Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §7.4 Partial Fractions, #1 · Calculus · Techniques of integration

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

Find the numbers $A$ and $B$ to split $1/ (x^{2} - x)$ :
$\frac{1}{x ( x - 1 )} = \frac{A}{x} + \frac{B}{x - 1} .$
Cover up $x$ and set $x = 0$ to find $A$ . Cover up $x - 1$ and set $x = 1$ to find $B$ . Then integrate.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §7.4 Partial Fractions, #1

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