Grade 12th passIntegral Calculus
What is integration of function x^x.................???
1 Answer
Umakant biswal
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
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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