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### Finding an Indefinite Integral In Exercises 15- 3…

02:21
University of Houston

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Problem 25

Finding an Indefinite Integral In Exercises 15- 36 , find the indefinite integral and check the result by differentiation.
$\int \frac{x+6}{\sqrt{x}} d x$

$$\frac{2}{3} \sqrt{x}(x+18)+C$$

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## Video Transcript

very questions. 15 we have definitely rule. In fact, by six most were vets. Yes. So what I did was I took X to the negative 1/2 gallon nine x six and I further simplified back by distributing No ext. Negative. 1/2 times x of the first week at our exponents. And that becomes X to the positive 1/2 but six times x to the negative one. Yes. And then I integrated. They add one. I am ex to the three halves Monster Wide body. No. Um six. Thanks. Add 11 10. Bye Bye, then. Six people and see that this would be 32 there. Thanks to the three halves must 12 x, you have one c. So now gonna factor out of 2/3 X to the 1/2 2/3 exit. Someone had just give me X My first term. This is, um, 12. So when I factor out to third nicely dividing so I get and good bye. I have 36. What is the 18 in my constant in that man