Integration by parts: int x ln x^2 dx So what I did first was make u=lnx^2 and dv=x Then I solved by getting the derivative of u and the anti derivative of dv and I got du=1/x^2 and v=x^2/2 then I did the formula int udv=uv−int vdu which then after plugging in the numbers and simplifying got me ( x^2)/(2) ln x^2 -(1)/(2x) +C

spoofing44

spoofing44

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2022-08-29

Integration by parts: x ln x 2 d x
Problem: x ln x 2 d x
So what I did first was make u = ln x 2 and d v = x
Then I solved by getting the derivative of u and the anti derivative of d v and I got d u = 1 / x 2 and v = x 2 / 2 then I did the formula
u d v = u v v d u
which then after plugging in the numbers and simplifying got me
x 2 2 ln x 2 1 2 x + C
Is this the right way to do the problem and answer?

Answer & Explanation

Dayana Doyle

Dayana Doyle

Beginner2022-08-30Added 17 answers

First note that ln ( x 2 ) = 2 ln ( x ). Now we have
u = 2 ln ( x ) ,     d u = 2 x d x ,     d v = x d x ,     v = x 2 2
Integration by parts tells us that
2 x ln ( x ) d x = 2 ln ( x ) x 2 2 2 x x 2 2 d x
= ln ( x ) x 2 x d x
= ln ( x ) x 2 x 2 2 + C
Camila Mccann

Camila Mccann

Beginner2022-08-31Added 3 answers

Assuming it's x ln 2 ( x )(because this way the second case will be also evaluated in here anyway) Hints;
f d g = f g g d f
f = ln 2 x , d f = 2 ln x x d x , g = x 2 2 , d g = x d x
Hints for the second integral;
f = ln x , d f = 1 x d x , g = x 2 2 , d g = x d x

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