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Evaluate the indefinite integral.

$ \displaystyle \int \frac{x}{1 + x^4} \, dx $

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02:15

Frank Lin

Calculus 1 / AB

Chapter 5

Integrals

Section 5

The Substitution Rule

Integration

Campbell University

Harvey Mudd College

Baylor University

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.

04:21

Evaluate the integral.

00:40

Evaluate the indefinite in…

02:34

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01:39

Evaluate the given indefin…

00:56

okay, Given the problem, the first thing you know you could do is we can rewrite the denominator as one plus ax squared squared D backs. Now we know that you is equivalent to x squared, which means that de X is equivalent to one divide by two acts d'you, which means now we have the integral of one over one plus u squared times one over two acts d'you, which means factoring out the 1/2. We know we have 1/2 times inverse tangent because this is inverse tangent plus c. And then remember what you is x squared plus C.

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