Question Number 119752 by Bird last updated on 26/Oct/20 $${find}\:{I}_{\lambda} =\int_{\mathrm{0}} ^{\infty} \:\:\frac{{ch}\left(\mathrm{1}+\lambda{cosx}\right)}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$$$\left(\lambda\:{real}\:>\mathrm{0}\right) \\ $$ Answered by mathmax by abdo last…
Question Number 185284 by Mingma last updated on 19/Jan/23 Answered by MJS_new last updated on 20/Jan/23 $$\mathrm{one}\:\mathrm{method}: \\ $$$$\int\frac{\mathrm{sin}\:{x}\:\mathrm{cos}\:{x}}{\mathrm{sin}^{\mathrm{3}} \:{x}\:+\mathrm{cos}^{\mathrm{3}} \:{x}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\mathrm{cos}\:\left({x}+\frac{\pi}{\mathrm{4}}\right)\:\rightarrow\:{dx}=−\frac{{dt}}{\mathrm{sin}\:\left({x}+\frac{\pi}{\mathrm{4}}\right)}\right] \\ $$$$=−\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}\int\frac{\mathrm{2}{t}^{\mathrm{2}}…
Question Number 119750 by 675480065 last updated on 26/Oct/20 $$\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{1019}} {\prod}}\left[\frac{\mathrm{2k}}{\mathrm{2k}−\mathrm{1}}\right]=? \\ $$ Answered by Bird last updated on 26/Oct/20 $$\prod_{{k}=\mathrm{1}} ^{\mathrm{1019}} \left[\frac{\mathrm{2}{k}}{\mathrm{2}{k}−\mathrm{1}}\right]\:=\prod_{{k}=\mathrm{1}} ^{\mathrm{1019}}…
Question Number 54209 by cesar.marval.larez@gmail.com last updated on 31/Jan/19 Answered by Joel578 last updated on 31/Jan/19 $${I}\:=\:\int\:\frac{\mathrm{tan}^{−\mathrm{1}} {x}}{\mathrm{1}\:+\:{x}^{\mathrm{2}} }\:{dx} \\ $$$${u}\:=\:\mathrm{tan}^{−\mathrm{1}} \:{x}\:\:\:\rightarrow\:{du}\:=\:\frac{{dx}}{\mathrm{1}\:+\:{x}^{\mathrm{2}} } \\ $$$${dv}\:=\:\frac{{dx}}{\mathrm{1}\:+\:{x}^{\mathrm{2}}…
Question Number 119696 by bemath last updated on 26/Oct/20 $${For}\:{a}<{b}\:{then}\:\underset{{a}} {\overset{{b}} {\int}}\:\left({x}−{a}\right)\left({x}−{b}\right)\:{dx}\: \\ $$$${equal}\:{to}\:\_ \\ $$ Answered by TANMAY PANACEA last updated on 26/Oct/20 $$\int_{{a}}…
Question Number 119681 by TANMAY PANACEA last updated on 26/Oct/20 $$\int_{\mathrm{0}} ^{\pi} \sqrt{\frac{\mathrm{1}+{cos}\mathrm{2}{x}}{\mathrm{2}}}\:{dx} \\ $$$$\int_{\mathrm{0}} ^{\infty} \left[{ne}^{−{x}} \right]{dx} \\ $$ Answered by bemath last updated…
Question Number 54102 by gunawan last updated on 29/Jan/19 $$\mathrm{the}\:\mathrm{absolute}\:\mathrm{value} \\ $$$$\int_{\mathrm{10}} ^{\mathrm{19}} \frac{\mathrm{cos}\:{x}}{\mathrm{1}+{x}^{\mathrm{8}} }\:{dx}\:\mathrm{is}… \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 29/Jan/19 $${from}\:{enclosed}\:{graph}\:{below}\:{it}\:{is}\:{clear}\:{that}…
Question Number 54074 by rahul 19 last updated on 28/Jan/19 $${Evaluate}\:: \\ $$$$\left.\mathrm{1}\right)\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{dx}}{\:\sqrt{\mathrm{1}+{x}}+\sqrt{\mathrm{1}−{x}}+\mathrm{2}}\: \\ $$$$ \\ $$$$\left.\mathrm{2}\right)\:\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{2}} \frac{{ln}\left(\mathrm{1}+\mathrm{2}{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right) \\…
Question Number 54070 by rahul 19 last updated on 28/Jan/19 $${Evaluate}\:: \\ $$$$\left.\mathrm{1}\right) \\ $$$$\:\int_{−\mathrm{1}} ^{\:\mathrm{1}} \mathrm{cot}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}\right).\left(\mathrm{co}{t}^{−\mathrm{1}} \frac{{x}}{\:\sqrt{\mathrm{1}−\left({x}^{\mathrm{2}} \right)^{\mid{x}\mid} }}\right){dx} \\ $$$$\left.\mathrm{2}\right) \\…
Question Number 54073 by cesar.marval.larez@gmail.com last updated on 28/Jan/19 Answered by estudiante last updated on 28/Jan/19 $${Vemos}\:{q}\:{es}\:{una}\:{integral}\:{impropia}\:{de}\:{tipo}\:{I}: \\ $$$$\underset{{R}\rightarrow\infty} {\mathrm{lim}}\:\int_{{a}} ^{{R}} {x}^{{n}} {dx}\:=\:\underset{{R}\rightarrow\infty} {\mathrm{lim}}\:\mid\frac{{x}^{{n}+\mathrm{1}} }{{n}+\mathrm{1}}\mid_{{a}}…