Question Number 166723 by cortano1 last updated on 26/Feb/22 $$\:\:\:\int\:\frac{\sqrt[{\mathrm{5}}]{\mathrm{x}}\:−\mathrm{1}}{\:\sqrt{\mathrm{x}}\:+\:\mathrm{1}}\:\mathrm{dx}=? \\ $$ Answered by MJS_new last updated on 26/Feb/22 $$\int\frac{{x}^{\mathrm{1}/\mathrm{5}} −\mathrm{1}}{{x}^{\mathrm{1}/\mathrm{2}} +\mathrm{1}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}={x}^{\mathrm{1}/\mathrm{10}} \:\rightarrow\:{dx}=\mathrm{10}{t}^{\mathrm{9}}…
Question Number 101178 by bemath last updated on 01/Jul/20 $$\int\:\frac{\left(\sqrt{\mathrm{x}}−\mathrm{x}\right)^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} }\:\mathrm{dx}\:? \\ $$ Answered by bobhans last updated on 01/Jul/20 $$\int\:\frac{{x}−\mathrm{2}{x}^{\frac{\mathrm{3}}{\mathrm{2}}} +{x}^{\mathrm{2}} }{{x}^{\mathrm{2}} }\:{dx}\:=\:\int\frac{\mathrm{1}}{{x}}−\frac{\mathrm{2}}{\:\sqrt{{x}}}\:+\mathrm{1}\:{dx}…
Question Number 35635 by ajfour last updated on 21/May/18 Commented by ajfour last updated on 21/May/18 $${Find}\:{the}\:{volume}\:{common}\:{to}\:{the} \\ $$$${two}\:{spheres}. \\ $$ Answered by ajfour last…
Question Number 35632 by abdo mathsup 649 cc last updated on 21/May/18 $${let}\:\varphi\left({x}\right)=\:\frac{\mathrm{1}}{\:\sqrt{{a}^{\mathrm{2}} −{x}^{\mathrm{2}} }}\:\:{if}\:\mid{x}\mid<{a}\:\:{and}\:\varphi\left({x}\right)=\mathrm{0}\:{if}\:\mid{x}\mid\geqslant{a} \\ $$$${find}\:{the}\:{fourier}\:{transform}\:{of}\:\varphi\:. \\ $$ Commented by abdo mathsup 649 cc…
Question Number 166707 by amin96 last updated on 25/Feb/22 $$\frac{\mathrm{8}}{\mathrm{1}×\mathrm{5}×\mathrm{9}}+\frac{\mathrm{8}}{\mathrm{5}×\mathrm{9}×\mathrm{13}}+\frac{\mathrm{8}}{\mathrm{9}×\mathrm{13}×\mathrm{17}}+\ldots+\frac{\mathrm{1}}{\mathrm{41}×\mathrm{45}×\mathrm{49}}=? \\ $$$$ \\ $$$$ \\ $$$$\boldsymbol{{by}}\:\boldsymbol{{M}}.\boldsymbol{{A}} \\ $$ Answered by mahdipoor last updated on 25/Feb/22…
Question Number 35631 by abdo mathsup 649 cc last updated on 21/May/18 $${let}\:{U}_{{n}} =\:\int_{\mathrm{0}} ^{\infty} \:\:\:{e}^{−\frac{{t}}{{n}}} \:\:{arctan}\left({t}\right){dt} \\ $$$${find}\:{a}\:{equivalent}\:{of}\:{U}_{{n}} \:\:\left({n}\rightarrow+\infty\right) \\ $$ Terms of Service…
Question Number 166702 by metamorfose last updated on 25/Feb/22 $$\int{e}^{{x}} {ln}\left({x}\right){dx}=..??? \\ $$ Commented by mkam last updated on 25/Feb/22 $${u}\:=\:{lnx}\:\rightarrow\:{du}\:=\:\frac{{dx}}{{x}}\:\:,\:{dv}\:=\:{e}^{{x}} \:\Rightarrow\:{v}\:=\:{e}^{{x}} \\ $$$$ \\…
Question Number 35629 by abdo mathsup 649 cc last updated on 21/May/18 $${let}\:\:{f}\left({x},{y}\right)\:=\:\int_{{x}} ^{{y}} \:\:\frac{{ln}\left({t}\right){ln}\left(\mathrm{1}−{t}\right)}{{t}}{dt}\:\:{with}\:\mathrm{0}<{x}<{y}<\mathrm{1} \\ $$$${give}\:{f}\left({x},{y}\right)\:{at}\:{form}\:{of}\:{serie}\:. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 35630 by abdo mathsup 649 cc last updated on 21/May/18 $$\left.\mathrm{1}\right)\:{find}\:{the}\:{value}\:{of}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{1}−{cos}\left({xt}\right)}{{t}^{\mathrm{2}} }\:{e}^{−{t}} {dt} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{\mathrm{1}−{cos}\left({t}\right)}{{t}^{\mathrm{2}} }\:{e}^{−{t}} \:{dt}\:. \\ $$…
Question Number 35628 by abdo mathsup 649 cc last updated on 21/May/18 $${find}\:{the}\:{value}\:{of}\:\:{I}\:\:=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{ln}\left({t}\right){ln}\left(\mathrm{1}−{t}\right)}{{t}}{dt} \\ $$ Commented by abdo mathsup 649 cc last updated…