MHB Solve Exponential Integral: \int \frac{2^{x}\cdot 3^{x}}{9^{x}-4^{x}}dx

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The discussion focuses on solving the exponential integral \(\int \frac{2^{x}\cdot 3^{x}}{9^{x}-4^{x}}dx\). A user seeks hints to tackle this complex problem. A suggested approach involves rewriting the integral as \(\int \frac{1}{\frac{3^{x}}{2^x}-\frac{2^{x}}{3^x}}dx\). This transformation aims to simplify the expression for easier integration. The conversation highlights the challenge of the integral and the need for strategic manipulation to find a solution.
Yankel
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Hello

I am trying to solve this exponential integral, it's quite complicated. Any hints ?

\int \frac{2^{x}\cdot 3^{x}}{9^{x}-4^{x}}dxmany thanks
 
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\int \frac{ 1}{\frac{3^{x}}{2^x}-\frac{2^{x}}{3^x}}dx
 
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