How to integrate xln(x+1)? . I tried integrating by parts and ended up with: int x ln(x+1) dx = 1/2 x^2ln(x+1) - 1/2int(x^2)/(x+1)dx

deksteenk9

deksteenk9

Answered question

2022-09-30

How to integrate x ln ( x + 1 )?
I am trying to compute x ln ( x + 1 ) d x. I tried integrating by parts and ended up with:
x ln ( x + 1 ) d x = 1 2 x 2 ln ( x + 1 ) 1 2 x 2 x + 1 d x
but I'm stuck here.

Answer & Explanation

Demarion Thornton

Demarion Thornton

Beginner2022-10-01Added 11 answers

Write x 2 = x 2 1 + 1 so that
x 2 x + 1 = x 2 1 x + 1 + 1 x + 1 = ( x 1 ) + 1 x + 1
Chasity Kane

Chasity Kane

Beginner2022-10-02Added 2 answers

x 2 x + 1 d x = x 2 1 x + 1 d x + d x x + 1 = ( x 1 ) d x + d x x + 1 = x 2 2 x + ln ( x + 1 ) + c

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