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Problem

Evaluate the indefinite integral. $ \displayst…

00:43

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Problem 33 Medium Difficulty

Evaluate the indefinite integral.

$ \displaystyle \int \cos (1 + 5t) \, dt $

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Frank Lin

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Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 5

Integrals

Section 5

The Substitution Rule

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Integrals

Integration

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Video Thumbnail

05:53

Integrals - Intro

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.

Video Thumbnail

40:35

Area Under Curves - Overview

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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Video Transcript

we know that you is wonderful. Five t which means that to you as five d. T. And readiness in terms of DT alone we have, do you divide by five, which means we can pull out the constant of 1/5 multiply it by the integral of co sign you to you, which integrating this gives us 1/5 sign. You plus C on deacon. Backed up to you is one plus five t. We have 1/5 sign one plus five t plus c.

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Calculus: Early Transcendentals

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Top Calculus 1 / AB Educators

Catherine Ross

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Calculus 1 / AB Courses

Lectures

Video Thumbnail

05:53

Integrals - Intro

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.

Video Thumbnail

40:35

Area Under Curves - Overview

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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