Problem

Find the general indefinite integral. $ \disp…

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Problem 11 Easy Difficulty

Find the general indefinite integral.

$ \displaystyle \int \frac{1 + \sqrt{x} + x}{x} \, dx $

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Video Transcript

Alright, so here we have an integral. Looks a little bit messy but we can do a trick and divide each term by X. Um basically we have a common denominator. So we'll just split apart each part and have it divided by X. And then see what we get it cleans up a bit enough that we can solve this. So the first term is one of her acts. The second term I can rewrite as X to the 1/2. Uh Well I'll go ahead and show you the steps extra one half over X. And then we have just one here and so we'll just clean up before we do the anti derivative. We'll go ahead and clean up this middle term. I can subtract exponents. So one half minus one is X to the minus a half. Alright, now we're ready to take the anti derivative. So um the anti derivative of one over X is natural log of absolute value of acts. We're gonna do a reverse power rule on the middle term. So I'm going to add one to the exponents minus a half plus one is positive a half. And we divide by that number, we just put up there and then plus X plus C. So we're almost there. We can and it's just um the middle term, I can multiply top and bottom by two, that will give me two and I'll rewrite it a square root of X looks a little nicer square root of X plus X plus E. And there it is. That is the anti derivative of our given function. Okay, hopefully that helped to have a wonderful day.

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