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Category: Integration

find-in-terms-of-n-the-value-of-A-n-0-1-k-1-n-1-x-2-2xcos-kpi-n-1-dx-with-n-from-N-

Question Number 31460 by abdo imad last updated on 08/Mar/18 $${find}\:{in}\:{terms}\:{of}\:\:{n}\:{the}\:{value}\:{of} \\ $$$${A}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\prod_{{k}=\mathrm{1}} ^{{n}−\mathrm{1}} \left({x}^{\mathrm{2}} \:−\mathrm{2}{xcos}\left(\frac{{k}\pi}{{n}}\right)\:+\mathrm{1}\right){dx}\:\:\:{with}\:{n}\:{from}\:{N}^{\bigstar} . \\ $$ Commented by abdo…

solve-cosec-2-x-2-dx-

Question Number 162512 by vishal1234 last updated on 30/Dec/21 $${solve}\:\int\sqrt{{cosec}^{\mathrm{2}} {x}−\mathrm{2}}\:{dx} \\ $$ Commented by MJS_new last updated on 30/Dec/21 $$\mathrm{2}\:\mathrm{steps}\:\mathrm{are}\:\mathrm{necessary} \\ $$$$\left(\mathrm{1}\right)\:{t}=\mathrm{cos}\:{x} \\ $$$$\left(\mathrm{2}\right)\:{u}=\sqrt{\mathrm{2}}{t}+\sqrt{\mathrm{2}{t}^{\mathrm{2}}…

0-log-x-x-1-x-9-

Question Number 162513 by Lordose last updated on 30/Dec/21 $$\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{log}\left(\mathrm{x}\right)}{\left(\mathrm{x}+\mathrm{1}\right)\left(\mathrm{x}+\mathrm{9}\right)} \\ $$ Answered by abdullahoudou last updated on 30/Dec/21 $${x}−>\frac{\mathrm{9}}{{x}} \\ $$ Answered…

find-0-1-dx-x-1-2x-2-1-

Question Number 96962 by mathmax by abdo last updated on 05/Jun/20 $$\mathrm{find}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{dx}}{\:\sqrt{\mathrm{x}+\mathrm{1}}+\sqrt{\mathrm{2x}^{\mathrm{2}} +\mathrm{1}}} \\ $$ Answered by MJS last updated on 06/Jun/20 $$\int\frac{{dx}}{\:\sqrt{{x}+\mathrm{1}}+\sqrt{\mathrm{2}{x}^{\mathrm{2}}…