Question Number 139889 by qaz last updated on 02/May/21 $$\int_{\mathrm{0}} ^{\mathrm{4}} \frac{\mathrm{tan}^{−\mathrm{1}} {x}}{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{2}}{dx}=? \\ $$ Commented by qaz last updated on 02/May/21 $${I}=\int_{\mathrm{0}} ^{\mathrm{4}}…
Question Number 74355 by Mr. K last updated on 22/Nov/19 $${let}\:{f}\left({x}\right),\:{g}\left({x}\right)\:{and}\:{h}\left({x}\right)\:{be}\:{functions} \\ $$$$\mathbb{R}\rightarrow\mathbb{R},\:{given}\:{by} \\ $$$${f}\left({x}\right)={x}^{\mathrm{2}} ,\:{if}\:{x}\geqslant\mathrm{0}\:{and}\:{x}+\mathrm{1}\:{if}\:{x}<\mathrm{0} \\ $$$${g}\left({x}\right)={x}^{\mathrm{2}} −\mathrm{4},\:{if}\:{x}\geqslant\mathrm{2}\:{and}\:\frac{\mathrm{1}}{\mathrm{2}−{x}}\:{if}\:{x}<\mathrm{2} \\ $$$${h}\left({x}\right)=\mathrm{3}^{−{x}} ,\:{if}\:{x}\leqslant\mathrm{0}\:{and}\:\mathrm{3}^{{x}} \:{if}\:{x}\geqslant\mathrm{0} \\ $$$${Calculate}\:\frac{{f}\left(\mathrm{2}\right)+{f}\left({g}\left(\mathrm{2}\right)\right)}{{f}\left({g}\left({h}\left(−\mathrm{1}\right)\right)\right)}.…
Question Number 74352 by mathmax by abdo last updated on 22/Nov/19 $${let}\:{U}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:\:\:\frac{\mathrm{1}}{{k}^{\mathrm{2}} +{k}+\mathrm{1}}\:\:{find}\:{a}\:{equivalent}\:{of}\:{U}_{{n}} \:\:\:\left({n}\rightarrow+\infty\right) \\ $$$$ \\ $$ Answered by mind is…
Question Number 74353 by mathmax by abdo last updated on 22/Nov/19 $${let}\:\:{A}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:\:\frac{\mathrm{1}}{{k}+\sqrt{{k}^{\mathrm{2}} +\mathrm{1}}} \\ $$$$\left.\mathrm{1}\right){find}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{a}\:{equivalent}\:{of}\:{A}_{{n}} \:\:{when}\:{n}\rightarrow+\infty \\ $$$$ \\…
Question Number 8816 by javawithstonefish last updated on 29/Oct/16 $${how}\:{can}\:{we}\:{solve} \\ $$$${y}''{f}\left({x}\right)+{y}'{f}_{\mathrm{2}} \left({x}\right)=\mathrm{0} \\ $$$${y}=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 74350 by mathmax by abdo last updated on 22/Nov/19 $${findf}\left({a}\right)=\:\int_{−\infty} ^{+\infty} \:\frac{{arctan}\left({cosx}\right)}{{x}^{\mathrm{2}} +{a}^{\mathrm{2}} }{dx}\:{witha}>\mathrm{0} \\ $$ Commented by abdomathmax last updated on 23/Nov/19…
Question Number 74351 by mathmax by abdo last updated on 22/Nov/19 $${find}\:{the}\:{value}\:{of}\:\:\sum_{{n}=\mathrm{1}} ^{+\infty} \:\:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{\left(\mathrm{4}{n}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{2}} } \\ $$ Commented by ~blr237~ last updated on…
Question Number 74348 by mathmax by abdo last updated on 22/Nov/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{arctan}\left({sin}\left({x}^{\mathrm{2}} \right)\right)}{{x}^{\mathrm{2}} +\mathrm{1}}{dx} \\ $$ Commented by mathmax by abdo last updated…
Question Number 74349 by mathmax by abdo last updated on 22/Nov/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{cos}\left(\mathrm{2}\pi{x}\right)}{\left({x}^{\mathrm{2}} +\mathrm{3}\right)^{\mathrm{2}} }{dx} \\ $$ Commented by abdomathmax last updated on 23/Nov/19…
Question Number 74346 by mathmax by abdo last updated on 22/Nov/19 $${find}\:\int\:\:\frac{{x}+\sqrt{{x}+\mathrm{1}}}{\mathrm{2}\sqrt{{x}−\mathrm{1}}+\mathrm{3}}{dx} \\ $$ Answered by MJS last updated on 24/Nov/19 $$\int\frac{{x}+\sqrt{{x}+\mathrm{1}}}{\mathrm{3}+\mathrm{2}\sqrt{{x}−\mathrm{1}}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\mathrm{2}\sqrt{{x}−\mathrm{1}}\:\rightarrow\:{dx}=\sqrt{{x}−\mathrm{1}}{dt}\right] \\…