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Evaluate the indefinite integral.$\int \frac{\sin 2 x}{1+\cos ^{2} x} d x$

$\frac{-5(2 x+5)^{9}}{36}+c$

Calculus 1 / AB

Calculus 2 / BC

Chapter 5

Integrals

Section 4

The Substitution Rule

Integration Techniques

Campbell University

Baylor University

University of Michigan - Ann Arbor

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 indefinite in…

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this question asks us to evaluate the indefinite integral We know that we can make Are you what is impromptu? Seize to expose five. Therefore, we know that 1/2 d'you is RDX, cause the derivative of five is simply Xerox. It's a constant. Therefore, we know we have 1/2 times 1/2 which is 1/4 we can pull 1/4 out because it's a constant and we have you to the ninth minus five you to the eighth D'You increased the export it by one divide by the new exponents. So 10 1/10 time's 1/4 is gonna be 40 On the bottom we have 1/4 is the constant on the outside and then nine times four is 36. Last step is back substitute Endure us to expose five. Make sure that you do this. You should not have you in your final answer

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