Evaluate the following integrals. Include absolute values only when needed. \int

eiraszero11cu

eiraszero11cu

Answered question

2021-12-20

Evaluate the following integrals. Include absolute values only when needed.
ln2x+2lnx1xdx

Answer & Explanation

Pansdorfp6

Pansdorfp6

Beginner2021-12-21Added 27 answers

Step 1
given integral, ln2x+2lnx1xdx
we have to find the given integral.
Step 2
here , ln2x+2lnx1xdx
substitute lnx=t1xdxdt=11xdx=dt
ln2x+2lnx1xdx=(t2+2t1)dt
=t2dt+2tdt1dt

=t2dt+2tdt1dt

=t33+2t22t+constant

=t33+t2t+constant
undo substitution t=lnx
ln2x+2lnx1xdx=ln3x3+ln2xlnx+constant
this is the required answer

Annie Gonzalez

Annie Gonzalez

Beginner2021-12-22Added 41 answers

ln2(x)+2ln(x)1xdx
Substitution u=ln(x)dudx=1xdx=xdu, we use:
ln2(x)=u2
=(u2+2u1)du
Lets
nick1337

nick1337

Expert2021-12-28Added 777 answers

(ln(x))2ln(x)1xdx
Let us
1xdx=d(ln(x)),t=ln(x)
put the expression 1 / x under the differential sign, i.e.: Then the original integral can be written as follows:
(t2+2t1)dt
This is a tabular integral:
t2+2t1dt=t33+t2t+C
To write down the final answer, it remains to substitute log(x) instead of t.
ln(x)33+ln(x)2ln(x)+C

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