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Evaluate: intx^x1n(e x)dx...

Evaluate: `intx^x1n(e x)dx`

Text Solution

Verified by Experts

The correct Answer is:
`x^(x)+C`
`I=int x^(x) " In "(ex)dx=int x^(x) (1+"In "x)dx`
` "Let "t=x^(x)=e^(x"In"x)" then " (dt)/(dx)=x^(x)(x xx (1)/(x)+"In "x)`
` or dt=x^(x)(1+"In "x)dx or I=intdt=t+C=x^(x)+C`
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