Integration of products.

1. Mar 24, 2014

Bikkehaug

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. 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.

2. Mar 24, 2014

Ray Vickson

What is preventing you from integrating $(1/t)(t^3/3) = t^2 /3$?

Last edited: Mar 24, 2014
3. Mar 24, 2014

Bikkehaug

I thought I needed to do partial integration again for that one, since it's another set of products?

4. Mar 24, 2014

PeroK

You've done the hard bit!

5. Mar 24, 2014

micromass

The integral

$$\int x^n dx$$

is a special case and you should have it memorized.

6. Mar 24, 2014

PeroK

You are allowed to simplify things before integrating them.

7. Mar 24, 2014

Staff: Mentor

Problems involving integration or differentiation definitely should be posted in Calculus & Beyond, so this is the right forum section.

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