How do you do integration with partial fractions?

Question

For example, 

http://fog.ccsf.cc.ca.us/~wjeh/math110B/calculus2_exercise_methods_of_integration_answers.pdf

4a. I don't get how the answer is reached...do you long divide first? and if so what do you do with the result of the long division? integrate them both?

匿名 · Accepted Answer

Yes, you need to do long division first.  Your quotient should be composed of a polynomial and a rational expression.  Just to make sure you know, long division is made easier if you write x^2 as (x^2 + 0x + 0.  Also, recall that the integral of a sum is the sum of the integrals.

The final, integrated expression you should get is x^2/2 - 4x + 16 ln|x + 4| + C.  Good luck!

? · Answer

The setup: 2x+4=(A/x-2)+(B/x+4)+(C/x^2+4) Now you purely get a effortless denominator and resolve for A,B,C via looking the place the equations equivalent 0 and as quickly as you resolve for A,B,C you plug your solutions in to the 1st equation I confirmed and then combine those new equations

How do you do integration with partial fractions?

2 個解答