Explanation Given: The given integral is, ∫ 2 x + 1 x ( x 2 + 4 ) d x Approach: Integration by parts: an integral of the form ∫ p ( x ) q ( x ) d x can be evaluated when p ( x ) and q ( x ) are polynomials in x . Consider the first case when the degree of p ( x ) is less than the degree of q ( x ) . To evaluate the integral, first determine the partial fraction decomposition of the integrand. The result will always be integrable, although a substitution must be needed to carry out the integration. Calculation: Consider the given integral. ∫ 2 x + 1 x ( x 2 + 4 ) d x Simplify the above integral using partial fraction decomposition. 2 x + 1 x ( x 2 + 4 ) = A x + B x + C x 2 + 4 … ( 1 ) Multiply both side by x ( x 2 + 4 ) . 2 x + 1 x ( x 2 + 4 ) × x ( x 2 + 4 ) = A x × x ( x 2 + 4 ) + B x + C ( x 2 + 4 ) × x ( x 2 + 4 ) 2 x + 1 = A ( x 2 + 4 ) + B x 2 + C x 2 x + 1 = x 2 ( A + B ) + C x + 4 A Equate the coefficients of like powers of x on both the sides. C = 2 4 A = 1 A = 1 4 A + B = 0 B = − A B = − 1 4 Substitute 1 4 for A , − 1 4 for B and 2 for C in equation ( 1 )

Differential Equations And Linear Algebra, Books A La Carte Edition (4th Edition)

4th Edition

ISBN: 9780321985811

Author: Stephen W. Goode, Scott A. Annin

Publisher: Pearson (edition 4)

See similar textbooks

Videos

Question

Chapter C, Problem 9P

To determine

To find:

The integral ∫2x+1x(x2+4)dx.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter C, Problem 8P

Chapter C, Problem 10P

Students have asked these similar questions

2) If Mand N be two water hyper Plane ofx Show that MUN and MN is hy Per Plane ofx with prove and Examplame. or 3) IS AUB is convex set and affine set or blensed set or symmetre setorsubsie.... Show that A and B is convex or affine or Hensedsed or symmetivce or subspace. 4) 18 MUN is independence show that Prove or ExPlane Mand Nave independend. or not. 5) Jet X be Vector Pace over I show that is xty tnx st Xty 3 fix→ F s-t f(x) (9) Jet Mand N be two blanced set of Xbe Vector space show tha MUNIS ansed set

Find a polynomial with integer coefficients that satisfies the given conditions. T(x) has degree 4, zeros i and 1 + i, and constant term 12.

How to solve 2542000/64132 without a calculator?

Chapter C Solutions

Differential Equations And Linear Algebra, Books A La Carte Edition (4th Edition)

Ch. C - Prob. 1P Ch. C - Problems For Problems 1-22, evaluate the given...Ch. C - Prob. 3P Ch. C - Prob. 4P Ch. C - Prob. 5P Ch. C - Prob. 6P Ch. C - Prob. 7P Ch. C - Prob. 8P Ch. C - Prob. 9P Ch. C - Prob. 10P

Ch. C - Prob. 11P Ch. C - Prob. 12P Ch. C - Prob. 13P Ch. C - Prob. 14P Ch. C - Prob. 15P Ch. C - Prob. 16P Ch. C - Prob. 17P Ch. C - Prob. 18P Ch. C - Prob. 19P Ch. C - Prob. 20P Ch. C - Prob. 21P Ch. C - Prob. 22P

Knowledge Booster

$Algebra$

Learn more about

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

The integral ∫ 2 x + 1 x ( x 2 + 4 ) d x .

Solution Summary: The author explains how the integral can be evaluated using partial tion decomposition of the integrand.

Videos

To find:

The integral ∫2x+1x(x2+4)dx.

Want to see the full answer?

Chapter C Solutions

The integral ∫ 2 x + 1 x ( x 2 + 4 ) d x .

Solution Summary: The author explains how the integral can be evaluated using partial tion decomposition of the integrand.

Videos

To find: The integral ∫2x+1x(x2+4)dx.

Want to see the full answer?

Chapter C Solutions

To find:

The integral ∫2x+1x(x2+4)dx.