Explanation Given information: x 3 x 2 − 2 x + 1 Formula: ∫ 1 x d x = ln | x | + C a ln | x | = ln | x a | Calculation: Express the integrand through long division eliminating the cubic term as below. x 3 x 2 − 2 x + 1 = x + 2 x 2 − x x 2 + 2 x + 1 Express the integrand through long division eliminating the square term as below. x 3 x 2 − 2 x + 1 = x + 2 + 3 x − 2 x 2 − 2 x + 1 = x + 2 + 3 x − 2 ( x − 1 ) 2 Express the integrand as a sum of partial fractions with undetermined coefficients. x + 2 + 3 x − 2 ( x − 1 ) 2 = x + 2 + A x − 1 + B ( x − 1 ) 2 (1) Simplify the above equation. 3 x − 2 ( x − 1 ) 2 = A ( x − 1 ) 2 + B ( x − 1 ) ( x − 1 ) 3 3 x − 2 = A ( x − 1 ) + B 3 x − 2 = A x + B − A (2) Equate the coefficient of the x term on both the sides of equation (2)

Thomas' Calculus: Early Transcendentals, Books a la Carte Edition (14th Edition)

14th Edition

ISBN: 9780134439440

Author: Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher: PEARSON

See similar textbooks

Concept explainers

Quadratic Equation

When it comes to the concept of polynomial equations, quadratic equations can be said to be a special case. What does solving a quadratic equation mean? We will understand the quadratics and their types once we are familiar with the polynomial equations …

Demand and Supply Function

The concept of demand and supply is important for various factors. One of them is studying and evaluating the condition of an economy within a given period of time. The analysis or evaluation of the demand side factors are important for the suppliers to …

Videos

Question

Chapter 8.5, Problem 18E

To determine

The integral through expansion of integrand as a sum of partial fractions.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.5, Problem 17E

Chapter 8.5, Problem 19E

Students have asked these similar questions

the correct answer is Ccould you please show me how to do it using the residue theorem

Use the information to find and compare Δy and dy. (Round your answers to four decimal places.) y = x4 + 7 x = −3 Δx = dx = 0.01 Δy = dy =

4. A car travels in a straight line for one hour. Its velocity, v, in miles per hour at six minute intervals is shown in the table. For each problem, approximate the distance the car traveled (in miles) using the given method, on the provided interval, and with the given number of rectangles or trapezoids, n. Time (min) 0 6 12 18|24|30|36|42|48|54|60 Speed (mph) 0 10 20 40 60 50 40 30 40 40 65 a.) Left Rectangles, [0, 30] n=5 b.) Right Rectangles, [24, 42] n=3 c.) Midpoint Rectangles, [24, 60] n=3 d.) Trapezoids, [0, 24] n=4

Chapter 8 Solutions

Thomas' Calculus: Early Transcendentals, Books a la Carte Edition (14th Edition)

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.