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Evaluate the indefinite integral.
$ \displaystyle \int (x^2 + 1)(x^3 + 3x)^4 \, dx $
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01:28
Frank Lin
Calculus 1 / AB
Chapter 5
Integrals
Section 5
The Substitution Rule
Integration
Campbell University
Oregon State University
Boston College
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.
00:55
Evaluate the indefinite in…
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08:47
Evaluate the integral.
We know that you is x cubed plus three acts. Which means that D'You the derivative tried by three is X squared plus one the axe. Which means we're evaluating the integral. We can pull out the constant from thirds and then using the power rule, we know we increase the exploited by one divide by the new exponents. Now back. Substitute us execute plus three AKs. What?
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