# 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

Staff Emeritus
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.