Integral of $$$\frac{\left(a + b x^{3}\right)^{\frac{2}{3}}}{x^{6} \left(a d - b d x^{3}\right)}$$$ with respect to $$$x$$$

The calculator will find the integral/antiderivative of $$$\frac{\left(a + b x^{3}\right)^{\frac{2}{3}}}{x^{6} \left(a d - b d x^{3}\right)}$$$ with respect to $$$x$$$, with steps shown.

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Find $$$\int \frac{\left(a + b x^{3}\right)^{\frac{2}{3}}}{x^{6} \left(a d - b d x^{3}\right)}\, dx$$$.