How do you integrate int (1-x^2)/((x-9)(x-5)(x+2))dx using partial fractions?
1 Answer
Explanation:
We can rewrite the integrand expression in this way
Making
1/90=A/-9+B/-5+C/2
0=A/-8+B/-4+C/3
0=A/-10+B/-6+C/1
Or
Solving the system of variables
So
A=(Delta A)/Delta=(-7/3240)/(77/64800)=-1/11*20=-20/11
B=(Delta B)/Delta=(11/10800)/(77/64800)=1/7*6=6/7
C=(Delta C)/Delta=(-1/21600)/(77/64800)=-1/77*3=-3/77
Then the original expression becomes
=-20/11int dx/(x-9)+6/7int dx/(x-5)-3/77int dx/(x+2)
=-20/11ln|x-9|+6/7ln|x-5|-3/77ln|x+2|+const.