Question Number 42188 by maxmathsup by imad last updated on 19/Aug/18 $${let}\:{x}>\mathrm{0}\:\:\:{calculate}\:\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{+\infty} \:\:{e}^{−{t}} \:\mid{sin}\left({xt}\right)\mid\:{dt} \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 42189 by maxmathsup by imad last updated on 19/Aug/18 $${calculate}\:\:{f}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−{t}^{\mathrm{2}} } \:{arctan}\left({xt}^{\mathrm{2}} \right){dt} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 107706 by bemath last updated on 12/Aug/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\checkmark\mathcal{B}{e}\mathcal{M}{ath}\checkmark \\ $$$$\:\left(\mathrm{1}\right)\:\:\:\:\:\:\:\:\:\:\:\underset{\mathrm{0}} {\overset{\infty} {\int}}\:\frac{\sqrt{{x}}}{\mathrm{1}+{x}^{\mathrm{3}} }\:{dx}\:? \\ $$$$\:\:\left(\mathrm{2}\right)\:\:\:\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left(\pi\:\mathrm{cos}\:^{\mathrm{2}} {x}\right)}{{x}^{\mathrm{2}} }\: \\ $$$$\left(\mathrm{3}\right)\:{If}\:{g}\left({x}\right)=\:\mathrm{1}+\sqrt{{x}}\:{and}\:\left({g}\circ{f}\right)\left({x}\right)=\mathrm{3}+\mathrm{2}\sqrt{{x}}\:+{x} \\ $$$$\:\:\:{find}\:{f}\left({x}\right) \\…
Question Number 107695 by bemath last updated on 12/Aug/20 $$\:\:\:\spadesuit\mathcal{B}{e}\mathcal{M}{ath}\spadesuit \\ $$$$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{{x}−\mathrm{1}}{\left({x}+\mathrm{1}\right)\mathrm{ln}\:{x}}\:{dx}\:?\: \\ $$ Answered by mnjuly1970 last updated on 12/Aug/20 $${ans}:={ln}\left(\frac{\mathrm{2}}{\pi}\right)\: \\…
Question Number 42157 by Tawa1 last updated on 19/Aug/18 $$\:\int_{\:\mathrm{0}} ^{\:\infty} \:\:\frac{\mathrm{dx}}{\left(\mathrm{1}\:+\:\mathrm{x}^{\mathrm{n}} \right)} \\ $$ Commented by math khazana by abdo last updated on 19/Aug/18…
Question Number 107656 by bemath last updated on 12/Aug/20 Answered by john santu last updated on 12/Aug/20 $$\:\:\:\:\:\divideontimes\mathcal{JS}\divideontimes \\ $$$$\:\begin{cases}{\lambda=\mathrm{1}+{x}\sqrt{{x}}}\\{{dx}=\frac{\mathrm{2}{d}\lambda}{\mathrm{3}\sqrt{{x}}}}\end{cases} \\ $$$${I}=\int\:\sqrt{{x}}\:\sqrt{\mathrm{1}+{x}\sqrt{{x}}\:}\:{dx}\: \\ $$$${I}=\:\int\:\sqrt{{x}}\:\sqrt{\lambda}\:\left(\frac{\mathrm{2}{d}\lambda}{\mathrm{3}\sqrt{{x}}}\right)=\int\frac{\mathrm{2}}{\mathrm{3}}\lambda^{\frac{\mathrm{1}}{\mathrm{2}}} \:{d}\lambda…
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Question Number 107624 by mnjuly1970 last updated on 11/Aug/20 $$\:\:\:\:\:\:\:{please}\:{prove}: \\ $$$$\:\mathrm{A},\mathrm{B},{C}\:\:{are}\:{angles}\:{of} \\ $$$${triangle}. \\ $$$$\underset{{cylic}} {\sum}\frac{{sinA}+{sinB}}{{cosc}}\geqslant\mathrm{8}{cos}\frac{{A}}{\mathrm{2}}{cos}\frac{{B}}{\mathrm{2}}{cos}\frac{{C}}{\mathrm{2}}\:\:\:\:\:\:\: \\ $$$$ \\ $$ Terms of Service Privacy…
Question Number 42088 by maxmathsup by imad last updated on 17/Aug/18 $${find}\:\:\:\:\:\int\:\:\:\:\:\left(\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right){ln}\left(\mathrm{1}−\frac{\mathrm{1}}{{x}}\right){dx}\:\:. \\ $$ Commented by maxmathsup by imad last updated on 17/Aug/18 $${let}\:{A}\:=\:\int\:\:\left(\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{2}}…
Question Number 42085 by maxmathsup by imad last updated on 17/Aug/18 $${calculate}\:\:\:\:\int_{\mathrm{1}} ^{+\infty} \:\:\:\frac{\mathrm{2}{x}+\mathrm{1}}{\mathrm{3}\:+\left({x}+\mathrm{1}\right)^{\mathrm{3}} }{dx}\: \\ $$ Commented by maxmathsup by imad last updated on…