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Evaluate: int(e^x)/x\ {x\ (logx)^2+2logx...

Evaluate: `int(e^x)/x\ {x\ (logx)^2+2logx}\ dx`

Text Solution

Verified by Experts

Let `I =int frac{e^{x}}{x}[x(log x)^{2}+2 log x] d x`
` =int e^{x}[(log x)^{2}+frac{2 log x}{x}] d x`
Here, `f(x)=(log x)^{2}`
` Rightarrow f^{prime}(x)=frac{2 log x}{x}`
put `e^{x} f(x)=t`
` Rightarrow e^{x}(log x)^{2}=t`
Diff both sides W.r.tx
` {[e^{x}(log x)^{2}+e^{x} frac{2 log x}{x}] d x=d t }`
` ...
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