   Chapter 8.5, Problem 20E

Chapter
Section
Textbook Problem

Using Partial Fractions In Exercises 3-20: use partial fractions to find the indefinite integral. ∫ x 2 + 6 x + 4 x 4 + 8 x 2 + 16   d x

To determine

To calculate: The solution of indefinite integration x2+6x+4x4+8x2+16dx by making use of partial fraction.

Explanation

Given:

The indefinite integral x2+6x+4x4+8x2+16dx.

Formula used:

Integration, duU2+a2=1aarctan(Ua)+C

Calculation:

The integral function is,

x2+6x+4x4+8x2+16=x2+6x+4(x2+4)2

The above equation is written in partial fraction,

x2+6x+4(x2+4)2=Ax+Bx2+4+Cx+D(x2+4)2x2+6x+4=(Ax+B)(x2+4)2+(Cx+D)=Ax3+Bx2+4Ax+4B+Cx+D=Ax3+Bx2+(4A+C)x+(4B+D)

Equate the equation from the left side,

A=0,B=1,4A+C=6 And 4B+D=4

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Find more solutions based on key concepts 