Question Number 102905 by bemath last updated on 11/Jul/20 $${I}=\mathrm{2}\underset{\mathrm{0}} {\overset{\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}} {\int}}\:\frac{\mathrm{sin}^{−\mathrm{1}} \left({x}\right)}{{x}}\:{dx}\:−\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{\mathrm{tan}^{−\mathrm{1}} \left({x}\right)}{{x}}{dx} \\ $$ Answered by bramlex last updated on 11/Jul/20…
Question Number 37365 by math khazana by abdo last updated on 12/Jun/18 $${find}\:{L}^{−\mathrm{1}} \left\{\:\:\frac{\mathrm{1}}{\left({a}+{x}\right)^{\mathrm{2}} }\right\}\:\:{and}\:{L}^{−\mathrm{1}} \left\{\frac{\mathrm{1}}{\left({a}+{x}\right)^{\mathrm{3}} }\right\}\:. \\ $$ Commented by prof Abdo imad last…
Question Number 37366 by math khazana by abdo last updated on 12/Jun/18 $${let}\:{f}\left({x}\right)\:=\:\frac{{e}^{−\frac{{x}}{{a}}} }{{a}} \\ $$$${find}\:{L}\left({f}\left({x}\right)\right). \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 37364 by math khazana by abdo last updated on 12/Jun/18 $${calculate}\:\:{L}\left\{\:\frac{{x}^{{n}−\mathrm{1}} \:{e}^{−{ax}} }{\left({n}−\mathrm{1}\right)!}\right\}\:{then}\:{conclude} \\ $$$${L}^{−\mathrm{1}} \left\{\:\:\frac{\mathrm{1}}{\left({a}+{x}\right)^{{n}} }\right\} \\ $$ Commented by prof Abdo…
Question Number 37362 by math khazana by abdo last updated on 12/Jun/18 $${find}\:{L}\left({cos}\left({wx}\right)\right)\:{and}\:{L}\left({sin}\left({wx}\right)\right) \\ $$$${L}\:{is}\:{laplace}\:{transform}\:\:. \\ $$ Commented by math khazana by abdo last updated…
Question Number 37361 by math khazana by abdo last updated on 12/Jun/18 $${calculate}\:\int_{\mathrm{0}} ^{+\infty} \:\:\frac{{ln}\left({x}\right)}{\mathrm{1}+{x}^{\mathrm{3}} }\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 37360 by math khazana by abdo last updated on 12/Jun/18 $${calculate}\:\int_{\mathrm{0}} ^{+\infty} \:\:\:\:\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{3}} } \\ $$ Commented by math khazana by abdo last…
Question Number 37359 by math khazana by abdo last updated on 12/Jun/18 $${let}\:\:\:{g}\left({x}\right)=\:\frac{{ln}\left({z}\right)}{\mathrm{1}+{z}^{\mathrm{3}} }\:\:{give}\:{the}\:{poles}\:{z}_{{i}} \:{of}\:{g}\:{and} \\ $$$${calculate}\:{Res}\left({g}\:,{z}_{{i}} \right)\: \\ $$$$ \\ $$ Commented by math…
Question Number 102894 by bramlex last updated on 11/Jul/20 $$\int\:\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+…}}}}}\:\mathrm{dx}\: \\ $$ Answered by bemath last updated on 11/Jul/20 $${y}=\sqrt{{x}+\sqrt{{x}+\sqrt{{x}+\sqrt{{x}+\sqrt{…}}}}}\: \\ $$$${y}^{\mathrm{2}} \:=\:{x}+{y}\:\Rightarrow{y}^{\mathrm{2}} −{y}−{x}\:=\:\mathrm{0} \\…
Question Number 37357 by math khazana by abdo last updated on 12/Jun/18 $${let}\:{a}>\mathrm{0}\:{b}\:{from}\:{C}\:{and}\:\:{Re}\left({b}\right)>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{b}\:{cos}\left({ax}\right)}{{x}^{\mathrm{2}} \:+{b}^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{x}\:{sin}\left({ax}\right)}{{x}^{\mathrm{2}} \:+{b}^{\mathrm{2}} }\:{dx}.…