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# Determine whether each integral is convergent or divergent. Evaluate those that are convergent.$\displaystyle \int_1^\infty \frac{dx}{\sqrt{x} + x \sqrt{x}}$

## Converges to $\frac{\pi}{2}$

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Integration Techniques

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### Video Transcript

The problem is you tell me why this integral is convergent where there weren't. If you don't know howto find its anti derivative of this function, you can think about my thereto u substitution. But this question we're kind like you is equal to U until Max Then is he going to you? Squire? And the axe is it got you to you. You Now this nd grow is equal to you You, you over you us, you squire. I will see you. And from well, I'm Tio infinity. We can kinds out you So this is called Chu integral from one to infinity. Two times you over. One pass Useless now by the definition of an improper into your o This is the code to the limit he goes to in planete into girl from one to t The function is who the over one plus you square And this is your coat too, Lim. He goes to vanity and anti derivative of the function One over one plus your square is our tenant. You This is a culture too. Terms, lieutenant, you from one two You this you come too. Two hams. Our tenant You minus ten in one. That's what he goes to infinity. I've tended to you goes too high over to answer if you come too. Two towns. I already too minus octane in one. If we go too Hi over, for his answer is you go to hi Over two this integral has converted and the value is high over too.

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Integration Techniques

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