Question Number 171171 by Sotoberry last updated on 09/Jun/22
Commented by Rasheed.Sindhi last updated on 09/Jun/22
$${What}\:{to}\:{do}? \\ $$
Commented by Sotoberry last updated on 09/Jun/22
$$\left.{integration}\:{by}\:{partial}\:{fraction}\:{sir}\::\right) \\ $$
Answered by cortano1 last updated on 09/Jun/22
$$\:{I}=\int\:\frac{{x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{3}}{\left({x}−\mathrm{1}\right)\left({x}^{\mathrm{2}} −{x}−\mathrm{1}\right)}\:{dx} \\ $$$$\:=\:−\mathrm{2ln}\:\mid{x}−\mathrm{1}\mid+\frac{\mathrm{3}}{\mathrm{2}}\mathrm{ln}\:\mid{x}^{\mathrm{2}} −{x}−\mathrm{1}\mid+\frac{\mathrm{1}}{\:\sqrt{\mathrm{5}}}\mathrm{ln}\:\mid\frac{\mathrm{2}{x}−\mathrm{1}−\sqrt{\mathrm{5}}}{\mathrm{2}\sqrt{{x}^{\mathrm{2}} −{x}−\mathrm{1}}}\mid+{c}\: \\ $$