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Evaluate the integral.

$ \displaystyle \int \frac{3t - 2}{t + 1}\ dt $

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Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 4

Integration of Rational Functions by Partial Fractions

Integration Techniques

Campbell University

Harvey Mudd College

Baylor University

Idaho State University

Lectures

01:53

In mathematics, integration is one of the two main operations in calculus, with its inverse, differentiation, being the other. Given a function of a real variable, an antiderivative, integral, or integrand is the function's derivative, with respect to the variable of interest. The integrals of a function are the components of its antiderivative. The definite integral of a function from a to b is the area of the region in the xy-plane that lies between the graph of the function and the x-axis, above the x-axis, or below the x-axis. The indefinite integral of a function is an antiderivative of the function, and can be used to find the original function when given the derivative. The definite integral of a function is a single-valued function on a given interval. It can be computed by evaluating the definite integral of a function at every x in the domain of the function, then adding the results together.

27:53

In mathematics, a technique is a method or formula for solving a problem. Techniques are often used in mathematics, physics, economics, and computer science.

00:55

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01:58

Let's evaluate the integral of three T minus two over T plus one. Look, First thing I noticed is that the numerator has degree. One denominator also has degree one. And whenever the numerator has degree greater than or equal to the denominator, we should do long division. So here three teen, divine and bitey is three. Multiply out that three subject, we have minus five. So all the are doing here is rewriting this original fraction. The question was three and then the remainder was minus five and then we have our original quotient on the bottom. Now for this integral. It may help you to use U substitution here if that plus one is bothering you. But in either case, the first enroll. So we have three t and then for the second one will have minus five natural log he plus one and then plus your constancy of integration. And there's our answer

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