How Do You Integrate 3t^2(1+t^3)^4?

[unique_pavadrin]

Homework Statement

Integrate the following:
$$\int {3t^2 \left( {1 + t^3 } \right)^4 \,\,dt}$$

Homework Equations

$$\begin{array}{l}<br /> \int {\left( {a + bx} \right)^n \,\,dx = \frac{{\left( {a + bx} \right)^{n + 1} }}{{a\left( {n + 1} \right)}} + c} \\ <br /> \int {x^n \,\,dx = \frac{{x^{n + 1} }}{{n + 1}} + c} \\ <br /> \end{array}$$

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

 

[cristo]

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

 

[unique_pavadrin]

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

 

[TheoMcCloskey]

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

 

[cristo]

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

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

 

[unique_pavadrin]

okay i can solve the problem now, thanks all

 

[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.