Question Number 122528 by mnjuly1970 last updated on 17/Nov/20 $$\:\:\:\:\:…{nice}\:\:{calculus}… \\ $$$$\:\:\:\Omega\:=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} {xsin}\left({x}\right).{cos}\left({x}\right){ln}\left({sin}\left({x}\right).{ln}\left({cos}\left({x}\right)\right){dx}\right. \\ $$$$\overset{???} {=}\:\frac{\pi}{\mathrm{16}}−\frac{\pi^{\mathrm{3}} }{\mathrm{192}}\:\checkmark \\ $$ Answered by mindispower last updated…
Question Number 122506 by mathace last updated on 17/Nov/20 Answered by TANMAY PANACEA last updated on 17/Nov/20 $$\int\frac{{ln}\left(\mathrm{1}+\left({x}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{2}} \right)}{{x}\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}{dx} \\ $$$${x}={seca} \\ $$$$\int\frac{{ln}\left(\mathrm{1}+{tan}^{\mathrm{4}}…
Question Number 188036 by Michaelfaraday last updated on 25/Feb/23 $$\int\mathrm{2}^{{x}} {e}^{{x}} {dx} \\ $$ Answered by MJS_new last updated on 25/Feb/23 $$\int\mathrm{2}^{{x}} \mathrm{e}^{{x}} {dx}=\int\mathrm{e}^{\left(\mathrm{1}+\mathrm{ln}\:\mathrm{2}\right){x}} {dx}=\frac{\mathrm{e}^{\left(\mathrm{1}+\mathrm{ln}\:\mathrm{2}\right){x}}…
Question Number 122496 by benjo_mathlover last updated on 17/Nov/20 $$\:\:{V}=\underset{\mathrm{0}} {\overset{\mathrm{3}} {\int}}\:\frac{{x}\:{dx}}{\:\sqrt{{x}+\mathrm{1}}+\sqrt{\mathrm{5}{x}+\mathrm{1}}} \\ $$$$\:{T}=\underset{−\pi/\mathrm{2}} {\overset{\pi/\mathrm{2}} {\int}}\sqrt{\mathrm{cos}\:{x}−\mathrm{cos}\:^{\mathrm{3}} {x}}\:{dx}\: \\ $$ Answered by Dwaipayan Shikari last updated…
Question Number 188035 by Michaelfaraday last updated on 25/Feb/23 $${solve} \\ $$$$\int\frac{{x}^{\mathrm{2}} }{\left({a}+{bx}\right)^{\mathrm{2}} }{dx} \\ $$ Answered by MJS_new last updated on 25/Feb/23 $$\int\frac{{x}^{\mathrm{2}} }{\left({a}+{bx}\right)^{\mathrm{2}}…
Question Number 188034 by Michaelfaraday last updated on 25/Feb/23 $${solve} \\ $$$$\int\frac{{x}^{\mathrm{2}} +\mathrm{3}}{{x}^{\mathrm{6}} \left({x}^{\mathrm{2}} +\mathrm{1}\right)}{dx} \\ $$ Answered by MJS_new last updated on 25/Feb/23 $$\int\frac{{x}^{\mathrm{2}}…
Question Number 56938 by maxmathsup by imad last updated on 26/Mar/19 $${let}\:{A}_{{n}} =\int\int_{{W}_{{n}} } {e}^{−{xy}} \sqrt{{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} }{dxdy}\:\:\:{with}\:{W}_{{n}} =\left[\frac{\mathrm{1}}{{n}},{n}\left[×\left[\frac{\mathrm{1}}{{n}},{n}\left[\right.\right.\right.\right. \\ $$$$\left.\mathrm{1}\right)\:{find}\:{A}_{{n}} {interms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}}…
Question Number 56939 by maxmathsup by imad last updated on 26/Mar/19 $${calculate}\:\int\:\:\:\:\frac{{dx}}{\left({x}+\mathrm{1}\right)^{\mathrm{3}} \left({x}^{\mathrm{2}} −\mathrm{3}{x}\:+\mathrm{2}\right)} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{2}} ^{+\infty} \:\:\frac{{dx}}{\left({x}+\mathrm{1}\right)^{\mathrm{3}} \left({x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}\right)} \\ $$ Commented by turbo…
Question Number 56937 by maxmathsup by imad last updated on 27/Mar/19 $$\mathrm{1}.\:{calculate}\:\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:{ln}\left(\mathrm{1}+{xtan}\theta\right){d}\theta \\ $$$$\mathrm{2}.\:\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {f}\left({x}\right){dx} \\ $$ Terms of Service Privacy Policy…
Question Number 56935 by maxmathsup by imad last updated on 27/Mar/19 $$\mathrm{1}.\:{calculate}\:\:{U}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\left({x}^{\mathrm{3}} −\mathrm{2}{x}+\mathrm{1}\right){e}^{−{n}\left[{x}\right]} {dx}\:\:{with}\:{n}\:{integr}\:{natural}\:{and}\:{n}\geqslant\mathrm{1} \\ $$$$\mathrm{2}.\:{find}\:{nature}\:{of}\:\Sigma\:{U}_{{n}} \\ $$ Commented by maxmathsup by…