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Evaluate the integral.

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

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Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 5

Strategy for Integration

Integration Techniques

Campbell University

Harvey Mudd College

Baylor University

Lectures

01:53

In mathematics, integration is one of the two main operations in calculus, with its inverse, differentiation, being the other. Given a function of a real variable, an antiderivative, integral, or integrand is the function's derivative, with respect to the variable of interest. The integrals of a function are the components of its antiderivative. The definite integral of a function from a to b is the area of the region in the xy-plane that lies between the graph of the function and the x-axis, above the x-axis, or below the x-axis. The indefinite integral of a function is an antiderivative of the function, and can be used to find the original function when given the derivative. The definite integral of a function is a single-valued function on a given interval. It can be computed by evaluating the definite integral of a function at every x in the domain of the function, then adding the results together.

27:53

In mathematics, a technique is a method or formula for solving a problem. Techniques are often used in mathematics, physics, economics, and computer science.

02:02

02:12

05:55

02:18

03:42

Evaluate the indicated int…

01:36

Evaluate the following int…

01:05

Evaluate the integral.…

01:27

Evaluate the definite inte…

02:09

03:29

01:17

04:51

Find the Integral of \int …

Let's start off here by doing the use up. Let's just take you to be the entire denominator. Then here we will have to use the general from calculus. Teo, do the derivative, so I do the outer one first. So I'm using the power ruler. But that I have to go and also take the derivative of the inside. So here, let me I guess Let me write it as one over to radical X. That's the derivative but the inside. So we're all here. We're using the Kane rule. And to make this problem a little easier I'd like to re write all this in terms of you. So this is just one over to you Times one over to and I'll have to fill in this blank here and then the x So I need two for just rewrite radical exterior. So I'll just get that from this equation to square both sides. It's a practice one. So you just get you squared minus one instead of radical X and was good. And take this equation here and solvent for DX. So you have d X equals two times two is four we have Are you here and then you squared minus one. Do you? So now, after using our use up, we have one over you. And then we have R D X, which was for you. You squared minus one. Do you? Let's pull off the four. Cancel those use. We have you squared minus one, So just generate this. Using the power rule. Don't forget your constant of integration. See? And then the last appears to just replace you back in with a radical. So we have here you to the third power and then minus four times you and that's your final answer.

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