Question Number 80925 by M±th+et£s last updated on 08/Feb/20 $$\int_{−\infty} ^{\infty} \frac{{cos}\left({x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx}\:=\frac{\pi}{{e}} \\ $$ Commented by mathmax by abdo last updated on 10/Feb/20 $${I}=\int_{−\infty}…
Question Number 80921 by jagoll last updated on 08/Feb/20 $$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\frac{{xdx}}{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}\:=\:? \\ $$ Commented by john santu last updated on 08/Feb/20 $${correction}\: \\ $$$$\underset{\mathrm{0}}…
Question Number 146455 by physicstutes last updated on 13/Jul/21 $$\mathrm{Given}\:\mathrm{that}\:\:{F}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{{x}} \frac{{t}^{\mathrm{2}} }{\:\sqrt{{t}^{\mathrm{2}} +\mathrm{1}}}{dt}\: \\ $$$$\:\mathrm{Show}\:\mathrm{that}\:{F}\left({x}\right)\:\mathrm{is}\:\mathrm{an}\:\mathrm{increasing}\:\mathrm{function} \\ $$ Answered by gsk2684 last updated on 13/Jul/21…
Question Number 80914 by TawaTawa last updated on 07/Feb/20 $$\left(\mathrm{1}\right) \\ $$$$\mathrm{Integrate}\:\:\mathrm{F}\left(\mathrm{x},\:\mathrm{y}\right)\:\:=\:\:\mathrm{x}^{\mathrm{2}} \:\:\:\mathrm{over}\:\mathrm{the}\:\mathrm{region}\:\mathrm{bounded}\:\mathrm{by}\:\:\:\mathrm{y}\:\:=\:\:\mathrm{x}^{\mathrm{2}} , \\ $$$$\mathrm{x}\:\:=\:\:\mathrm{2}\:\:\mathrm{and}\:\mathrm{x}\:\:=\:\:\mathrm{1} \\ $$$$ \\ $$$$\left(\mathrm{2}\right) \\ $$$$\mathrm{Integrate}\:\:\:\:\mathrm{G}\left(\mathrm{x},\:\mathrm{y}\right)\:\:=\:\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \:\:\:\:\mathrm{over}\:\mathrm{the}\:\mathrm{region}\:\mathrm{bounded}\:\mathrm{by}\:\mathrm{the}\: \\…
Question Number 146429 by qaz last updated on 13/Jul/21 $$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\mathrm{n}\centerdot\mathrm{ln}\frac{\mathrm{2n}+\mathrm{1}}{\mathrm{2n}−\mathrm{1}}−\mathrm{1}\right)=? \\ $$ Commented by qaz last updated on 14/Jul/21 $$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\mathrm{n}\centerdot\mathrm{ln}\frac{\mathrm{2n}+\mathrm{1}}{\mathrm{2n}−\mathrm{1}}−\mathrm{1}\right) \\…
Question Number 80882 by mr W last updated on 07/Feb/20 Commented by jagoll last updated on 07/Feb/20 $${in}\:{complex}\:{analysis}? \\ $$ Commented by ajfour last updated…
Question Number 80846 by TawaTawa last updated on 07/Feb/20 Commented by mathmax by abdo last updated on 07/Feb/20 $${we}\:{havw}\:\int_{−\pi} ^{\pi} {costdt}\:=\mathrm{2}\int_{\mathrm{0}} ^{\pi} {cost}\:{dt}\:=\mathrm{2}\left[{sint}\right]_{\mathrm{0}} ^{\pi} =\mathrm{0}…
Question Number 146361 by gsk2684 last updated on 13/Jul/21 $${find}\:\int\frac{\mathrm{1}}{{x}^{{n}} +\mathrm{1}}{dx}\:{for}\:{n}\in{N} \\ $$ Answered by mathmax by abdo last updated on 13/Jul/21 $$\mathrm{z}^{\mathrm{n}} \:+\mathrm{1}=\mathrm{0}\:\Rightarrow\mathrm{z}^{\mathrm{n}} \:=\mathrm{e}^{\left(\mathrm{2k}+\mathrm{1}\right)\mathrm{i}\pi}…
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Question Number 80770 by zainal tanjung last updated on 06/Feb/20 $$\int\mathrm{x}^{\mathrm{2}} +\mathrm{3x}\:\mathrm{dx}=.. \\ $$ Commented by zainal tanjung last updated on 06/Feb/20 $$\mathrm{you}\:\mathrm{are}\:\mathrm{right}.\:\mathrm{good}. \\ $$…