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What is the integration of x raised to x???????????????

What is the integration of x raised to x???????????????

Grade:12

1 Answers

Umakant biswal
5349 Points
7 years ago
dear aky
let J = ∫ x^x dx 
take natural log on both side 
ln(J) = ln ∫ x^x dx = ∫ ln(x^x) dx = ∫ xln(x) dx 
using integration by parts 
ln (J) = [((x^2)/2)ln(x)] - ∫ ((x^2)/2)(1/x) dx
= [((x^2)/2)ln(x)] - ∫ (x/2) dx
ln (J) = ln[(x^2)/exp]^[(x^2)/4] 
take exponentials on both sides 
J = [(x^2)/exp]^[(x^2)/4] + Arbitrary Constant
HOPE IT CLEARS 
REGARDS 
 

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