Calculus problem. Is my approach correct so far?

by Rishi Fri May 10, 2013 6:55 pm

Someone posted this on the MIT open courseware website for the Calculus course

TenaciousT:
how do I deal with the square power in this problem:
Integrate: [ln(x))^2]
…

My approach

1. f(x) = [ln(x) ^ 2]

2. Let u = ln(x)

du/dx= 1/x

x*du = dx

[ln(x) ^ 2] = (u ^2) * (x * du)

Now x can be written as (e ^ ln(x))

∫[ln(x) ^ 2 dx] = ∫[(u ^ 2) * (e ^ u) du]

3. Then I can use the Integration by parts for solving ∫[(u ^ 2) * (e ^ u) du]

by MaxEntropy_Man Fri May 10, 2013 7:12 pm

Rishi wrote:Someone posted this on the MIT open courseware website for the Calculus course

TenaciousT:
how do I deal with the square power in this problem:
Integrate: [ln(x))^2]
…

My approach

1. f(x) = [ln(x) ^ 2]

2. Let u = ln(x)

du/dx= 1/x

x*du = dx

[ln(x) ^ 2] = (u ^2) * (x * du)

Now x can be written as (e ^ ln(x))

∫[ln(x) ^ 2 dx] = ∫[(u ^ 2) * (e ^ u) du]

3. Then I can use the Integration by parts for solving ∫[(u ^ 2) * (e ^ u) du]

seems fine to me.

Calculus problem. Is my approach correct so far?

Calculus problem. Is my approach correct so far?

Re: Calculus problem. Is my approach correct so far?