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

Question

Umakant biswal · Answer

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

Thank you for registering.

Register Now and Win Upto 25% Scholorship for a Full Academic Year !

Enter Your Details

Registration done!

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

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

1 Answers

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

Other Related Questions on Zoology

ASK QUESTION

Answer and earn gift vouchers

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Complete Self Study Package designed by Industry Leading Experts

Live 1-1 coding classes to unleash the Creator in your Child

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Register Now & Win Upto 25% Scholorship