The integral $\int\frac{{\rm d}x}{(x+3)^{\frac87}(x-2)^{\frac 67}}$ I need to solve the integral
$$\int\frac{{\rm d}x}{(x+3)^{\frac87}(x-2)^{\frac 67}}$$
I can't seem to be able to set it in a suitable form; and I know it has to do something with the fact that $\frac87+\frac67=2$ which here would be a negative integer; but I still can't integrate it. The question is from a book and Answer was "None of these" So I don't know the answer; 
Thank you!
The other options are:
$$\frac{7}{5}\left(\frac{x+3}{x-2}\right)^{\frac{1}{7}}$$ 
$$\frac{7}{5}\left(\frac{x-2}{x+3}\right)^{\frac{-1}{7}}$$
$$\frac{5}{7}\left(\frac{x-2}{x+3}\right)^{\frac{1}{7}}$$ + constant of integration

Let $$I = \int\frac{1}{(x+3)^{\frac{8}{7}}\cdot (x-2)^{\frac{6}{7}}}dx = \int\frac{1}{\left(\frac{x-2}{x+3}\right)^{\frac{6}{7}}\cdot (x+3)^2}dx$$
Now Put $$\left(\frac{x-2}{x+3}\right) = t\Rightarrow 1-\frac{5}{x+3} =t$$
So we get $$\frac{1}{(x+3)^2}dx = \frac{dt}{5}$$
So we get $$I = \frac{1}{5}\int t^{-\frac{6}{7}}dx = \frac{7}{5}t^{\frac{1}{7}}+\mathcal{C} = \frac{7}{5}\cdot \left(\frac{x-2}{x+3}\right)^{\frac{1}{7}}+\mathcal{C}$$
