Question Number 94432 by Tony Lin last updated on 18/May/20
$$\int\:\frac{{x}^{{n}} −{x}^{{n}−\mathrm{2}} }{\underset{{r}=\mathrm{0}} {\overset{\mathrm{2}{n}} {\sum}}{C}_{{r}} ^{\mathrm{2}{n}} {x}^{{r}} }{dx}=? \\ $$$${The}\:{result}\:{is}\:{a}\:{little}\:{pretty} \\ $$
Commented by PRITHWISH SEN 2 last updated on 18/May/20
$$\int\frac{\mathrm{x}^{\mathrm{n}} −\mathrm{x}^{\mathrm{n}−\mathrm{2}} }{\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{2n}} }\mathrm{dx}=\int\frac{\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }\right)}{\left(\frac{\mathrm{1}}{\mathrm{x}}+\mathrm{x}+\mathrm{2}\right)^{\mathrm{n}} }\mathrm{dx}\:\:\mathrm{put}\:\mathrm{x}+\frac{\mathrm{1}}{\mathrm{x}}+\mathrm{2}=\mathrm{t} \\ $$
Commented by Tony Lin last updated on 19/May/20
$${thanks}\:{sir} \\ $$
Commented by PRITHWISH SEN 2 last updated on 19/May/20
$$\mathrm{welcome}\:\mathrm{sir} \\ $$