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Evaluate the indefinite integral.

$ \displaystyle \int x^3 \sqrt{x^2 + 1} \, dx $

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02:56

Frank Lin

Calculus 1 / AB

Chapter 5

Integrals

Section 5

The Substitution Rule

Integration

Jinglei M.

July 22, 2022

where is the "-" sign come from?

Missouri State University

Campbell University

Harvey Mudd College

University of Nottingham

Lectures

05:53

In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.

40:35

In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.

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This is the integral we are trying to integrate, which means that we know that you can beat the inside of the square root betweens writing this detox, the derivative is do you over to X and the derivative of one is simply Xerox. It's constant. Therefore, now we can write this oz 1/2 because it's the constant. So it goes on the outside. Integrate us. Remember the exponents increased by one divide by the exponents. This is the power rule outlined in the textbook back. Substitute us X squared plus one. And don't forget your pussy.

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