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

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Homework Help Overview

The discussion revolves around the integration of the function t² * ln(t) using integration by parts. Participants are exploring whether this topic falls under pre-calculus or calculus, indicating some uncertainty about the classification of the problem.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • One participant attempts to apply integration by parts, defining u and v, and expresses uncertainty about the next steps after deriving an expression involving an integral of (1/t)(t³/3). Another participant questions the need for further integration by parts for this resulting expression, suggesting it may be simpler than initially thought.

Discussion Status

Participants are actively engaging with the problem, with one providing a partial solution and others offering guidance on the next steps. There is a recognition that the initial integration by parts has been successfully executed, but uncertainty remains about how to proceed with the resulting integral.

Contextual Notes

There is a mention of potential confusion regarding the appropriate forum for posting, as well as a suggestion that integration or differentiation topics belong in the Calculus & Beyond section, which may influence the participants' approach to the problem.

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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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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:
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?
 
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!
 
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.
 
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.
 
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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