------------------------------- - ------------------------------------------ - ------------------------------------------ + ------------------------ + ------------------------ + ----------------------------------|
 | /     2\                 \                 6                                       12                                           12                                  6                          6                               6                 /
 | |9 - x |                                                                                                                                                                                                                                          
 | |------|                                                                                                                                                                                                                                          
 | \  3   /                                                                                                                                                                                                                                          
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$$\int \frac{\sqrt[3]{9 x}}{\frac{1}{3} \left(9 - x^{2}\right)}\, dx = C - 3 \cdot 3^{\frac{2}{3}} \left(\frac{\sqrt[3]{3} \log{\left(\sqrt[3]{x} - \sqrt[3]{3} \right)}}{6} + \frac{\sqrt[3]{3} \log{\left(\sqrt[3]{x} + \sqrt[3]{3} \right)}}{6} - \frac{\sqrt[3]{3} \log{\left(4 x^{\frac{2}{3}} - 4 \sqrt[3]{3} \sqrt[3]{x} + 4 \cdot 3^{\frac{2}{3}} \right)}}{12} - \frac{\sqrt[3]{3} \log{\left(4 x^{\frac{2}{3}} + 4 \sqrt[3]{3} \sqrt[3]{x} + 4 \cdot 3^{\frac{2}{3}} \right)}}{12} + \frac{3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} \sqrt[3]{x}}{3} - \frac{\sqrt{3}}{3} \right)}}{6} - \frac{3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} \sqrt[3]{x}}{3} + \frac{\sqrt{3}}{3} \right)}}{6}\right)$$

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