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Category: Integration

e-cos-1-x-dx-

Question Number 65485 by aliesam last updated on 30/Jul/19 $$\int{e}^{{cos}^{−\mathrm{1}} \left({x}\right)} \:{dx} \\ $$ Answered by MJS last updated on 31/Jul/19 $$\int\mathrm{e}^{\mathrm{arccos}\:{x}} {dx}= \\ $$$$\:\:\:\:\:\left[{t}=\mathrm{arccos}\:{x}\:\rightarrow\:{dx}=−\mathrm{sin}\:{t}\:{dt}\right]…

find-U-n-0-1-x-2-x-2-x-2-4n-2-dx-n-from-N-and-n-1-study-nature-of-the-serie-2-n-2-U-n-

Question Number 65455 by mathmax by abdo last updated on 30/Jul/19 $${find}\:{U}_{{n}} =\:\int_{\mathrm{0}} ^{+\infty} \:\:\:\frac{\left(−\mathrm{1}\right)^{{x}} }{\mathrm{2}^{{x}^{\mathrm{2}} } \left({x}^{\mathrm{2}} \:+\mathrm{4}{n}^{\mathrm{2}} \right)}{dx}\:\:\:\:\:\left({n}\:{from}\:{N}\:{and}\:{n}\geqslant\mathrm{1}\right) \\ $$$${study}\:{nature}\:{of}\:{the}\:{serie}\:\:\Sigma\:\mathrm{2}^{{n}^{\mathrm{2}} } {U}_{{n}} \\…

Question-65450

Question Number 65450 by imron876 last updated on 30/Jul/19 Commented by Prithwish sen last updated on 30/Jul/19 $$\left.\mathrm{1}\right)\:\mathrm{a}=\mathrm{b}=\mathrm{c}=\mathrm{d}=\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\mathrm{a}=\mathrm{c}=\mathrm{1},\mathrm{b}=\mathrm{d}=\mathrm{0} \\ $$$$\left.\mathrm{3}\right)\mathrm{b}=\mathrm{d}=\mathrm{1},\mathrm{a}=\mathrm{c}=\mathrm{0} \\ $$$$\left.\mathrm{4}\right)\mathrm{a}=\mathrm{1}\:\mathrm{c}=−\mathrm{1}\:\mathrm{b}=\mathrm{d}=\mathrm{0} \\…

find-f-x-0-pi-4-ln-cost-xsint-dt-

Question Number 65445 by mathmax by abdo last updated on 30/Jul/19 $${find}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {ln}\left({cost}\:+{xsint}\right){dt}\:\:\: \\ $$ Commented by Prithwish sen last updated on 30/Jul/19 $$\mathrm{f}\left(\mathrm{x}\right)\:=\:\frac{\pi−\mathrm{2}\sqrt{\mathrm{2}}}{\mathrm{8}}\:\mathrm{ln}\mid\mathrm{1}+\mathrm{x}^{\mathrm{2}}…

0-log-2-x-sin-x-2-dx-i-had-solved-that-already-and-answ-pi-2-2pi-32-

Question Number 130979 by mnjuly1970 last updated on 31/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\phi\:=\int_{\mathrm{0}} ^{\:\infty} {log}^{\mathrm{2}} \left({x}\right){sin}\left({x}^{\mathrm{2}} \right){dx}=? \\ $$$$\:\:\:\:\:{i}\:{had}\:{solved}\:{that}\:{already}\:\:{and}: \\ $$$$\:\:\:{answ}\:\::\:=\:−\frac{\pi^{\mathrm{2}} \sqrt{\mathrm{2}\pi}\:}{\mathrm{32}} \\ $$$$\:\:\:\:\: \\ $$$$\:\:\:…

0-pi-2-x-sec-x-csc-x-dx-

Question Number 130958 by bramlexs22 last updated on 31/Jan/21 $$\:\int_{\:\mathrm{0}} ^{\:\pi/\mathrm{2}} \:\frac{{x}}{\mathrm{sec}\:{x}+\mathrm{csc}\:{x}}\:{dx} \\ $$ Commented by benjo_mathlover last updated on 31/Jan/21 $$\mathrm{M}\:=\:\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\frac{\mathrm{x}}{\mathrm{sec}\:\mathrm{x}+\mathrm{csc}\:\mathrm{x}}\:\mathrm{dx}\:=\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}}…