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Solving Homogeneous Differential Equations

Solve:- ∫e l...

Question

Solve:-
$\int \frac{e l o g x}{x}$

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Solution

$\int \frac{e l o g x}{x} d x$

take $l o g x = t$

$\frac{1}{x} d x = d t$

$\int \frac{e l o g x}{x} d x = \int e t d t = \frac{e t^{2}}{2} + c$

$= \frac{e (l o g x)^{2}}{2} + c$

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