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Problem 19

Finding an Indefinite Integral In Exercises 15- 36 , find the indefinite integral and check the result by differentiation.
$\int\left(x^{3 / 2}+2 x+1\right) d x$

$$\frac{2 x^{\frac{5}{2}}}{5}+x^{2}+x+C$$

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## Video Transcript

All right. Impression 19. We have the into grow X to the three halves plus two X plugs one and shivers to be ex. So I'm taking the 1st 1 I'm gonna add 123 hands and I get and to the five hands and I'm good. Multiply that by the reciprocal Like to fix exit five hands less as one. So I have X. Where'd nuts? Yes, Scene. So what? The fat ones by hand. Times to Betsy one. That's my coefficient. And then I subtract one from the five. Have and I would get my three halves. Then onto the x squared term, I would get to X to the first power onto the plus one. The derivative of X would be just one. And then I have to add plus C because if I had plugs 10 it would have dropped off. It would not be in my integral something