∫logx3xdx=
13logx2+c
23logx2+c
Explanation for the correct option:
Finding the value of ∫logx3xdx:
Consider the given Equation as,
I=∫logx3xdxI=13∫logxxdx
Let us assume that
logx=t⇒1x×12xdx=dt⇒1xdx=2dt
Then I becomes,
I=13∫logxxdx=23∫tdt=23t22+cI=13t2+c
Substituting the value of t the above equation becomes,
I=13logx2+c
Hence, the correct answer is Option (A).