Answered: x +1 「マ-x-6 dx. х2 — х — | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.7: Distinguishable Permutations And Combinations

Problem 3E

See similar textbooks

Related questions

Question

x +1
「マ-x-6
dx.
х2 — х —

Expert Solution

Step 1

The integral is $\int \frac{x + 1}{x^{2} - x - 6} d x$ .

Factorize the denominator.

$\begin{array}{rcl} x^{2} - x - 6 & = & x^{2} - 3 x + 2 x - 6 \\ = & x (x - 3) + 2 (x - 3) \\ = & (x - 3) (x + 2) \end{array}$

Thus, the integral becomes.

$\int \frac{x + 1}{(x - 3) (x + 2)} d x$

Step 2

Now consider the function $\frac{x + 1}{(x - 3) (x + 2)}$ .

Split the terms.

$\begin{array}{rcl} \frac{x + 1}{(x - 3) (x + 2)} & = & \frac{A}{x - 3} + \frac{B}{x + 2} \\ = & \frac{A (x + 2) + B (x - 3)}{(x - 3) (x + 2)} \\ = & \frac{A x + 2 A + B x - 3 B}{(x - 3) (x + 2)} \\ = & \frac{x (A + B) + (2 A - 3 B)}{(x - 3) (x + 2)} \end{array}$

On comparing the coefficients of both sides of the above equation,

$\begin{array}{rcl} A + B & = & 1 . . . . . . (1) \\ 2 A - 3 B & = & 1 . . . . . . (2) \end{array}$

Multiply to equation (1) and then add it with equation (2).

$\begin{array}{rcl} 5 A & = & 4 \\ A & = & \frac{4}{5} \end{array}$

Substitute $\frac{4}{5}$ for A equation (1).

$\begin{array}{rcl} \frac{4}{5} + B & = & 1 \\ B & = & 1 - \frac{4}{5} \\ = & \frac{1}{5} \end{array}$

Step by step

Solved in 3 steps

Blurred answer

Similar questions

A crime-scene investigator has 3.4 ounces of a sample. He needs to conduct four tests that each require 0.6 ounces of the sample, and one test that requires 0.8 ounces of the sample. How much of the sample remains after he uses it for the five tests?

Recommended textbooks for you

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Algebra: Structure And Method, Book 1

Algebra: Structure And Method, Book 1

Algebra

ISBN:

9780395977224

Author:

Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:

McDougal Littell

Intermediate Algebra

Intermediate Algebra

Algebra

ISBN:

9781285195728

Author:

Jerome E. Kaufmann, Karen L. Schwitters

Publisher:

Cengage Learning

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Algebra: Structure And Method, Book 1

Algebra: Structure And Method, Book 1

Algebra

ISBN:

9780395977224

Author:

Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:

McDougal Littell

Intermediate Algebra

Intermediate Algebra

Algebra

ISBN:

9781285195728

Author:

Jerome E. Kaufmann, Karen L. Schwitters

Publisher:

Cengage Learning

Algebra for College Students

Algebra for College Students

Algebra

ISBN:

9781285195780

Author:

Jerome E. Kaufmann, Karen L. Schwitters

Publisher:

Cengage Learning

Big Ideas Math A Bridge To Success Algebra 1: Stu…

Big Ideas Math A Bridge To Success Algebra 1: Stu…

Algebra

ISBN:

9781680331141

Author:

HOUGHTON MIFFLIN HARCOURT

Publisher:

Houghton Mifflin Harcourt

SEE MORE TEXTBOOKS