- #1
Cosmophile
- 111
- 2
Hey, all! I'm learning partial fraction decomposition from Serge Lang's "A First Course in Calculus." In it, he gives the following example:
\int\frac{x+1}{(x-1)^2(x-2)}dx
He then decomposes this into the following sum:
\frac{x+1}{(x-1)^2(x-2)} = \frac{c_1}{x-1}+\frac{c_2}{(x-1)^2}+\frac{c_3}{x-2}
My question is this: On the right hand side (RHS), ##x-1## and ##(x-1)^2## appear. Why is this the case, when the original denominator only had the ##(x-1)^2##? I hope this makes sense, and any help here is greatly appreciated!
\int\frac{x+1}{(x-1)^2(x-2)}dx
He then decomposes this into the following sum:
\frac{x+1}{(x-1)^2(x-2)} = \frac{c_1}{x-1}+\frac{c_2}{(x-1)^2}+\frac{c_3}{x-2}
My question is this: On the right hand side (RHS), ##x-1## and ##(x-1)^2## appear. Why is this the case, when the original denominator only had the ##(x-1)^2##? I hope this makes sense, and any help here is greatly appreciated!
