Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §7.4 Partial Fractions, #2 · Calculus · Techniques of integration

Find the numbers … and … to split …: … \frac{1}{x^2-1}=\frac{A}{x-1}+\frac{B}{x+1}

Find the numbers $A$ and $B$ to split $1/ (x^{2} - 1)$ :
$\frac{1}{x ^{2} - 1} = \frac{A}{x - 1} + \frac{B}{x + 1} .$
Multiply by $x - 1$ and set $x = 1$ . Multiply by $x + 1$ and set $x = - 1$ . Integrate. Then find $A$ and $B$ again by method 1—with numerator $A (x + 1) + B (x - 1)$ equal to 1.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §7.4 Partial Fractions, #2

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