Grade 12Zoology

What is the integration of x^x????????¿???????????????????????????????????????????

A k y

9 Years agoGrade 12

1 Answer

Umakant biswal

9 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