Integral of ln(3x)/x I believe this should be a simple problem but I don't have an answer key to confirm if this is right, and some of the similar questions I can find online seem to be giving more complicated solutions.The problem is: int (ln (3x))/(x)dx

Deon Moran

Deon Moran

Answered question

2022-10-11

Integral of ln ( 3 x ) / x
I believe this should be a simple problem but I don't have an answer key to confirm if this is right, and some of the similar questions I can find online seem to be giving more complicated solutions.
The problem is:
ln ( 3 x ) x d x
And this is my solution, based on the fact that ln ( a x ) d x = 1 x
u = ln ( 3 x )
d u d x = 1 x
d u = 1 x d x
So:
ln ( 3 x ) x d x = u d u
u 2 2 + C
( ln ( 3 x ) ) 2 2 + C
Is that right?

Answer & Explanation

Hamnetmj

Hamnetmj

Beginner2022-10-12Added 21 answers

One way to check the result. Since
ln ( 3 x ) x d x = ( ln ( 3 x ) ) 2 2 + C
then
d d x ( ln ( 3 x ) ) 2 2 + C
should be the initial function. Hence, doing the differentiation
1 2 d d x ( ln ( 3 x ) ) 2 = ln ( 3 x ) d d x ln ( 3 x ) = ln ( 3 x ) 1 3 x 3 = ln ( 3 x ) x .
This is your initial function, and hence your integration was correct.

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