SOLUTION: Please help me solve this equation: Evaluate the integral {{{ int ( 1/ (x+2x^2+x^3), dx ) }}} using the method of partial fractions.

Algebra ->  Test -> SOLUTION: Please help me solve this equation: Evaluate the integral {{{ int ( 1/ (x+2x^2+x^3), dx ) }}} using the method of partial fractions.      Log On


   

Question 356207: Please help me solve this equation:
Evaluate the integral +int+%28+1%2F+%28x%2B2x%5E2%2Bx%5E3%29%2C+dx+%29+ using the method of partial fractions.
Answer by jrfrunner(365) About Me  (Show Source):
You can put this solution on YOUR website!
factor the denomiator x%2B2x%5E2%2Bx%5E3%29=x%2A%28x%2B1%29%5E2
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now set
+int+%28+1%2F+%28x%2B2x%5E2%2Bx%5E3%29%2C+dx+%29+ = int+%28%28A%2Fx%2BB%2F%28x%2B1%29%2Bc%2F%28x%2B1%29%5E2%29%29
this integrates into
A%2Aln%28abs%28x%29%29%2BB%2Aln%28abs%28x%2B1%29%29-2C%2A%28X%2B1%29%5E%28-1%29+ constant
==
find A, B, and C by multiplying A%2Fx%2BB%2F%28x%2B1%29%2Bc%2F%28x%2B1%29%5E2%29 by the common denominator x%2A%28x%2B1%29%5E2 and setting the numerator equal to its original numerator of 1.
A%2A%28x%2B1%29%5E2%2BB%2Ax%2A%28x%2B1%29%2Bc%2Ax=1
select 3 different values of x and solve for A, B and C
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choose 3 convenient X values ie -1,0,1
x=0: +A%2A%280%2B1%29%5E2+%2B+b%2A0%2A%280%2B1%29%2Bc%2A0=1 => A=1
x=-1: +A%2A%28-1%2B1%29%5E2+%2B+b%2A-1%2A%28-1%2B1%29%2Bc%2A%28-1%29=1 => -C=1 or C=-1
you get the idea?