Question Number 33589 by abdo imad last updated on 19/Apr/18 $$\left.\mathrm{1}\right)\:{decompose}\:{F}\left({x}\right)\:=\:\:\:\frac{\mathrm{1}}{\left({x}^{\mathrm{2}} +\mathrm{4}\right)\left({x}−\mathrm{3}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int_{\mathrm{4}} ^{+\infty} \:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{4}\right)\left({x}−\mathrm{3}\right)^{\mathrm{2}} }\:. \\ $$ Commented by math khazana…
Question Number 33587 by abdo imad last updated on 19/Apr/18 $${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\pi} {ln}\:\left({x}^{\mathrm{2}} \:−\mathrm{2}{x}\:{cos}\theta\:+\mathrm{1}\right){d}\theta\:\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$$${give}\:{a}\:{simple}\:{form}\:{of}\:{f}\left({x}\right). \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 99120 by M±th+et+s last updated on 18/Jun/20 $${prove}\:{that}: \\ $$$$\int_{−\frac{\mathrm{1}}{\mathrm{2}}} ^{\infty} {e}^{−\left(\mathrm{4}{x}^{\mathrm{6}} +\mathrm{12}{x}^{\mathrm{5}} +\mathrm{15}{x}^{\mathrm{4}} +\mathrm{10}{x}^{\mathrm{3}} +\mathrm{4}{x}^{\mathrm{2}} +{x}\right)} {dx} \\ $$$$=\frac{\sqrt[{\mathrm{8}}]{{e}}}{\mathrm{3}}\left[\frac{\Gamma\left(\frac{\mathrm{1}}{\mathrm{6}}\right)^{\frac{−\mathrm{1}}{\mathrm{2}}} }{\mathrm{2}\sqrt[{\mathrm{3}}]{\mathrm{2}}}\mathrm{1}{F}\mathrm{2}\left(_{\mathrm{1}/\mathrm{3},\mathrm{2}/\mathrm{3}} ^{\mathrm{1}/\mathrm{6}} \mid\frac{−\mathrm{1}}{\mathrm{69}/\mathrm{2}}\:\right)\:+\frac{\Gamma\left(\mathrm{5}/\mathrm{6}\right)}{\mathrm{128}\sqrt[{\mathrm{3}}]{\mathrm{4}}}\mathrm{1}{F}\mathrm{2}\left(_{\mathrm{4}/\mathrm{3},\mathrm{5}/\mathrm{3}}…
Question Number 99114 by M±th+et+s last updated on 18/Jun/20 $${calculate}: \\ $$$$\int\sqrt{{x}}{sinh}^{−\mathrm{1}} \left({x}\right){dx} \\ $$$${where}\:{sinh}^{−\mathrm{1}} \left({x}\right)\:{is}\:{the}\:{inverse}\:{hyperbolic}\: \\ $$$${sine}\:{function} \\ $$$$ \\ $$$$ \\ $$ Answered…
Question Number 33570 by Joel578 last updated on 19/Apr/18 $${A}\:=\:\underset{{n}=\mathrm{2}} {\overset{\mathrm{2017}} {\sum}}\:\left[\underset{\mathrm{1}} {\overset{{n}} {\int}}\:\mathrm{2tan}^{−\mathrm{1}} \:{x}\:+\:\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{2}{x}}{\mathrm{1}\:+\:{x}^{\mathrm{2}} }\right)\:{dx}\right] \\ $$$${B}\:=\:\underset{{n}=\mathrm{2}} {\overset{\mathrm{2017}} {\prod}}\:\left[\underset{\mathrm{1}} {\overset{{n}} {\int}}\:\mathrm{2tan}^{−\mathrm{1}} \:{x}\:+\:\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{2}{x}}{\mathrm{1}\:+\:{x}^{\mathrm{2}}…
Question Number 33544 by math khazana by abdo last updated on 19/Apr/18 $$\left.\mathrm{1}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\:{e}^{−{tx}^{\mathrm{2}} } }{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx}\:{with}\:{t}\:>\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{\left(\mathrm{1}−{e}^{−{x}^{\mathrm{2}} } \right)}{{x}^{\mathrm{2}} \left(\mathrm{1}+{x}^{\mathrm{2}}…
Question Number 164605 by amin96 last updated on 19/Jan/22 Answered by Zaynal last updated on 19/Jan/22 $$\frac{\mathrm{In}\left(\mathrm{2}\right)^{\mathrm{2}} }{\mathrm{2}}−\frac{\mathrm{2}}{\mathrm{12}} \\ $$ Terms of Service Privacy Policy…
Question Number 33531 by Yozzzzy last updated on 18/Apr/18 $$\int_{\mathrm{0}} ^{\infty} \frac{{e}^{−{x}^{\mathrm{2}} } }{{x}^{\mathrm{2}} +\mathrm{1}}{dx}=? \\ $$ Commented by Rasheed.Sindhi last updated on 18/Apr/18 $$\mathrm{Ve}….\mathrm{ry}\:\mathrm{happy}\:\mathrm{to}\:\mathrm{see}\:\mathrm{you}\:\mathrm{back}\:\mathrm{again},\:…
Question Number 164598 by Zaynal last updated on 19/Jan/22 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{Prove}}\:\boldsymbol{\mathrm{that}}; \\ $$$$\:\:\:\:\:\:\int_{−\infty} ^{\infty} \:\boldsymbol{{y}}\:\boldsymbol{{tan}}\:\boldsymbol{{x}}\:+\:\boldsymbol{{y}}^{\mathrm{3}} \:\:\boldsymbol{{tan}}\:\:\boldsymbol{{x}}\:\boldsymbol{{dx}}\:=\:\boldsymbol{{undefined}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 164600 by mathlove last updated on 19/Jan/22 Answered by Zaynal last updated on 19/Jan/22 $$\mathrm{1}.\:\frac{\mathrm{1}}{\mathrm{5}}\mathrm{arcsec}\left(\frac{\mathrm{2}}{\mathrm{5}}\boldsymbol{{x}}\right)+\boldsymbol{\mathrm{C}} \\ $$$$\mathrm{2}.\frac{\mathrm{a}\boldsymbol{{rctan}}\left(\frac{\boldsymbol{{t}}^{\mathrm{2}} }{\mathrm{8}}\right)}{\mathrm{16}}\:+\:\boldsymbol{{C}}\:,\boldsymbol{{C}}\in\mathbb{R} \\ $$$$\mathrm{3}.\frac{\boldsymbol{\mathrm{arcsin}}\left(\frac{\mathrm{7}\boldsymbol{\mathrm{y}}}{\mathrm{3}}\right)}{\mathrm{7}}+\boldsymbol{\mathrm{C}},\mathrm{C}\in\mathbb{R} \\ $$ Answered…