Evaluate the integral of (1 + 3x)/((1 - x)(3x - 5)) dx. A. 2 ln(absolute 1 - x) - 3 ln(absolute...


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

Become a member to unlock this answer!

View this answer

We start by writing the partial fraction decomposition of the integrand as

{eq}\ \ \ \ \ \dfrac{1+3x}{(1-x)(3x-5)} = \dfrac{A}{1-x} +...

See full answer below.

Learn more about this topic:

How to Integrate Functions With Partial Fractions


Chapter 13 / Lesson 10

Learn about integration by partial fractions. Explore how to make partial fractions and then how to integrate fractions. See examples of integrating fractions.

Related to this Question

Explore our homework questions and answers library