Question

integration of( 2^x - 3^x )^2 / 2^x × 3^x​

Answer 1

Step-by-step explanation:

We have,

$\int \frac{( {2}^{x} - {3}^{x} ) ^{2} }{ {2}^{x} . {3}^{x} } dx$

$= \int \frac{ {( {2}^{x}) }^{2} + {( {3}^{x} )}^{2} - 2. {2}^{x} . {3}^{x} }{ {2}^{x} . {3}^{x} }dx$

$= \int ( \frac{ {2}^{x} }{ {3}^{x} } + \frac{ {3}^{x} }{ {2}^{x} } - 2)dx$

See attachment