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$\int x^{x} \ln (e x) d x is equal to$

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a

xx+c

b

x.ln x+c

c

(ln x)x+c

d

xln x+c

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detailed solution

Correct option is A

I=∫xxln⁡(ex)dx=∫xx(1+ln⁡x)dx let t=xx=exln⁡x⇒dtdx=xxx⋅1x+ln⁡x=xx1+ln⁡x⇒ dt=xx(1+ln⁡x)dx∴ I=∫dt=t+C=xx+C

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