# Integrate 3t^2(1+t^3)^4

1. Jun 21, 2007

### unique_pavadrin

1. The problem statement, all variables and given/known data
Integrate the following:
$$\int {3t^2 \left( {1 + t^3 } \right)^4 \,\,dt}$$

2. Relevant equations
$$\begin{array}{l} \int {\left( {a + bx} \right)^n \,\,dx = \frac{{\left( {a + bx} \right)^{n + 1} }}{{a\left( {n + 1} \right)}} + c} \\ \int {x^n \,\,dx = \frac{{x^{n + 1} }}{{n + 1}} + c} \\ \end{array}$$

3. The attempt at a solution
I am unsure on how to integrate problems such as these. Is there another rule? or is it a combination of rules? Many thanks to all help provided,
unique_pavadrin

2. Jun 21, 2007

### cristo

Staff Emeritus
One way would be to integrate by parts a few times. There's probably a quicker way that someone else may spot though.

3. Jun 21, 2007

### unique_pavadrin

how would i integrate by parts in there situations? thanks\

4. Jun 21, 2007

### TheoMcCloskey

No need for integration by parts. Look at the "1 + t^3" term. What is it's derivitive. This problem can be solve by a simple substitution. Do you see it?

5. Jun 21, 2007

### cristo

Staff Emeritus
Haha, nice.. I knew there would be a quicker way!

6. Jun 22, 2007

### unique_pavadrin

okay i can solve the problem now, thanks all

7. Jun 22, 2007

### Gib Z

Longer than a substitution, but shorter than integration by parts a few times, would be the expansion of the factorized expression and integrate term by term.

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