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Evaluate the indefinite integral.$\int \frac{x}{\left(x^{2}+1\right)^{2}} d x$

$-\frac{1}{2\left(x^{2}+1\right)}+C$

Calculus 1 / AB

Calculus 2 / BC

Chapter 5

Integrals

Section 4

The Substitution Rule

Integration Techniques

Oregon State University

Harvey Mudd College

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 integral. $\i…

we have the integral over off X over X squared plus one. The whole thing is squared. The X we're gonna let you is equal to X squared plus one so that d'you is equal to two. X t x or d'you divided by two is equal to x t X pulling the 1/2 out and then substituting the stuff in. We end up with you to the power of native to do you which is equal to a negative 1/2 you to the power of negative one plus c back substituting. We end up with negative 1/2 times x squared plus one to the power of negative one plus seat.

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