Integration Substitution Problem

**NumbersNumbersNumbers** · December 1st 2008, 12:01 PM

I'm having issues with the following substitution problem:

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

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

Where do I go from here?

**flyingsquirrel** · December 1st 2008, 12:08 PM

Hi,

Originally Posted by NumbersNumbersNumbers

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

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

If $u=x^2+4x+7$ then $\frac{\mathrm{d}u}{\mathrm{d}x}=2x+4$ so $<br /> \mathrm{d}u=(2x+4)\mathrm{d}x=2(x+2)\mathrm{d}x$

Where do I go from here?

Where do you want to go ?

**NumbersNumbersNumbers** · December 1st 2008, 12:10 PM

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.

**flyingsquirrel** · December 1st 2008, 12:21 PM

Originally Posted by NumbersNumbersNumbers

I'm stuck.

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

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

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