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# Find the most general antiderivative of the function. (Check your answers by differentiation.)$f(x) = 1 + 2\sin x + 3/\sqrt{x}$

## See explanation for result.

Derivatives

Differentiation

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##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

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### Video Transcript

So for this problem we're looking to take the anti derivative of the given function. So our function is cases F of X equals one Plus 2 Cynics. Okay. Mhm. Plus three over the square root of X is our function. Um And I would like to write three over the square root of act as three times X to the negative one half. That's gonna help us in the long run when we keep the anti derivative. Well we know that the anti derivative of this constant, we're just the X. Class. We know that the anti drone of cynics is a negative co signs will have negative to cosign X class when we add we'll have three times when we add one to the exponents here. That'll be one half. So three X to the one half divided by one half will mean multiplied by to also be a six X. The one half final answer.

California Baptist University

#### Topics

Derivatives

Differentiation

Volume

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

Lectures

Join Bootcamp