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# Find the general indefinite integral. Illustrate by graphing several members of the family on the same screen.$\displaystyle \int \biggl( \cos x + \frac{1}{2}x \biggr) \,dx$

## $$\sin x+\frac{1}{4} x^{2}+C$$

Integrals

Integration

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##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

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### Video Transcript

uh we're asked to find the anti derivative of co sign effects plus one half X. Dx. And you could memorize rules because I have some students that have to memorize what they intend derivative of coastline is. But to me I just think about or what derivative, well uh something would give me co sign positive coastline and that answer is positive sign. So I have correctly done that one. And then just remember that you add one to your experiment and you multiply by the reciprocal of that exponents. So in about one half times one half, Which I know is 1/4. And I just need to remember about your plus C. So this is your correct answer and can double check that's correct by taking the derivative of them. Is it true that the derivative of Sinus Cosan? Yeah. Is it true that the derivative a warm fourth X. Squared is one fx. Yet. Is it true that the derivative of a constant zero which we don't right up here. But it is. So we have the correct answer.

#### Topics

Integrals

Integration

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

Lectures

Join Bootcamp