What is the antiderivative of \ln x?

Juan Hewlett

Juan Hewlett

Answered question

2021-12-13

What is the antiderivative of lnx?

Answer & Explanation

stomachdm

stomachdm

Beginner2021-12-14Added 33 answers

We should use integration by parts:
udv=uvvdu
Where u and v are functions of x.
u=lnx=
dudx=1x
du=1xdx
and
dv=dx
dv=dx
v=x
Thus, we have:
lnxdx=(lnx)(x)(x)(1xdx)
xlnx1dx=xlnxx+C
Jeffery Autrey

Jeffery Autrey

Beginner2021-12-15Added 35 answers

lnxdx=xlnxx+C

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