Question Number 123154 by liberty last updated on 23/Nov/20 Answered by benjo_mathlover last updated on 23/Nov/20 $$\:{let}\:{t}=\mathrm{sin}\:\:{q}\:\Rightarrow{dt}\:=\:\mathrm{cos}\:{q}\:{dq} \\ $$$$\eta\:\left({x}\right)=\:\int\:\sqrt{\mathrm{1}−\mathrm{sin}\:^{\mathrm{2}} {q}}\:\left(\mathrm{cos}\:{q}\:{dq}\right) \\ $$$$\eta\:\left({x}\right)=\:\int\left(\frac{\mathrm{1}+\mathrm{cos}\:\mathrm{2}{q}}{\mathrm{2}}\right)\:{dq}\: \\ $$$$\eta\:\left({x}\right)=\:\frac{{q}+\frac{\mathrm{1}}{\mathrm{2}}\mathrm{sin}\:\mathrm{2}{q}}{\mathrm{2}}\:+\:{c}\: \\…
Question Number 123060 by mnjuly1970 last updated on 22/Nov/20 $$\:\:\:\:\:\:\:\:\:\:….\:\:\:{nice}\:\:{calculus}\:…. \\ $$$$\:\:\:{evaluate}\:::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Omega\overset{???} {=}\int_{−\infty} ^{\:\infty} \frac{{x}^{\mathrm{2}} }{\left(\mathrm{1}+{e}^{{x}} \right)\left(\mathrm{1}+{e}^{−{x}} \right)}{dx} \\ $$ Answered by mindispower…
Question Number 123037 by benjo_mathlover last updated on 22/Nov/20 $$\:\:\int\:\frac{\sqrt{\mathrm{1}−{x}}}{\mathrm{1}−\sqrt{{x}}}\:{dx} \\ $$$$ \\ $$ Answered by MJS_new last updated on 22/Nov/20 $$\int\frac{\sqrt{\mathrm{1}−{x}}}{\mathrm{1}−\sqrt{{x}}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\frac{\sqrt{\mathrm{1}−{x}}}{\mathrm{1}−\sqrt{{x}}}\:\rightarrow\:{dx}=\mathrm{2}\sqrt{{x}}\left(\mathrm{1}−\sqrt{{x}}\right)\sqrt{\mathrm{1}−{x}}\right] \\…
Question Number 123034 by benjo_mathlover last updated on 21/Nov/20 Answered by mathmax by abdo last updated on 21/Nov/20 $$\chi\:=\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{ln}\left(\mathrm{x}\right)}{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\mathrm{dx}\:\:\Rightarrow\chi=_{\mathrm{x}=\frac{\mathrm{1}}{\mathrm{t}}} \:\:\:−\int_{\mathrm{0}} ^{\infty} \:\:\frac{−\mathrm{lnt}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{t}^{\mathrm{2}}…
Question Number 123033 by benjo_mathlover last updated on 21/Nov/20 $${Evaluate}\:{the}\:{integral}\: \\ $$$$\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\sqrt[{\mathrm{3}}]{\mathrm{1}−{x}^{\mathrm{7}} }\:−\:\sqrt[{\mathrm{7}}]{\mathrm{1}−{x}^{\mathrm{3}} }\:{dx}\:. \\ $$ Commented by MJS_new last updated on 22/Nov/20…
Question Number 57490 by Abdo msup. last updated on 05/Apr/19 $$\left.\mathrm{1}\right){findF}\left({a}\right)=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{cos}\left({ln}\left(\mathrm{2}+{x}^{\mathrm{2}} \right)\right)}{{a}^{\mathrm{2}} \:+{x}^{\mathrm{2}} }{dx}\:\:{witha}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{cos}\left({ln}\left(\mathrm{2}+{x}^{\mathrm{2}} \right)\right)}{\mathrm{4}+{x}^{\mathrm{2}} }{dx}. \\ $$ Commented…
Question Number 57487 by Abdo msup. last updated on 05/Apr/19 $${calculate}\:{lim}_{{x}\rightarrow\mathrm{1}} \:\:\:\int_{{x}} ^{{x}^{\mathrm{2}} } \:\:\:\:\frac{{arctan}\left({t}\right)}{{sint}}{dt}\:. \\ $$ Commented by kaivan.ahmadi last updated on 05/Apr/19 $${zero}…
Question Number 123023 by mnjuly1970 last updated on 21/Nov/20 $$\:\:\:\:\:\:\:\:\:\:…\:{advanced}\:\:{calculus}… \\ $$$${calculate}::: \\ $$$$\:\:\:\:\:\mathrm{I}:\overset{???} {=}\:\int_{\mathrm{0}} ^{\:\pi} \frac{{x}}{\mathrm{1}−{sin}\left({x}\right){cos}\left({x}\right)}{dx} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:………………………….. \\ $$ Answered by mnjuly1970 last…
Question Number 123020 by mnjuly1970 last updated on 21/Nov/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{advanced}\:\:{calculus}.. \\ $$$$ \\ $$$$\:\:\:{calculate}\:::\:\:\:\emptyset=\int_{\mathrm{0}} ^{\:\pi} \frac{\pi}{\mathrm{1}−{sin}\left({x}\right){cos}\left({x}\right)}{dx}=??? \\ $$$$\:\:\:\:\:\:\:\:……………….. \\ $$ Answered by Dwaipayan Shikari last…
Question Number 188552 by normans last updated on 03/Mar/23 Commented by normans last updated on 03/Mar/23 $$\:{use}\:{a}\:{quick}\:{trick}\:{to}\:{solve}\:{the}\:{problem}. \\ $$$$\:{thank}\:{you}..\: \\ $$ Terms of Service Privacy…