Question Number 112488 by mathdave last updated on 08/Sep/20 $${solve} \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{\mathrm{1}+{x}^{\mathrm{4}} }{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 112489 by mathdave last updated on 08/Sep/20 $${solve} \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{ln}^{\mathrm{2}} \left(\mathrm{sin}{x}\right){dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 112487 by mathdave last updated on 08/Sep/20 $${solve} \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{ln}\left(\mathrm{1}+{x}^{\mathrm{3}} \right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 177975 by aurpeyz last updated on 11/Oct/22 Answered by mr W last updated on 11/Oct/22 $$\angle{ACB}={x}/\mathrm{2} \\ $$$$\angle{BAC}={y} \\ $$$$\angle{B}=\mathrm{180}−{x}/\mathrm{2}−{y} \\ $$$$\angle{ADC}=\mathrm{180}−\angle{B}={x}/\mathrm{2}+{y} \\…
Question Number 112393 by ZiYangLee last updated on 07/Sep/20 $${gf}^{−\mathrm{1}} \left({x}\right)=\mathrm{3}{x}−\mathrm{2} \\ $$$${fg}\left({x}\right)=\mathrm{12}{x}−\mathrm{8} \\ $$$$ \\ $$$$\mathrm{then}\:{g}^{\mathrm{2}} \left({x}\right)=? \\ $$ Commented by ZiYangLee last updated…
Question Number 112366 by mathdave last updated on 07/Sep/20 Answered by mathmax by abdo last updated on 07/Sep/20 $$\mathrm{let}\:\mathrm{S}_{\mathrm{n}} =\mathrm{n}\:\sum_{\mathrm{k}=\mathrm{1}} ^{\mathrm{n}−\mathrm{1}} \:\frac{\mathrm{ln}\left(\mathrm{k}+\mathrm{n}\right)−\mathrm{ln}\left(\mathrm{n}\right)}{\mathrm{n}^{\mathrm{2}} \:+\mathrm{k}^{\mathrm{2}} }\:\Rightarrow \\…
Question Number 112369 by mathdave last updated on 07/Sep/20 $${prove}\:{that}\: \\ $$$$\int_{\mathrm{0}} ^{\infty} \left(\frac{\mathrm{tanh}{x}}{{x}^{\mathrm{3}} }−\frac{\mathrm{sech}^{\mathrm{2}} {x}}{{x}^{\mathrm{2}} }\right){dx}=\frac{\mathrm{7}}{\pi^{\mathrm{2}} }\zeta\left(\mathrm{3}\right) \\ $$$${where}\:\zeta\left(\mathrm{3}\right)={apery}'{s}\:{constant} \\ $$ Terms of Service…
Question Number 177900 by yaslm last updated on 10/Oct/22 Answered by Ar Brandon last updated on 11/Oct/22 $${I}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{sin}^{{n}} {xdx} \\ $$$${I}_{{n}+\mathrm{2}} =\int_{\mathrm{0}}…
Question Number 112364 by john santu last updated on 07/Sep/20 $$\left(\mathrm{1}\right)\:{Let}\:{z}\:=\:\sqrt{\mathrm{3}+\mathrm{4}{i}}\:+\:\sqrt{−\mathrm{3}−\mathrm{4}{i}}\:,\:{where} \\ $$$${square}\:{root}\:{is}\:{taken}\:{with}\:{positive}\: \\ $$$${real}\:{part}.\:{Then}\:{Re}\left({z}\right)\:{is}\:\_ \\ $$$$\left({a}\right)\mathrm{3}\:\:\:\:\:\left({b}\right)\:\mathrm{4}\:\:\:\:\:\left({c}\right)\:\mathrm{2}\:\:\:\:\:\left({d}\right)\:\mathrm{1} \\ $$$$\left(\mathrm{2}\right){Suppose}\:{a},{b},{c}\:{are}\:{in}\:{AP}\:{and}\:{a}^{\mathrm{2}} ,{b}^{\mathrm{2}} ,{c}^{\mathrm{2}} \\ $$$${are}\:{in}\:{GP}.\:{If}\:{a}<{b}<{c}\:{and}\:{a}+{b}+{c}=\frac{\mathrm{3}}{\mathrm{2}}, \\ $$$${then}\:{a}\:=\:\_…
Question Number 177884 by DAVONG last updated on 10/Oct/22 Answered by mr W last updated on 10/Oct/22 $$\mathrm{6}\:{black}\:{and}\:{n}\:{red}\:{balls}\:{in}\:{bag}. \\ $$$${to}\:{take}\:\mathrm{3}\:{balls}\:{there}\:{are}\:{totally} \\ $$$${C}_{\mathrm{3}} ^{{n}+\mathrm{6}} \:{ways}. \\…