Question Number 54240 by 951172235v last updated on 01/Feb/19 Commented by rahul 19 last updated on 01/Feb/19 $${a}=\mathrm{2}\:,\:{b}=\mathrm{3},{c}=\mathrm{8},{d}=\mathrm{2008}. \\ $$ Answered by rahul 19 last…
Question Number 119773 by bemath last updated on 26/Oct/20 $$\underset{−\mathrm{4}} {\overset{\mathrm{4}} {\int}}\:{x}^{\mathrm{3}} \sqrt{\mathrm{16}−{x}^{\mathrm{2}} \:}\:\mathrm{sec}\:{x}\:{dx}\: \\ $$ Answered by MJS_new last updated on 27/Oct/20 $${f}\left({x}\right)={x}^{\mathrm{3}} \sqrt{\mathrm{16}−{x}^{\mathrm{2}}…
Question Number 119762 by mathmax by abdo last updated on 26/Oct/20 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{\mathrm{x}^{\mathrm{4}} \mathrm{dx}}{\left(\mathrm{2x}+\mathrm{1}\right)^{\mathrm{5}} \left(\mathrm{3x}+\mathrm{1}\right)^{\mathrm{8}} } \\ $$ Answered by Olaf last updated on…
Question Number 54224 by rahul 19 last updated on 31/Jan/19 $$\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \frac{\mathrm{sin}{x}+\mathrm{cos}{x}}{\mathrm{16}+\mathrm{9sin2}{x}}\:{dx}\:=? \\ $$ Commented by Meritguide1234 last updated on 01/Feb/19 $$\Rightarrow\int_{\mathrm{0}} ^{\pi/\mathrm{4}} \frac{\mathrm{sinx}+\mathrm{cosx}}{\mathrm{25}−\mathrm{9}\left(\mathrm{sinx}−\mathrm{cosx}\right)^{\mathrm{2}}…
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…