# Determine all primitive functions

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1. Sep 3, 2016

### beyondlight

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

Determine all primitive functions for the function:

2x(x^2+3)^4

2. The attempt at a solution

When i expanded i got the primitive to be:

2(x^9/9)+3x^8+18x^6+54x^4+81x^2

But this was wrong. I am not sure I have understood the question. Help?

2. Sep 3, 2016

### Staff: Mentor

I have moved this thread, as it is not a precalculus problem.

Apparently the problem asks you to find all antiderivatives of 2x(x2 + 3)4. In other words, carry out this integration: $\int 2x(x^2 + 3)^4 dx$. The answer should have a highest degree term of x10. Don't forget the constant of integration.
Instead of expanding the binomial in parentheses, think about a simple substitution that you can do.

3. Sep 3, 2016

### beyondlight

One possible substitution is 2x(z)^4

But I am not sure how to proceed from here...

4. Sep 3, 2016

### Staff: Mentor

If z = x^2 + 3, what is dz?
A very simple substitution will work, and you're on the right track,
When you use substitution to evaluate an integral, you're using the chain rule in reverse.