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What is integration of function x^x.................???

What is integration of function x^x.................???

Grade:12th pass

1 Answers

Umakant biswal
5349 Points
6 years ago
DEAR ABHISHEK 
​let J = ∫ x^x dx 
take natural logs on both sides
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 NOW 
REGARDS 
 

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