Question Number 185880 by cortano1 last updated on 29/Jan/23 $$\:\:\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\:\frac{\sqrt[{\mathrm{3}}]{\mathrm{tan}\:{x}}}{\left(\mathrm{sin}\:{x}+\mathrm{cos}\:{x}\right)^{\mathrm{2}} }\:{dx}=? \\ $$ Commented by MJS_new last updated on 29/Jan/23 $$\mathrm{simply}\:\mathrm{use}\:{t}=\sqrt[{\mathrm{3}}]{\mathrm{tan}\:{x}} \\ $$…
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Question Number 185873 by test1234 last updated on 29/Jan/23 $$\left(\mathrm{1}\right)\:\int\pi{x}^{\mathrm{2}} +\sqrt{\frac{{xe}^{\pi} }{{x}^{\mathrm{2}} }}{dx}=? \\ $$$$\left(\mathrm{2}\right)\:\int\frac{\mathrm{ln}\:\left({x}\right)+\mathrm{ln}\:\left(\frac{−{z}}{{x}}\right)}{{x}^{{z}} }+{z}^{{x}} {dx}=? \\ $$ Answered by JDamian last updated on…
Question Number 54797 by afachri last updated on 11/Feb/19 $$ \\ $$$$ \\ $$$$\:\:\:\int\:\:\sqrt{\:\boldsymbol{{x}}\:+\:\sqrt{\:\boldsymbol{{x}}\:+\:\sqrt{\boldsymbol{{x}}\:+\:\sqrt{\:…..}}}}\:\:\boldsymbol{{dx}}\:\:=\:\:\:? \\ $$$$ \\ $$ Answered by Smail last updated on 11/Feb/19…
Question Number 185863 by normans last updated on 29/Jan/23 Commented by MJS_new last updated on 02/Feb/23 $$\mathrm{do}\:\mathrm{you}\:\mathrm{gain}\:\mathrm{satisfaction}\:\mathrm{by}\:\mathrm{posting} \\ $$$$\mathrm{complicated}\:\mathrm{nonsense}? \\ $$ Answered by MJS_new last…
Question Number 185848 by Mingma last updated on 28/Jan/23 Answered by Frix last updated on 28/Jan/23 $$\int\sqrt{\mathrm{e}^{{x}} +\mathrm{2}}{dx}\:\overset{{t}=\sqrt{\mathrm{e}^{{x}} +\mathrm{2}}} {=}\:\mathrm{2}\int\frac{{t}^{\mathrm{2}} }{{t}^{\mathrm{2}} −\mathrm{2}}{dt}= \\ $$$$=\mathrm{2}\int{dt}+\sqrt{\mathrm{2}}\int\frac{{dt}}{{t}−\sqrt{\mathrm{2}}}−\sqrt{\mathrm{2}}\int\frac{{dt}}{{t}+\sqrt{\mathrm{2}}}= \\…
Question Number 120316 by Bird last updated on 30/Oct/20 $${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{{xcosx}}{{cos}\left(\mathrm{2}{x}\right)}{dx} \\ $$ Answered by mathmax by abdo last updated on 30/Oct/20 $$\mathrm{let}\:\mathrm{I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}}…
Question Number 54777 by maxmathsup by imad last updated on 10/Feb/19 $${let}\:{u}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{sin}\left({nx}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} \:+\mathrm{6}}{dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\:{u}_{{n}} \:\:\:{and}\:{lim}\:{u}_{{n}} \left({n}\rightarrow+\infty\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{nature}\:{of}\:\Sigma\:{u}_{{n}} \:\:\:{and}\:{calaculate}\:{it}. \\…
Question Number 185837 by test1234 last updated on 28/Jan/23 $$\int\frac{{cx}+{b}^{\mathrm{2}} }{\mathrm{2}{x}}−\frac{{cx}+\mathrm{2}{b}^{\mathrm{2}} }{\mathrm{4}{x}}+\frac{\left({cx}\right)^{\mathrm{2}} +\mathrm{4}{b}^{\mathrm{2}} }{\mathrm{8}{x}}{dx}=? \\ $$ Commented by MJS_new last updated on 28/Jan/23 $$\mathrm{seriously}? \\…
Question Number 185836 by greougoury555 last updated on 28/Jan/23 $$\:\left(\mathrm{1}\right)\:\:\:\:\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{{dx}}{\mathrm{2}{x}^{\mathrm{4}} −\mathrm{2}{x}^{\mathrm{2}} +\mathrm{1}}=? \\ $$$$\left(\mathrm{2}\right)\:\underset{\mathrm{0}} {\overset{\infty} {\int}}\:\frac{{x}^{\mathrm{1}/\mathrm{4}} }{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx}=? \\ $$ Answered by Ar…