int (ln^3 x)/(x) dx Is this the same as int ((ln x)^3)/(x)dx?

scherezade29pc

scherezade29pc

Answered question

2022-07-21

Help me with this
ln 3 x x   d x
Is this the same as
( ln x ) 3 x   d x ?

Answer & Explanation

akademiks1989rz

akademiks1989rz

Beginner2022-07-22Added 16 answers

Unfortunately, "shorthand" can lead to ambiguity:
ln 3 x = ( ln ( ln ( ln x ) ) ? or ln 3 x = ( ln x ) 3 ?
But as you suspected, in this context, and given the integral, I'm am quite sure that ln 3 x = ( ln x ) 3 , much like sin 2 ( x ) = ( sin x ) 2 . So your integral amounts to:
ln 3 x x   d x = ( ln x ) 3 x d x
Let u = ln ( x ) , ; d u = d x x
( ln x ) 3 x d x = u 3 d u = 1 4 u 4 + C
= 1 4 ( ln x ) 4 + C = 1 4 ln 4 x + C

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?