Question Number 86472 by Chi Mes Try last updated on 28/Mar/20 Answered by TANMAY PANACEA. last updated on 28/Mar/20 $$\int_{−\mathrm{1}} ^{\mathrm{1}} {xdx}−\int_{−\mathrm{1}} ^{\mathrm{1}} \left[{x}\right]{dx} \\…
Question Number 86447 by Chi Mes Try last updated on 28/Mar/20 Commented by mathmax by abdo last updated on 29/Mar/20 $${let}\:{f}\left({t}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left({t}\sqrt{{x}^{\mathrm{2}} +{a}^{\mathrm{2}} }\right)}{\left(\mathrm{1}+{x}^{\mathrm{2}}…
Question Number 20908 by j.masanja06@gmail.com last updated on 07/Sep/17 $${integrate}\:{with}\:{respect}\:{to}\:{x}\: \\ $$$$\int\left(\frac{\mathrm{2}{x}+\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{8}}\right){dx} \\ $$ Answered by Joel577 last updated on 07/Sep/17 $${I}\:=\:\int\:\frac{\mathrm{2}{x}\:+\:\mathrm{1}}{\left({x}\:+\:\mathrm{2}\right)^{\mathrm{2}} \:+\:\mathrm{4}}\:{dx} \\…
Question Number 151983 by puissant last updated on 24/Aug/21 $$\int_{−\infty} ^{+\infty} \left(\frac{\mathrm{1}−{ix}}{\mathrm{1}+{ix}}\right)^{{n}} \left(\frac{\mathrm{1}+{ix}}{\mathrm{1}−{ix}}\right)^{{m}} \frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$ Answered by Olaf_Thorendsen last updated on 24/Aug/21 $$\mathrm{I}\:=\:\int_{−\infty}…
Question Number 20905 by NECx last updated on 07/Sep/17 $$\int{e}^{{x}^{\mathrm{2}} } {dx} \\ $$ Commented by NECx last updated on 07/Sep/17 $${please}\:{help} \\ $$ Answered…
Question Number 86431 by M±th+et£s last updated on 28/Mar/20 $$\int\sqrt{{x}−\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}\:}\:{dx} \\ $$ Answered by jagoll last updated on 28/Mar/20 $$\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\:=\:\mathrm{x}−\mathrm{t}\: \\ $$$$\mathrm{x}^{\mathrm{2}} +\mathrm{1}\:=\:\mathrm{x}^{\mathrm{2}}…
Question Number 86428 by jagoll last updated on 28/Mar/20 $$\int\:\:\frac{\mathrm{dx}}{\mathrm{a}\:\mathrm{cos}\:\mathrm{x}\:+\:\mathrm{b}\:\mathrm{sin}\:\mathrm{x}}? \\ $$ Commented by jagoll last updated on 28/Mar/20 $$\mathrm{standard}\:\mathrm{solving} \\ $$$$\mathrm{a}\:\mathrm{cos}\:\mathrm{x}\:+\:\mathrm{b}\:\mathrm{sin}\:\mathrm{x}\:=\:\mathrm{k}\:\mathrm{cos}\:\left(\mathrm{x}−\theta\right) \\ $$$$\int\:\frac{\mathrm{dx}}{\mathrm{k}\:\mathrm{cos}\:\left(\mathrm{x}−\theta\right)}\:=\:\frac{\mathrm{1}}{\mathrm{k}}\int\:\mathrm{sec}\:\left(\mathrm{x}−\theta\right)\:\mathrm{dx} \\…
Question Number 151958 by mnjuly1970 last updated on 24/Aug/21 $${f}\:\left(\:{x}\:\right)\:=\:{a}\:−\sqrt{\frac{{x}}{\mathrm{1}+{x}}\:}\:\:\:,\:{D}_{\:{f}} \::\:\left[\:\mathrm{0},\:\infty\right) \\ $$$$,\:{a}\geqslant\:\mathrm{1}\:\:\:,\:\:{h}\:\left({x}\:\right):=\sqrt{\frac{\:{f}^{\:−\mathrm{1}} \left({a}−{ax}\:\right)}{{f}^{\:−\mathrm{1}} \left(\:{a}−\:\mathrm{2}{x}\:\right)}} \\ $$$$\:\:\:\:\:\:\:\:\:\:{D}_{\:{h}} \:=\:?\:\:\:\left(\:\:\:{D}\::=\:{Domain}\:\right) \\ $$$$\:\:\:\:\:\:\:\:\:\: \\ $$ Terms of Service…
Question Number 151951 by mnjuly1970 last updated on 24/Aug/21 $$ \\ $$$$\:\:\:\:\:{nice}\:…\:{mathematics} \\ $$$$\:\:\:\:\:\:\mathrm{S}:=\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:\zeta\:\left(\mathrm{2}{n}\:\right)}{{n}\:.\:\mathrm{16}^{\:{n}} }\:=\:?\:……\blacksquare \\ $$$$ \\ $$ Commented by Tawa11 last…
Question Number 20873 by Joel577 last updated on 05/Sep/17 $$\int_{\mathrm{1}} ^{\mathrm{5}} \frac{{e}^{{x}} }{{x}^{\mathrm{2}} }\:{dx} \\ $$ Answered by alex041103 last updated on 08/Sep/17 $${First}\:{we}\:{apply}\:{integration}\:{by}\:{parts} \\…