Evaluate the integral of (1 + 3x)/((1 - x)(3x - 5)) dx. A. 2 ln(absolute 1 - x) - 3 ln(absolute...
Question:
Evaluate {eq}\int \frac{1 + 3x}{(1 - x)(3x - 5)} \, \mathrm{d}x {/eq}.
A. {eq}2 \ln \left|1-x \right| - 3 \ln \left| 3x-5 \right| + C {/eq}
B. {eq}2 \ln \left|1-x \right| - 27 \ln \left| 3x-5 \right| + C {/eq}
C. {eq}-2 \ln \left|1-x \right| - 3 \ln \left| 3x-5 \right| + C {/eq}
D. {eq}-2 \ln \left|1-x \right| - 9 \ln \left| 3x-5 \right| + C {/eq}
Evaluating an Integral with Partial Fractions
Given the integral of a rational function in which the denominator may be factored, we find the partial fraction decomposition of the function. We then use this form to determine the indefinite integral of the original function.
Answer and Explanation: 1
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View this answerWe start by writing the partial fraction decomposition of the integrand as
{eq}\ \ \ \ \ \dfrac{1+3x}{(1-x)(3x-5)} = \dfrac{A}{1-x} +...
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Chapter 13 / Lesson 10Learn about integration by partial fractions. Explore how to make partial fractions and then how to integrate fractions. See examples of integrating fractions.