Question Number 65293 by mathmax by abdo last updated on 27/Jul/19 $$\left.\mathrm{1}\right)\:{calculate}\:\int_{−\infty} ^{+\infty} \:\:\frac{{dx}}{{x}−{a}}\:\:{with}\:{a}\:\in{C} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{values}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{{x}^{\mathrm{4}} \:+\mathrm{1}}\:\:{and}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{{x}^{\mathrm{6}} \:+\mathrm{1}} \\ $$$${by}\:{using}\:{the}\:{decomposition}\:{inside}\:{C}\left({x}\right). \\…
Question Number 65290 by mathmax by abdo last updated on 27/Jul/19 $${f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{dt}}{{x}+{e}^{{t}} }\:\:\:{with}\:\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{aexplicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{dt}}{\mathrm{2}+{e}^{{t}} } \\ $$$$\left.\mathrm{3}\right)\:{find}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 65288 by mathmax by abdo last updated on 27/Jul/19 $$\left.\mathrm{1}\right)\:{let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{+\infty} \:\:\:\frac{{dt}}{{t}^{\mathrm{3}} \:+{x}^{\mathrm{3}} }\:\:\:{with}\:{x}>\mathrm{0} \\ $$$${calculate}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{also}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dt}}{\left({t}^{\mathrm{3}} \:+{x}^{\mathrm{3}} \right)^{\mathrm{2}} }…
Question Number 65287 by mathmax by abdo last updated on 27/Jul/19 $${let}\:{f}\left({x}\right)\:={x}\mid{x}\mid\:\:\:\:\mathrm{2}\pi\:{periodic}\:\:{odd} \\ $$$${developp}\:{f}\:{at}\:{fourier}\:{series} \\ $$ Commented by mathmax by abdo last updated on 28/Jul/19…
Question Number 65286 by mathmax by abdo last updated on 27/Jul/19 $$\left.\mathrm{1}\right){find}\:\:\:{f}\left({a}\right)=\int_{−\infty} ^{+\infty} \:\:{e}^{−{ax}^{\mathrm{2}} } {cos}\left(\mathrm{3}−{x}^{\mathrm{2}} \right){dx}\:\:{with}\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−\mathrm{3}{x}^{\mathrm{2}} } {cos}\left(\mathrm{3}−{x}^{\mathrm{2}} \right){dx} \\…
Question Number 130809 by bemath last updated on 29/Jan/21 $$\:\int\:\mathrm{tan}\:\mathrm{x}\:\sqrt{\mathrm{sin}\:\mathrm{x}}\:\mathrm{dx}\:? \\ $$ Answered by EDWIN88 last updated on 29/Jan/21 $${let}\:\sqrt{\mathrm{sin}\:{x}}\:=\:{u}\:\Rightarrow\mathrm{sin}\:{x}\:=\:{u}^{\mathrm{2}} \\ $$$$\:\mathrm{tan}\:{x}\:=\:\frac{{u}^{\mathrm{2}} }{\:\sqrt{\mathrm{1}−{u}^{\mathrm{4}} }}\: \\…
Question Number 130778 by EDWIN88 last updated on 28/Jan/21 $$\int\:\frac{\mathrm{3}{x}^{\mathrm{2}} −\mathrm{1}}{{x}^{\mathrm{4}} −\mathrm{1}}\:{dx}\: \\ $$ Answered by bemath last updated on 29/Jan/21 $$\:\frac{\mathrm{3x}^{\mathrm{2}} −\mathrm{1}}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)\left(\mathrm{x}^{\mathrm{2}} −\mathrm{1}\right)}\:=\:\frac{\mathrm{3}\left(\mathrm{x}^{\mathrm{2}}…
Question Number 130781 by EDWIN88 last updated on 28/Jan/21 $$\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{ln}\:\left(\mathrm{1}+{x}+{x}^{\mathrm{2}} +{x}^{\mathrm{3}} +…+{x}^{{n}} \right)}{{x}}\:{dx}? \\ $$ Answered by mathmax by abdo last updated on…
Question Number 130763 by Lordose last updated on 28/Jan/21 $$\mathrm{Q}.\mathrm{130626} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 130759 by mnjuly1970 last updated on 28/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:{calculus}\:… \\ $$$$\:{find}\::\:\phi\:=\int_{\mathrm{0}} ^{\:\infty} \left({x}^{\mathrm{2}} {ln}\left(\mathrm{1}+{e}^{{x}} \right)−{x}^{\mathrm{3}} \right){dx} \\ $$$$ \\ $$ Answered by mnjuly1970 last…