Question Number 35676 by abdo imad last updated on 21/May/18 $${find}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{{x}} \:{ch}^{\mathrm{4}} {t}\:{dt} \\ $$ Commented by abdo mathsup 649 cc last updated on…
Question Number 35677 by abdo imad last updated on 21/May/18 $${find}\:{F}\left({x}\right)=\int_{\mathrm{0}} ^{{x}} \:{e}^{−\mathrm{2}{t}} {cos}\left({t}+\frac{\pi}{\mathrm{4}}\right){dx}. \\ $$ Commented by prof Abdo imad last updated on 23/May/18…
Question Number 35675 by abdo imad last updated on 21/May/18 $${calculate}\:\:\int_{\mathrm{1}} ^{\mathrm{3}} \:\:\:\frac{{x}}{{e}^{{x}} \:−\mathrm{1}}{dx}\:.. \\ $$ Commented by prof Abdo imad last updated on 25/May/18…
Question Number 166725 by cortano1 last updated on 26/Feb/22 $$\:\:\:\int\:\frac{\mathrm{dx}}{\mathrm{3}+\mathrm{tan}\:\mathrm{x}}=? \\ $$ Commented by MJS_new last updated on 26/Feb/22 $$\int\frac{{dx}}{\mathrm{3}+\mathrm{tan}\:{x}}= \\ $$$$\:\:\:\:\:\left[{t}=\mathrm{tan}\:{x}\:\rightarrow\:{dx}=\frac{{dt}}{{t}^{\mathrm{2}} +\mathrm{1}}\right]= \\ $$$$=\int\frac{{dt}}{\left({t}+\mathrm{3}\right)\left({t}^{\mathrm{2}}…
Question Number 101192 by bemath last updated on 01/Jul/20 $$\int\:\frac{{x}}{\mathrm{1}+\mathrm{sin}\:{x}}\:{dx}\: \\ $$ Commented by bobhans last updated on 01/Jul/20 $$\mathrm{set}\:{z}\:=\:\frac{\pi}{\mathrm{2}}−{x}\:\Rightarrow\:{dx}\:=\:−{dz} \\ $$$${I}=\int\:\frac{\frac{\pi}{\mathrm{2}}−{z}}{\mathrm{1}+\mathrm{sin}\:\left(\frac{\pi}{\mathrm{2}}−{z}\right)}\:\left(−{dz}\right)\:=\:\int\:\frac{{z}−\frac{\pi}{\mathrm{2}}}{\mathrm{1}+\mathrm{cos}\:{z}}\:{dz} \\ $$$$=\:\int\:\left(\mathrm{z}−\frac{\pi}{\mathrm{2}}\right)\:\mathrm{d}\left(\mathrm{tan}\:\left(\frac{\mathrm{z}}{\mathrm{2}}\right)\right)\:=\:\left(\mathrm{z}−\frac{\pi}{\mathrm{2}}\right)\mathrm{tan}\:\left(\frac{\mathrm{z}}{\mathrm{2}}\right)+\mathrm{2}\:\mathrm{ln}\left(\mathrm{cos}\:\left(\frac{\mathrm{z}}{\mathrm{2}}\right)\right)\:+\:\mathrm{c} \\…
Question Number 166723 by cortano1 last updated on 26/Feb/22 $$\:\:\:\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…