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Evaluate the integral.

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

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$\int \frac{d x}{\sqrt{x}+x \sqrt{x}}=2 \tan ^{-1} \sqrt{x}+C$

Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 5

Strategy for Integration

Integration Techniques

Campbell University

Oregon State University

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Boston College

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.

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Evaluate the integral.…

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Evaluate the indefinite in…

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Evaluate the integrals.

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Evaluate the following int…

for this. Let's use the substitution and then here differentiate and rewrite. This is let's say one over to you dx and then solve this for DX. You get to you. Do you here also notice you have X So you square this equation here that gives you x Yeah, So up top, There's RDX. So we have to you, Do you then here we have you and then there's X. And then here there's you again. So now let's go ahead and cancel off one of those use top and bottom and we're left only with one one. Plus, he's weird here. If you don't remember this, you could do a substitution. Triggs, Um, And when you use that, you should have to ten in verse pussy and then finally go back to your U sub to rewrite this is to our ten and then square. Relax and then add your C. And that's our answer

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