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Evaluate the definite integral.
$ \displaystyle \int^3_0 \frac{dx}{5x + 1} $
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01:18
Frank Lin
Calculus 1 / AB
Chapter 5
Integrals
Section 5
The Substitution Rule
Integration
Missouri State University
University of Michigan - Ann Arbor
Idaho 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.
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from the problem we've been given, the first thing you can do is pull out the constant 1/5. Then we can rewrite the integral. Now we know as we established that you is five. Expose one rate. It's the denominator. Therefore, do you is simply five d backs. Therefore now the limits of integration change from five times 05 times three plus one on the top, which is 16 and five time zero post went on the bottom, which is simply one. So the constant remains on the outside as we just established our limits or from our bouncer from 1 to 16. Take the integral and we end up with four natural log with two divided by five.
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