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Problem

Evaluate the integral. $\int \frac{x-1}{x^{2}+2 x…

01:44

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Problem 14 Easy Difficulty

Evaluate the integral.

$ \displaystyle \int x \cosh ax dx $


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Wen Zheng
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Related Courses

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 7

Techniques of Integration

Section 1

Integration by Parts

Related Topics

Integration Techniques

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01:53

Integration Techniques - Intro

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.

Video Thumbnail

27:53

Basic Techniques

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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Watch More Solved Questions in Chapter 7

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Problem 13
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Problem 16
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Problem 50
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Problem 53
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Problem 73
Problem 74

Video Transcript

The problem is evaluated the integral x times coach, a x d x, the first, the coach a x. This is, by definition, this is a 2 x plus e to negative x over 2 point, and we have the derivative of coach a x coach x. So this this is the definition of coach x. The coach x derivative of this 1 is equal to sine x. This is 2 x minus e to 2 x over 2. Now for this problem, we were used the method of integration by parts. The formula is integral of u v. Prime dx is equal to: u times, v minus the integral of u prime times v d x for our problem. We can, let? U is equal to x and the prime is equal to poach 8 times x. Then? U, prime, is equal to 1, and v is equal to 1 over 8 times inch a x now integral x times, coach x x. This is equal to u times v, so this is 1 over a times x, times c n a x and minus integral of prime timotes is 1 a cinch a x x. This is equal to 1 over 8 times x, times x, minus 1 over a square cosine, the coach x and plus the constant number. This is the answer:

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Calculus: Early Transcendentals

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Integration Techniques

Top Calculus 2 / BC Educators
Grace He

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Catherine Ross

Missouri State University

Anna Marie Vagnozzi

Campbell University

Joseph Lentino

Boston College

Calculus 2 / BC Courses

Lectures

Video Thumbnail

01:53

Integration Techniques - Intro

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.

Video Thumbnail

27:53

Basic Techniques

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

Join Course
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