Thread: I think it is called an integral?

1. I 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.

2. Re: I think it is called an integral?

Originally Posted by alane1994
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.
Yes that is correct. You can check your own answer by taking the derivative. Integrals (anti derivatives) and derivatives "undo" each other.

3. Re: I think it is called an integral?

You take the derivative of $\displaystyle 3x^3+6x^2+4x+C$?

4. Re: I think it is called an integral?

Originally Posted by alane1994
You take the derivative of $\displaystyle 3x^3+6x^2+4x+C$?
Yes it gives

$\displaystyle 9x^2+12x+4=(3x+2)^2$ that was the integrand that you started with.

5. Re: 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.