How do you integrate int (x^3 +x^2+2x+1) / [(x^2+1) (x^2+2)] using partial fractions?
1 Answer
Explanation:
Note: If the denominator of the partial fraction is not factorable, always remember the degree of the numerator is one less. Like the problem
Step 1: Find the equivalent partial fraction
Step 2 Solve the partial fraction by multiply by Least common denominator to get
Step 3: Multiply/expand/foil the right hand side to get
Step 4: Set up the system of equation, using the corresponding coefficient for the corresponding terms
Step 5: Solve the system of equation
+(2 = 2A + C)
0 = 3C => C= 0 ,A= 1
+ (B +D = 1)
-B= 0=> B= 0, D= 1
Step 6: Write the equivalent partial fraction for the integral like this
Step 7 Integrate the integral
the first integral can be done by u substitution like this
let
Note:
The second integral is
Answer:
1/2 ln (x^2 +1) +1/sqrt(2) arctan(x/sqrt2) +"Constant"
I let my constant value to be
this is another answer: