The correct option is B e^xx^x+c ∫ e^xx^x(2+logx)dx ∫ e^x(1+(1+logx))dx ∫ e^x(x^x+x^x(1+logx))dx we know that dx^xdx=x^x(1+logx) It is ...

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How to Find the Inverse of a Function

∫ exxx2+log x...

Question

$\int e^{x} x^{x} (2 + log x) d x =$

x^{x} + c

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e^{x} l o g x + c

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e^{x} x^{x} + c

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e^{x} + x^{x} + c

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Solution

The correct option is B $e^{x} x^{x} + c$
$\int e^{x} x^{x} (2 + l o g x) d x$
$\int e^{x} (1 + (1 + l o g x)) d x$
$\int e^{x} (x^{x} + x^{x} (1 + l o g x)) d x$
we know that
$\frac{d x^{x}}{d x} = x^{x} (1 + l o g x)$
It is in the form of
$\int e^{x} (f (x) + f^{1} (x)) d x$
$= e^{x} f (x) + c$
$s o, \int e^{x} (x^{x} + x^{x} (1 + l o g x)) d x$
$= e^{x} - x^{x} + c$
$= (x e)^{x} + c$

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