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Evaluate: int((e/x)^x+(x/e)^x)lnx \ dx....

Evaluate: `int((e/x)^x+(x/e)^x)lnx \ dx`.

Text Solution

Verified by Experts

Let `((x)/(e))^(x)=t`
or `(((x)/(e))^(x) "In"(x)/(e)+x*((x)/(e))^(x-1)*(1)/(e))dx=dt`
or `((x)/(e))^(x)("In"(x)/(e)+1)dx=dt`
or `((x)/(e))^(x) "In"xdx=dt`
So, ` I=int((1)/(t^(2))+1)dt= -(1)/(t)+t+C`
`=((x)/(e))^(x)-((e)/(x))^(x)+C`
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