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Use Exercise 52 to find $ \displaystyle \int x^4 e^x dx $.

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Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 1

Integration by Parts

Integration Techniques

Missouri State University

Campbell University

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.

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Use Exercise 52 to find $\…

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Use Exercise 48 to find $\…

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Use the method of exercise…

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Find the indefinite integr…

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use the results of Exercis…

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01:17

The problem is use exercise 52 to find the integral of x 24 times from exercise 54. We have integral of x to m e 2 x, is equal to x, 2 n into x, minus n times integral of x 2 minus 12 x x. I now first we got n is equal to 1. We have x to x, dx is equal to x into x, minus t. This is an isis n minus 1, but this is is 1 and integral of into x is 2 x. Here i omit the constant number and n is equal to 2, integral of x, squared into x x, a c equal to x, squared into x minus 2 times this value, so this is x into x minus into so. This is x, squared minus 2 x plus 2 times. I wot here also metisecostant numbers. What n is equal to 3 integral of x to 3 power to dx is equal to x to raise power e to x, minus 3 times square x, squared minus 2 x, plus 2 into x and y n is equal to 4, an integral of x, 242 X, dx is equal to x, 24 into x times 4 times x, 23 into x, minus 3 x, squared minus 2 x, plus 2 e 2 x and the plus it's a constant number c. This is our result.

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