Question Number 170725 by Sotoberry last updated on 29/May/22 Answered by FelipeLz last updated on 30/May/22 $${u}\:=\:\mathrm{tan}^{−\mathrm{1}} \left({x}\right)\:\Rightarrow\:{du}\:=\:\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$$${dv}\:=\:\mathrm{1}{dx}\:\Rightarrow\:{v}\:=\:{x} \\ $$$$\int\mathrm{tan}^{−\mathrm{1}} \left({x}\right){dx} \\…
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Question Number 170722 by Sotoberry last updated on 29/May/22 Answered by MikeH last updated on 29/May/22 $${u}\:=\mathrm{sin}\:\theta \\ $$$${du}\:=\:\mathrm{cos}\:\theta\:{d}\theta \\ $$$${dv}\:=\:{e}^{\theta} {d}\theta \\ $$$${v}\:=\:{e}^{\theta} \\…
Question Number 39633 by abdo mathsup 649 cc last updated on 09/Jul/18 $${find}\:{the}\:{value}\:{of}\: \\ $$$${f}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\pi} {ln}\left({x}^{\mathrm{2}} \:−\mathrm{2}{x}\:{cos}\theta\:+\mathrm{1}\right){d}\theta\:\:{with}\:{x}\:{fromR}. \\ $$ Commented by math khazana by…
Question Number 170663 by kndramaths last updated on 28/May/22 Commented by kaivan.ahmadi last updated on 28/May/22 $${a}. \\ $$$$\mathrm{0}\leqslant{x}\leqslant{a}\:\:,\:\:\mathrm{0}\leqslant{y}\leqslant\sqrt{{a}^{\mathrm{2}} −{x}^{\mathrm{2}} } \\ $$$$\int\frac{{dx}}{{a}^{\mathrm{2}} +{x}^{\mathrm{2}} }{dx}=\frac{\mathrm{1}}{{a}}{arctg}\left(\frac{{x}}{{a}}\right)…
Question Number 170610 by Sotoberry last updated on 27/May/22 Answered by aleks041103 last updated on 27/May/22 $${IBP} \\ $$$$\int{udv}={uv}−\int{vdu} \\ $$$${u}={x}^{\mathrm{2}} +{x}+\mathrm{1} \\ $$$${v}={e}^{{x}} \\…
Question Number 170593 by 119065 last updated on 27/May/22 Commented by mkam last updated on 27/May/22 $$\int\:\left({x}+\mathrm{3}\:−\:\mathrm{3}\right)\:\left({x}+\mathrm{3}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} {dx}=\int\:\left({x}+\mathrm{3}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} −\mathrm{3}\left({x}+\mathrm{3}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} {dx} \\ $$$$ \\ $$$$=\:\frac{\mathrm{2}}{\mathrm{5}}\:\left({x}+\mathrm{3}\right)^{\frac{\mathrm{5}}{\mathrm{2}}} \:−\:\mathrm{2}\:\left({x}+\mathrm{3}\right)^{\frac{\mathrm{3}}{\mathrm{2}}}…
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Question Number 170590 by rs4089 last updated on 27/May/22 Commented by rs4089 last updated on 27/May/22 $${solve}\:{this}\:{or}\:{express}\:{in}\:{series}\:{of}\: \\ $$$${bernloullis}\:{numbers} \\ $$ Terms of Service Privacy…
Question Number 170580 by mnjuly1970 last updated on 27/May/22 $$ \\ $$$$\:\:\:{calculate} \\ $$$$\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\:\mathrm{F}_{{n}} }{{n}.\mathrm{3}^{\:{n}} }\:=\:?\:\:\: \\ $$$$ \\ $$ Answered by Mathspace…