1. ## Integration Substitution Problem

I'm having issues with the following substitution problem:

$\displaystyle F (x^2+4x+7)^3(x+2)dx$

Am I correct in assuming that $\displaystyle u=x^2+4x+7$ and $\displaystyle du=2x+2$? or does $\displaystyle du=x+2$?

Where do I go from here?

2. Hi,
Originally Posted by NumbersNumbersNumbers
$\displaystyle F (x^2+4x+7)^3(x+2)dx$

Am I correct in assuming that $\displaystyle u=x^2+4x+7$ and $\displaystyle du=2x+2$? or does $\displaystyle du=x+2$?
If $\displaystyle u=x^2+4x+7$ then $\displaystyle \frac{\mathrm{d}u}{\mathrm{d}x}=2x+4$ so $\displaystyle \mathrm{d}u=(2x+4)\mathrm{d}x=2(x+2)\mathrm{d}x$

Where do I go from here?
Where do you want to go ?

3. Originally Posted by flyingsquirrel
Where do you want to go ?
The math problem is for some homework, our instructor told us to "integrate the following expression via substitution". I'm stuck.

4. Originally Posted by NumbersNumbersNumbers
I'm stuck.
I don't understand why you are stuck. You were thinking about substituting $\displaystyle u=x^2+4x+7$, can you do this substitution ?

$\displaystyle \begin{cases}u=x^2+4x+7\\ (x+2)\,\mathrm{d}x=\frac12\,\mathrm{d}u \end{cases} \implies \int (x^2+4x+7)^3(x+2)\,\mathrm{d}x=\int \ldots \mathrm{d}u$