Question Number 126179 by mathmax by abdo last updated on 17/Dec/20 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)=\:\mathrm{e}^{−\mathrm{2x}} \:\mathrm{actan}\:\left(\mathrm{3x}+\mathrm{1}\right) \\ $$$$\left.\mathrm{1}\right)\mathrm{calculste}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{x}\right)\:\mathrm{and}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:\mathrm{if}\:\mathrm{f}\left(\mathrm{x}\right)=\Sigma\:\mathrm{a}_{\mathrm{n}} \mathrm{x}^{\mathrm{n}} \:\mathrm{determine}\:\mathrm{the}\:\mathrm{sequence}\:\mathrm{a}_{\mathrm{n}} \\ $$$$\left.\mathrm{3}\right)\:\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}…
Question Number 60637 by rajesh4661kumar@gamil.com last updated on 23/May/19 Commented by maxmathsup by imad last updated on 23/May/19 $$\int\:\:\:\:\frac{{sinx}}{\mathrm{1}−{sinx}}\:{dx}\:=−\int\frac{\mathrm{1}−{sinx}\:−\mathrm{1}}{\mathrm{1}−{sinx}}{dx}\:=−{x}\:+\int\:\:\frac{{dx}}{\mathrm{1}−{sinx}} \\ $$$$\int\:\:\frac{{dx}}{\mathrm{1}−{sinx}}\:=_{{tan}\left(\frac{{x}}{\mathrm{2}}\right)={t}} \:\:\:\:\:\:\int\:\:\frac{\mathrm{1}}{\mathrm{1}−\frac{\mathrm{2}{t}}{\mathrm{1}+{t}^{\mathrm{2}} }}\:\frac{\mathrm{2}{dt}}{\mathrm{1}+{t}^{\mathrm{2}} }\:=\mathrm{2}\:\int\:\:\:\frac{{dt}}{\mathrm{1}+{t}^{\mathrm{2}} −\mathrm{2}{t}}\:=\mathrm{2}\:\int\:\:\frac{{dt}}{\left({t}−\mathrm{1}\right)^{\mathrm{2}}…
Question Number 60631 by aliesam last updated on 23/May/19 $$\mathrm{prove}\:\mathrm{that}\underset{−\infty} {\overset{\infty} {\int}}\mathrm{x}^{\mathrm{5}} \mathrm{e}^{−\mathrm{x}^{\mathrm{2}} } \mathrm{sin}\left(\mathrm{x}^{\mathrm{3}} \right)\:\mathrm{dx}=\mathrm{0}.\mathrm{25474} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 60621 by fjdjdcjv last updated on 22/May/19 $${if}\:\pi\:{is}\:{rational}\:{then}\:{there} \\ $$$${exists}\:{a}\:{I}_{{n}} =\frac{{v}^{\mathrm{2}{n}} }{{n}!}\underset{\mathrm{0}} {\overset{\pi} {\int}}{x}^{{n}} \left({x}−\pi\right)^{{n}} {sin}\left({x}\right){dx} \\ $$$${can}\:{someone}\:{give}\:{a}\:{easier}\:{way}\:{to}\:{expaned}\:{this} \\ $$ Commented by MJS…
Question Number 60623 by yeshuaisrael1000@gmail.com last updated on 20/Oct/19 $$\mathrm{W}{hat}\:{are}\:{all}\:{intregal}\:{methods}\:{that}\:{exist} \\ $$$${like}\:{trigonometry}\:{sub}.\:{Gaussian}\:{method}\:{feyman}\:{method}\:? \\ $$$$ \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 126139 by mnjuly1970 last updated on 17/Dec/20 $$\:\:\:\:\:\:\: \\ $$$$\:\:{closed}\:\:{formula}\:…. \\ $$$$\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{x}^{{n}} {ln}\left({x}\right)}{\mathrm{1}+{x}}{dx}\:=? \\ $$$$\:\:\: \\ $$ Commented by Dwaipayan Shikari…
Question Number 126133 by I want to learn more last updated on 17/Dec/20 Answered by Dwaipayan Shikari last updated on 17/Dec/20 $$\int_{−\mathrm{2}} ^{\mathrm{2}} \left({x}^{\mathrm{3}} {cos}\frac{{x}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}}\right)\sqrt{\mathrm{4}−{x}^{\mathrm{2}}…
Question Number 60595 by maxmathsup by imad last updated on 22/May/19 $${let}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{ln}^{\mathrm{2}} \left({x}\right)}{\left(\mathrm{1}−{ax}\right)^{\mathrm{2}} }\:{dx}\:\:{with}\:\mid{a}\mid<\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{A}\left(\theta\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{ln}^{\mathrm{2}} \left({x}\right)}{\left(\mathrm{1}−\left({cos}\theta\right){x}\right)^{\mathrm{2}} }{dx}\:\:{with}\:\mathrm{0}<\theta<\frac{\pi}{\mathrm{2}} \\…
Question Number 60586 by Mr X pcx last updated on 22/May/19 $${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{ln}^{\mathrm{2}} \left({x}\right)}{\left(\mathrm{1}−{x}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx} \\ $$ Commented by maxmathsup by imad last…
Question Number 126073 by benjo_mathlover last updated on 17/Dec/20 Commented by benjo_mathlover last updated on 17/Dec/20 $${The}\:{graph}\:{of}\:{the}\:{differentiable}\: \\ $$$${function}\:{g}\:{with}\:{domain}\:−\mathrm{6}\leqslant{x}\leqslant\mathrm{2}\:{is} \\ $$$${shown}\:{in}\:{the}\:{figure}\:{above}.\:{The}\:{areas} \\ $$$${of}\:{the}\:{regions}\:{bounded}\:{by}\:{the}\:{x}−{axis} \\ $$$${and}\:{the}\:{graph}\:{of}\:{g}\:{on}\:{the}\:{intervals}\:\left[−\mathrm{6},−\mathrm{5}\right]…