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Evaluate the integral.
$ \displaystyle \int \frac{3t - 2}{t + 1}\ dt $
$$\int \frac{3 t-2}{t+1} d t=3 t-5 \ln |t+1|+C$$
Calculus 2 / BC
Chapter 7
Techniques of Integration
Section 4
Integration of Rational Functions by Partial Fractions
Integration Techniques
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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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