Question Number 122587 by bramlexs22 last updated on 18/Nov/20 $$\:\:\underset{\mathrm{1}} {\overset{\mathrm{16}} {\int}}\:\mathrm{arctan}\:\sqrt{\sqrt{{x}}\:−\mathrm{1}}\:{dx}\: \\ $$$$\:\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\mathrm{sin}\:\left(\mathrm{2}{x}\right)\:\mathrm{arctan}\:\left(\mathrm{sin}\:{x}\right)\:{dx}\: \\ $$ Answered by MJS_new last updated on 18/Nov/20…
Question Number 122572 by rs4089 last updated on 18/Nov/20 Answered by Olaf last updated on 18/Nov/20 $$\mathrm{With}\:\mathrm{Euler}'\mathrm{s}\:\mathrm{Gamma}\:\mathrm{function}\:\Gamma\:: \\ $$$$\int_{\mathrm{0}} ^{\infty} {e}^{−{x}} \mathrm{ln}{xdx}\:=\:\Gamma'\left(\mathrm{1}\right)\:=\:−\gamma \\ $$$$\mathrm{where}\:\gamma\:\mathrm{is}\:\mathrm{the}\:\mathrm{Euler}−\mathrm{Mascheroni} \\…
Question Number 188086 by universe last updated on 25/Feb/23 $$\:\:\:\: \\ $$$$\:\:\:\:\:\:\mathrm{I}\:\:\:=\:\:\:\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{tan}^{−\mathrm{1}} \left({x}/{a}\right)}{{x}\left({x}^{\mathrm{2}} +{b}^{\mathrm{2}} \right)}{dx} \\ $$ Answered by witcher3 last updated on…
Question Number 122544 by bramlexs22 last updated on 18/Nov/20 $$\:{any}\:{one}\:{can}\:{explain}\:{me}\:{about} \\ $$$${Fresnel}\:{integral}\:? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 122542 by bramlexs22 last updated on 18/Nov/20 $$\:\:\underset{\mathrm{0}} {\overset{\mathrm{3}} {\int}}\:\sqrt{\mathrm{1}+\mathrm{cos}\:\left({x}^{\mathrm{2}} \right)}\:{dx}\:? \\ $$ Answered by Olaf last updated on 18/Nov/20 $$\mathrm{I}\:=\:\int_{\mathrm{0}} ^{\mathrm{3}} \sqrt{\mathrm{1}+\mathrm{cos}\left({x}^{\mathrm{2}}…
Question Number 122528 by mnjuly1970 last updated on 17/Nov/20 $$\:\:\:\:\:…{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}}…