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Evaluate the indefinite integral. $ \displayst…
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Problem 36 Medium Difficulty

Evaluate the indefinite integral.

$ \displaystyle \int \frac{2^t}{2^t + 3} \, 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

Related Topics

Integrals

Integration

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Top Calculus 1 / AB Educators
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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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Watch More Solved Questions in Chapter 5

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Problem 78
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Video Transcript

we know that you is to to the t plus three, which means that de you is to the g natural over to D. T. Which means that u to the t dtv as do you over natural too. Which means we pull out one over natural with two times the integral one over you, do you? Which gives us one over Natural of two. Tim's Natural Look of You plus C, which gives a snatcher walk of tea to the two to the teeth plus three. Divide by natural of two, plus C is our solution.

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Calculus: Early Transcendentals

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Top Calculus 1 / AB Educators
Grace He

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Heather Zimmers

Oregon State University

Kayleah Tsai

Harvey Mudd College

Samuel Hannah

University of Nottingham

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.
Join Course
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