Question Number 95563 by peter frank last updated on 26/May/20
$$\int\frac{\mathrm{ax}^{\mathrm{2}} +\mathrm{bx}+\mathrm{c}}{\left(\mathrm{x}−\mathrm{p}\right)\left(\mathrm{x}−\mathrm{q}\right)\left(\mathrm{x}−\mathrm{r}\right)}\mathrm{dx} \\ $$
Answered by MJS last updated on 26/May/20
$$\int\frac{{ax}^{\mathrm{2}} +{bx}+{c}}{\left({x}−{p}\right)\left({x}−{q}\right)\left({x}−{r}\right)}{dx}= \\ $$$$=\frac{{ap}^{\mathrm{2}} +{bp}+{c}}{\left({p}−{q}\right)\left({p}−{r}\right)}\int\frac{{dx}}{{x}−{p}}+ \\ $$$$+\frac{{aq}^{\mathrm{2}} +{bq}+{c}}{\left({q}−{p}\right)\left({q}−{r}\right)}\int\frac{{dx}}{{x}−{q}}+ \\ $$$$+\frac{{ar}^{\mathrm{2}} +{br}+{c}}{\left({r}−{p}\right)\left({r}−{q}\right)}\int\frac{{dx}}{{x}−{r}} \\ $$$$\mathrm{it}'\mathrm{s}\:\mathrm{easy}\:\mathrm{now} \\ $$
Commented by 1549442205 last updated on 26/May/20
$$\mathrm{Allright},\mathrm{it}\:\mathrm{is}\:\mathrm{correct} \\ $$