Question Number 64418 by turbo msup by abdo last updated on 17/Jul/19 $$\left.\mathrm{1}\right){find}\:\int\:\:\:\frac{{dx}}{{x}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{dx}}{{x}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }} \\ $$ Commented by Prithwish sen…
Question Number 129946 by bemath last updated on 21/Jan/21 $$\:\int\:\frac{\mathrm{tan}\:\varphi+\mathrm{3}}{\mathrm{sin}\:\varphi}\:\mathrm{d}\varphi\:? \\ $$ Answered by liberty last updated on 21/Jan/21 $$\:\mathrm{T}\:=\:\int\:\left(\frac{\mathrm{1}}{\mathrm{cos}\:\varphi}\:+\:\frac{\mathrm{3}}{\mathrm{sin}\:\varphi}\right)\mathrm{d}\varphi \\ $$$$\:\mathrm{T}=\:\int\:\left(\mathrm{sec}\:\varphi+\mathrm{3csc}\:\varphi\right)\:\mathrm{d}\varphi\: \\ $$$$\:\mathrm{T}\:=\:\mathrm{ln}\:\mid\mathrm{sec}\:\varphi+\mathrm{tan}\:\varphi\mid−\mathrm{3ln}\:\mid\mathrm{cot}\:\varphi+\mathrm{csc}\:\varphi\mid\:+\:\mathrm{c} \\…
Question Number 64410 by mmkkmm000m last updated on 17/Jul/19 $$\int\mathrm{1}/\left(\mathrm{1}+{ysin}\theta\right){d}\theta \\ $$ Commented by mr W last updated on 17/Jul/19 $${see}\:{Q}\mathrm{64238}\:{sir}! \\ $$ Commented by…
Question Number 129936 by liberty last updated on 21/Jan/21 $$\:\mathrm{Nice}\:\mathrm{integral}\: \\ $$$$ \\ $$$$\:\:\int_{\mathrm{0}} ^{\:\infty} \:\mathrm{sin}\:\left({x}\right)\:\mathrm{ln}\:\left({x}\right)\:\mathrm{e}^{−{x}} \:{dx}\: \\ $$ Answered by Lordose last updated on…
Question Number 129926 by mnjuly1970 last updated on 20/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:\:{calculus}… \\ $$$$\:\:{evaluate}: \\ $$$$\:\:\:\underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\:\underset{{m}=\mathrm{0}} {\overset{\infty} {\sum}}\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{1}}{\left({k}+{m}+{n}\right)!}\right)=? \\ $$$$ \\ $$ Answered…
Question Number 64392 by mathmax by abdo last updated on 17/Jul/19 $$\left.\mathrm{1}\right){calculate}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\frac{{sin}\left({x}^{\mathrm{2}{n}} \right)}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{2}} }{dx}\:\:\:{with}\:{n}\:{integr}\:{natural} \\ $$$$\left.\mathrm{2}\right)\:{study}\:{the}\:{convergene}\:{of}\:\Sigma\:{A}_{{n}} \\ $$ Commented by mathmax…
Question Number 64390 by mathmax by abdo last updated on 17/Jul/19 $${calculate}\:\int_{\mathrm{1}} ^{+\infty} \:\:\frac{{dx}}{{x}\sqrt{\mathrm{4}+{x}^{\mathrm{2}} }} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 129921 by stelor last updated on 20/Jan/21 $$\int\frac{\mathrm{1}}{\left(\mathrm{1}−\mathrm{u}^{\mathrm{2}} \right)^{\mathrm{2}} \mathrm{u}^{\mathrm{5}} }\mathrm{du}=?? \\ $$$$\mathrm{please}… \\ $$ Answered by Ar Brandon last updated on 20/Jan/21…
Question Number 64382 by Chi Mes Try last updated on 17/Jul/19 $${please}\:\:{help}\:{with}\:{workings} \\ $$$$ \\ $$$$\int{Ln}\left[\sqrt{}\left(\mathrm{1}−{x}\right)+\sqrt{}\left(\mathrm{1}+{x}\right)\right]{dx} \\ $$ Answered by MJS last updated on 17/Jul/19…
Question Number 129907 by pticantor last updated on 20/Jan/21 $$\int\frac{\boldsymbol{{dx}}}{\boldsymbol{{sin}}^{\mathrm{3}} \boldsymbol{{xcos}}^{\mathrm{5}} \boldsymbol{{x}}}=??????? \\ $$ Answered by Ar Brandon last updated on 20/Jan/21 $$\mathcal{I}=\int\frac{\mathrm{dx}}{\mathrm{sin}^{\mathrm{3}} \mathrm{xcos}^{\mathrm{5}} \mathrm{x}}=\int\frac{\mathrm{cos}^{\mathrm{2}}…