Could someone check my math?

$\displaystyle \int(3x+2)^2 dx$

From that I got the answer.

$\displaystyle 3x^3+6x^2+4x+C$

Is that correct? I used the sum rule, then I used the power rule to get this. Thanks for any feedback.

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- Oct 16th 2012, 12:41 PMalane1994I think it is called an integral?
Could someone check my math?

$\displaystyle \int(3x+2)^2 dx$

From that I got the answer.

$\displaystyle 3x^3+6x^2+4x+C$

Is that correct? I used the sum rule, then I used the power rule to get this. Thanks for any feedback. - Oct 16th 2012, 12:45 PMTheEmptySetRe: I think it is called an integral?
- Oct 16th 2012, 12:48 PMalane1994Re: I think it is called an integral?
You take the derivative of $\displaystyle 3x^3+6x^2+4x+C$?

- Oct 16th 2012, 12:50 PMTheEmptySetRe: I think it is called an integral?
- Oct 16th 2012, 12:51 PMMarkFLRe: I think it is called an integral?
Another way to proceed is to let:

$\displaystyle u=3x+2\,\therefore\,du=3\,dx$ and we have:

$\displaystyle \frac{1}{3}\int u^2\,du=\frac{u^3}{9}+C=\frac{(3x+2)^3}{9}+C$

You can verify that this is equivalent to the form you gave.