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Category: Integration

calculate-0-x-2-1-x-2-1-x-5-7-12-

Question Number 166614 by qaz last updated on 23/Feb/22 $$\mathrm{calculate}::\:\:\:\int_{\mathrm{0}} ^{\infty} \frac{\left\{\mathrm{x}\right\}^{\mathrm{2}} \left(\mathrm{1}−\left\{\mathrm{x}\right\}\right)^{\mathrm{2}} }{\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{5}} }=\frac{\mathrm{7}}{\mathrm{12}}−\gamma \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

x-2-3-x-4-5x-2-9-dx-

Question Number 166610 by cortano1 last updated on 23/Feb/22 $$\:\:\:\:\int\:\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{3}}{\mathrm{x}^{\mathrm{4}} +\mathrm{5x}^{\mathrm{2}} +\mathrm{9}}\:\mathrm{dx}\:? \\ $$ Commented by MJS_new last updated on 23/Feb/22 $$\mathrm{in}\:\mathrm{this}\:\mathrm{case}: \\ $$$$\frac{{d}}{{dx}}\left[\frac{\mathrm{1}}{{a}}\mathrm{arctan}\:\frac{{ax}}{{b}−{x}^{\mathrm{2}}…

Question-166570

Question Number 166570 by cortano1 last updated on 22/Feb/22 Answered by bobhans last updated on 22/Feb/22 $$\:\mathrm{I}=\int\:\frac{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} +\mathrm{2}}{\left(\mathrm{x}+\mathrm{1}\right)\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}}\:\mathrm{dx}\:=\:\int\frac{\mathrm{x}+\mathrm{1}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}}\mathrm{dx}+\int\frac{\mathrm{2}}{\left(\mathrm{x}+\mathrm{1}\right)\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}}\mathrm{dx} \\ $$$$\mathrm{I}_{\mathrm{1}} =\frac{\mathrm{1}}{\mathrm{2}}\int\:\frac{\mathrm{d}\left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)}{\:\sqrt{\mathrm{x}^{\mathrm{2}}…