Question Number 186840 by cortano12 last updated on 11/Feb/23 $$\:\:\underset{\mathrm{9}} {\overset{\:\mathrm{16}} {\int}}\:\frac{\sqrt{\mathrm{4}−\sqrt{{x}}}}{{x}}\:{dx}\:=? \\ $$ Answered by horsebrand11 last updated on 11/Feb/23 $$\:\:{I}=\underset{\mathrm{9}} {\overset{\:\mathrm{16}} {\int}}\:\frac{\sqrt{\mathrm{4}−\sqrt{{x}}}}{{x}}\:{dx}\:=? \\…
Question Number 121300 by liberty last updated on 06/Nov/20 $$\:\:\int\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{3}} +\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}}\:? \\ $$ Commented by liberty last updated on 06/Nov/20 Answered by TANMAY PANACEA…
Question Number 55759 by maxmathsup by imad last updated on 03/Mar/19 $${calculate}\:{I}\:=\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{cost}}{\mathrm{3}\:+{sin}\left(\mathrm{2}{t}\right)}{dt}\:{and}\:{J}\:=\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{sint}}{\mathrm{3}\:+{cos}\left(\mathrm{2}{t}\right)}{dt}\:. \\ $$ Answered by MJS last updated on 04/Mar/19…
Question Number 55760 by maxmathsup by imad last updated on 03/Mar/19 $${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{cos}\left({xt}\right)}{\left({xt}^{\mathrm{2}} +{i}\right)^{\mathrm{2}} }{dx}\:\:\:{with}\:{x}\:{from}\:{R}\:\:{and}\:{x}\neq\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{extract}\:\:{A}\:={Re}\left({f}\left({x}\right)\right)\:{and}\:\:{B}\:={Im}\left({f}\left({x}\right)\right)\:{and}\:{find}\:{its}\:{values}\:. \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{cos}\left(\mathrm{2}{t}\right)}{\left(\mathrm{2}{t}^{\mathrm{2}} \:+{i}\right)^{\mathrm{2}}…
Question Number 186800 by universe last updated on 10/Feb/23 $$\boldsymbol{\mathrm{show}}\:\boldsymbol{\mathrm{that}} \\ $$$$\int_{\mathrm{0}} ^{\:\infty\:} \frac{\boldsymbol{\mathrm{tan}}^{−\mathrm{1}} \boldsymbol{\alpha{x}}\:\boldsymbol{\mathrm{tan}}^{−\mathrm{1}} \boldsymbol{\beta{x}}}{\boldsymbol{{x}}^{\mathrm{2}} }\boldsymbol{{dx}}\:=\:\frac{\boldsymbol{\pi}}{\mathrm{2}}\mathrm{log}\left\{\frac{\left(\boldsymbol{\alpha}+\boldsymbol{\beta}\right)^{\boldsymbol{\alpha}+\boldsymbol{\beta}} }{\boldsymbol{\alpha}^{\boldsymbol{\alpha}} \boldsymbol{\beta}^{\boldsymbol{\beta}} }\right\}\: \\ $$ Terms of Service…
Question Number 186780 by normans last updated on 10/Feb/23 $$ \\ $$$$\:\:\:\:\:\:\:\int\:\:\:\frac{\mathrm{1}\:+\:\boldsymbol{{sin}}\:\boldsymbol{{x}}\:+\:\boldsymbol{{cos}}\:\boldsymbol{{x}}}{\mathrm{1}\:+\:\boldsymbol{{sin}}\:\boldsymbol{{x}}}\:\:\boldsymbol{{dx}}\:\: \\ $$$$ \\ $$ Answered by Ar Brandon last updated on 10/Feb/23 $${I}=\int\frac{\mathrm{1}+\mathrm{sin}{x}+\mathrm{cos}{x}}{\mathrm{1}+\mathrm{sin}{x}}{dx}…
Question Number 55702 by ajfour last updated on 02/Mar/19 $${s}=\int_{\mathrm{0}} ^{\:{x}} \sqrt{\mathrm{1}+\left(\mathrm{3}{t}^{\mathrm{2}} +{p}\right)^{\mathrm{2}} }{dt}\:\:=\:? \\ $$$$\:\:\:\:{take}\:{p}=\mathrm{1}\:\:{for}\:{a}\:{special}\:{case}. \\ $$ Commented by rahul 19 last updated on…
Question Number 186771 by mnjuly1970 last updated on 10/Feb/23 $$ \\ $$$$\:\:\:\:\mathrm{Q}\::\:\:\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{integral}.\:\:\:\:\:\:\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{I}\:=\:\int_{\mathrm{0}} ^{\:\frac{\:\pi}{\:\mathrm{2}}} \:\frac{\:\:\mathrm{1}}{\:\mathrm{1}\:+\:\mathrm{sin}^{\:\mathrm{4}} \:\left(\:{x}\:\right)\:+\:\mathrm{cos}^{\:\mathrm{4}} \:\left(\:{x}\:\right)\:}\:\mathrm{d}{x}\:=\:\:?\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$ Answered…
Question Number 121224 by liberty last updated on 06/Nov/20 $$\:\:\:\:\int\:\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}\:\mathrm{tan}\:^{\mathrm{3}} \mathrm{x}\:\mathrm{dx}\: \\ $$ Answered by benjo_mathlover last updated on 06/Nov/20 $$\:\int\:\frac{\mathrm{sin}\:^{\mathrm{3}} \mathrm{x}}{\mathrm{cos}\:\mathrm{x}}\:\mathrm{dx}\:=\:−\int\:\frac{\left(\mathrm{1}−\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}\right)\:\mathrm{d}\left(\mathrm{cos}\:\mathrm{x}\right)}{\mathrm{cos}\:\mathrm{x}} \\…
Question Number 121225 by benjo_mathlover last updated on 06/Nov/20 $$\:\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\mathrm{x}^{\mathrm{5}} \:\sqrt{\frac{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }}\:\mathrm{dx}\:? \\ $$ Answered by liberty last updated on 06/Nov/20 $$\:\mathrm{let}\:\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}}…