Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §7.4 Partial Fractions, #19 · Calculus · Techniques of integration

Split … into

Split $\frac{3 x ^{2}}{x ^{3} - 1} = \frac{3 x ^{2}}{( x - 1 ) ( x ^{2} + x + 1 )}$ into $\frac{A}{x - 1} + \frac{B x + C}{x ^{2} + x + 1}$ .
(a) Cover up $x - 1$ and set $x = 1$ to find $A$ .
(b) Subtract $A / (x - 1)$ from the left side. Find $B x + C$ .
(c) Integrate all terms. Why do we already know
$ln (x^{3} - 1) = ln (x - 1) + ln (x^{2} + x + 1)$ ?

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §7.4 Partial Fractions, #19

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