Mathematics

Solve :
$$ \int e^x \left( log x + \dfrac {1}{x^2} \right) dx$$


SOLUTION
$$\begin{array}{l} \int { { e^{ x } } } \left( { \log  x+\frac { 1 }{ { { x^{ 2 } } } }  } \right) dx \\ \int { { e^{ x } }\left( { \log  x+\frac { 1 }{ x } -\frac { 1 }{ x } +\frac { 1 }{ { { x^{ 2 } } } }  } \right)  } dx \\ \int{{e^{x}(f(x)-f'(x))\ dx}}= e^x{f(x)}\\ ={ e^{ x } }\left( { \log  x-\frac { 1 }{ x }  } \right) +C \end{array}$$
Hence,
Solved. 
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Subjective Medium Published on 17th 09, 2020
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