Securing Higher Grades Costing Your Pocket? Book Your Assignment at The Lowest Price Now!


Get assignment help service to meet the high expectations of your professors

GET ASSIGNMENT HELP

Math Assignment Help With Integration Of Rational Functions

4.7 Integration Of Rational Functions:

A rational function is by definition the quotient of two polynomials.

For example

x3 etc…

(1 – x2) 1 + x2

Integration Of Rational Functions Assignment Help Order Now

are all rational functions. Remember in the rational function √x, ln(x) or |x| are not mentioned.

Steps to integrate the rational function

f(x) = P(x)

Q(x)

Step1: If degree(P) ≥ degree(Q) perform polynomial long-division. Otherwise go to step 2.

Step2: Factor the denominator Q(x) into irreducible polynomials: linear and irreducible quadratic polynomials.

Step3: Find the partial fraction decomposition.

Step4: Integrate the result of step 3.

Example: Find

∫(x5 + 2)/( x2 – 1) dx

Solution. Since the degree of the numerator is higher than the denominator, we should perform the long-division. We get

x5 + 2 = (x2- 1) (x2 + x) + x + 2

which implies

x5 + 2 = x3 + x + x +2

x2 – 1 x2– 1

the fraction x + 2

x2 – 1

on partial decomposition gives ;

x+ 2 = x + 2 B

x2 – 1 (x – 1) (x + 1) x + 1 x - 1

Therefore,

x + 2 = A(x-1) + B(x+1).

If we substitute x=1, we get B = 3/2 and we substitute x= -1, we get A = -1/2. Therefore, we have

x5 + = x2 + x – 1 3 1

x2 – 1 2 (x + 1) 2 (x – 1)

Now integrating,

∫(x5 + 2) / (x2 – 1) dx = ∫(x2 + x) dx  - ∫(1/2) (1/x + 1) dx  + ∫(3/2) (1/x – 1) dx

Since we have

∫(x2 + x) dx = x4 + x2

4 2

∫(1/x +1) dx = ln |x + 1|

And,

(1/x + 1) dx = ln|x – 1|

we get

∫ (x5 + 2)/(x2 – 1) dx = x4 + x2 – 1 ln|x + 1| + 3 ln|x – 1|

4 2 2 2

Email Based Assignment Help in Integration Of Rational Functions

To Schedule a Integration Of Rational Functions tutoring session Live chat
To submit Integration Of Rational Functions assignment click here.

Following are some of the topics in Rational Function in which we provide help:

Assignment Help Features
Assignment Help Services
  • Assignment Help
  • Homework Help
  • Writing Help
  • Academic Writing Assistance
  • Editing Services
  • Plagiarism Checker Online
  • Proofreading
  • Research Writing Help
QR Code Assignment Help
elearningfeeds