Evaluate the following integrals. Include absolute values only when needed. intfrac{ln^2x+2ln x-1}{x}dx

melodykap 2021-01-13 Answered
Evaluate the following integrals. Include absolute values only when needed.
ln2x+2lnx1xdx
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SoosteethicU
Answered 2021-01-14 Author has 102 answers
Given integtral, ln2x+2lnx1xdx
we have to find the given integral.
here,ln2x+2lnx1xdx
substitute lnx=t1xdxdt=11xdx=dt
,ln2x+2lnx1xdx=(t2+2t1)dt
=t2dt+2tdt1dt
=t33+2t22t+C
=t33+t2t+C
undo substitution t=lnx
ln2x+2lnx1xdx=ln3x3+ln2xlnx+C
this is the required answer
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