What is the antiderivative of ln(x+1)?
1 Answer
Jun 2, 2016
Explanation:
We have
I=intln(x+1)dx
We will use integration by parts:
intudv=uv-intvdu
For
Thus,
I=xln(x+1)-intx/(x+1)dx
Solving the remaining integral:
intx/(x+1)dx=int(x+1-1)/(x+1)dx=int1-1/(x+1)dx
=x-ln(x+1)+C
So,
I=xln(x+1)-(x-ln(x+1))+C
I=(x+1)ln(x+1)-x+C