How can I integrate t^2 * ln(t) using the integration by parts method?

  • Thread starter Bikkehaug
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In summary, the conversation discusses a problem involving integration and differentiation, specifically the integral of t^2 * ln(t). The individual has attempted to use integration by parts but is unsure of how to continue. They are reminded that they can simplify expressions before integrating and that the integral of x^n is a special case that should be memorized. The conversation concludes with confirmation that the question was posted in the correct forum section.
  • #1
Bikkehaug
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Homework Statement



I'm not sure if this is pre calculus or calculus and beyond. If I've posted in the wrong section, please feel free to move this topic.

∫t2 * lnt dt

Homework Equations





The Attempt at a Solution



I've tried using the integration by parts:

∫uv' dt = uv - ∫u'v dt

u = lnt u' = 1/t

v = t3 / 3 v' = t2

I then get the following:

lnt * t3 / 3 - ∫1/t * t3 / 3

I'm not sure where to continue from this.
 
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  • #2
Bikkehaug said:

Homework Statement



I'm not sure if this is pre calculus or calculus and beyond. If I've posted in the wrong section, please feel free to move this topic.

∫t2 * lnt dt

Homework Equations





The Attempt at a Solution



I've tried using the integration by parts:

∫uv' dt = uv - ∫u'v dt

u = lnt u' = 1/t

v = t3 / 3 v' = t2

I then get the following:

lnt * t3 / 3 - ∫1/t * t3 / 3

I'm not sure where to continue from this.

What is preventing you from integrating ##(1/t)(t^3/3) = t^2 /3##?
 
Last edited:
  • #3
Ray Vickson said:
What is preventing you from integrating ##(1/t)(t^3/3) = t^2 /3##?

I thought I needed to do partial integration again for that one, since it's another set of products?
 
  • #4
Bikkehaug said:
I then get the following:

lnt * t3 / 3 - ∫1/t * t3 / 3

I'm not sure where to continue from this.

You've done the hard bit!
 
  • #5
Bikkehaug said:
I thought I needed to do partial integration again for that one, since it's another set of products?

The integral

[tex]\int x^n dx [/tex]

is a special case and you should have it memorized.
 
  • #6
Bikkehaug said:
I thought I needed to do partial integration again for that one, since it's another set of products?

You are allowed to simplify things before integrating them.
 
  • #7
Bikkehaug said:
I'm not sure if this is pre calculus or calculus and beyond.
Problems involving integration or differentiation definitely should be posted in Calculus & Beyond, so this is the right forum section.
 

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