# I think it is called an integral?

• Oct 16th 2012, 12:41 PM
alane1994
I think it is called an integral?
Could someone check my math?

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

From that I got the answer.

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

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 PM
TheEmptySet
Re: I think it is called an integral?
Quote:

Originally Posted by alane1994
Could someone check my math?

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

From that I got the answer.

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

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.
• Oct 16th 2012, 12:48 PM
alane1994
Re: I think it is called an integral?
You take the derivative of $3x^3+6x^2+4x+C$?
• Oct 16th 2012, 12:50 PM
TheEmptySet
Re: I think it is called an integral?
Quote:

Originally Posted by alane1994
You take the derivative of $3x^3+6x^2+4x+C$?

Yes it gives

$9x^2+12x+4=(3x+2)^2$ that was the integrand that you started with.
• Oct 16th 2012, 12:51 PM
MarkFL
Re: I think it is called an integral?
Another way to proceed is to let:

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

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

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