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Find the general indefinite integral.

$ \displaystyle \int (u + 4)(2u + 1) \, du $

$$\frac{2}{3} u^{3}+\frac{9}{2} u^{2}+4 u+C$$

00:59

Frank L.

00:43

Amrita B.

Calculus 1 / AB

Chapter 5

Integrals

Section 4

Indefinite Integrals and the Net Change Theorem

Integration

Missouri State University

Harvey Mudd College

Baylor University

Idaho State University

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Calculate the integral.

right. The theme in this problem is that we need to do the power rule. Now, the power rule only applies uh If it's a some indifference of powers uh where you add one to the exponents and you divide by that new experiment and you need to remember plus C. Because the derivative of what we just found is equal this and there could have been a constant here because the derivative of a constant zero that we don't don't write down. So in this problem you actually need to do one more step because we can't use the power rule when there's a product in here. True. You plus one, do you? So your first step is actually rewriting this problem still has an interval, but distributing this in here. So we're looking at two U squared. Uh and then you'd have one, you Plus eight. You so they'll be nine, you and four times wanted to give me or you can double check my math is correct. And now I'm ready to do the power rule which is adding one to your experiments. Uh do this in green so you square becomes u. Cubed. And then you have to multiply by the reciprocal. Well two times 1 3rd is 2/3 Add 1 to your ex money, multiplied by their circles. Some people divide by that new number, but so nine divided which you is nine house uh for you because the drug for you was forward. And then don't forget about plus C. As I mentioned earlier, this is your correct answer Yeah.

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