<s>[INST] Integral $\int\frac{6^x}{9^x-4^x}dx $ How to solve this integral:
$$\int\frac{6^x}{9^x-4^x}dx $$
(I notice that $\frac{6^x}{9^x-4^x}=\frac{2^x3^x}{(3^x-2^x)(3^x+2^x)}$)
Thank you!
 [/INST] Note that $$\frac{1}4\cdot\frac{3^x+2^x}{3^x-2^x}-\frac{1}4\cdot\frac{3^x-2^x}{3^x+2^x}$$ is the integrand. Now use what @J.H. suggested.
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