Question Number 109086 by bobhans last updated on 21/Aug/20 $$\:\:\:\underset{\rightarrow} {\flat}\underset{\rightarrow} {{o}}\flat\underset{\multimap} {{h}an}\underset{\multimap} {{s}} \\ $$$$\left(\mathrm{1}\right)\:\left({x}^{\mathrm{2}} {e}^{−\frac{{y}}{{x}}} +{y}^{\mathrm{2}} \right)\:{dx}\:=\:{xy}\:{dy}\: \\ $$$$\left(\mathrm{2}\right)\left(\frac{{f}\left({x}\right)}{{x}}\right)'\:=\:{x}^{\mathrm{2}} {e}^{−{x}^{\mathrm{2}} } \:;\:{f}\left(\mathrm{1}\right)\:=\:\frac{\mathrm{1}}{{e}}\: \\…
Question Number 43550 by peter frank last updated on 11/Sep/18 $${prove}\:{that} \\ $$$$\int_{\:} \:\mathrm{4}_{\:\:\:\:\:} ^{\mathrm{4}^{\mathrm{4}^{{x}} } } .\mathrm{4}^{\mathrm{4}^{{x}} } .\mathrm{4}^{{x}} {dx}=\frac{\mathrm{4}^{\mathrm{4}^{{x}} } }{\left(\mathrm{log}\:\underset{{e}} {\mathrm{4}}\right)} \\…
Question Number 43551 by peter frank last updated on 11/Sep/18 $${evaluate}\:\int\frac{\mathrm{1}}{\mathrm{cos}\:\left({x}−{a}\right)\mathrm{cos}\:\left({x}−{b}\right)}{dx} \\ $$ Answered by MJS last updated on 12/Sep/18 $$\int\frac{{dx}}{\mathrm{cos}\left({x}−{a}\right)\mathrm{cos}\left({x}−{b}\right)}= \\ $$$$\:\:\:\:\:\left[{t}={x}−{a}\:\rightarrow\:{dx}={dt}\right] \\ $$$$=\int\frac{{dt}}{\mathrm{cos}\:{t}\:\mathrm{cos}\left({t}+{a}−{b}\right)}=…
Question Number 43539 by abdo.msup.com last updated on 11/Sep/18 $${calculate}\:\int\int_{\mathrm{0}\leqslant{x}\leqslant\mathrm{1}\:,\mathrm{0}\leqslant{y}\leqslant\mathrm{1}} \:\:\left({x}+\mathrm{2}{y}\right){e}^{\mathrm{2}{x}−{y}} {dxdy} \\ $$ Commented by maxmathsup by imad last updated on 16/Sep/18 $${let}\:{consider}\:{the}\:{diffeomorphisme}\:\left({u},{v}\right)\:\rightarrow\varphi\left({u},{v}\right)=\left(\varphi_{\mathrm{1}} \left({u},{v}\right),\varphi_{\mathrm{2}}…
Question Number 43538 by abdo.msup.com last updated on 11/Sep/18 $${calculate}\:\int\int_{\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }\:+\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }\:\leqslant\mathrm{1}} \left({x}^{\mathrm{2}} −{y}^{\mathrm{2}} \right){dxdy}\:{whit} \\ $$$${a}>\mathrm{0}\:{and}\:{b}>\mathrm{0}\:. \\ $$ Commented by maxmathsup by…
Question Number 174610 by Brahimmekkaoui last updated on 05/Aug/22 $${find}\:{the}\:{value}\:{of}\:{this}\:{integral}: \\ $$$${I}=\int_{\mathrm{0}} ^{\infty} \:\frac{{tan}^{−\mathrm{1}} \left({x}\right)}{\mathrm{1}+{x}+{x}^{\mathrm{2}} }\:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 43535 by maxmathsup by imad last updated on 11/Sep/18 $$\left.\mathrm{1}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{3}}} \:\sqrt{\mathrm{1}+{tan}\theta}{d}\theta\:. \\ $$ Commented by MJS last updated on 12/Sep/18 $$\mathrm{it}'\mathrm{s}\:\mathrm{possible}\:\mathrm{but}\:\mathrm{it}'\mathrm{s}\:\mathrm{a}\:\mathrm{long}\:\mathrm{way} \\…
Question Number 43517 by Raj Singh last updated on 11/Sep/18 Commented by maxmathsup by imad last updated on 11/Sep/18 $${let}\:{I}\:=\:\int\:\:\frac{{x}^{\mathrm{3}} \:+\mathrm{1}}{{x}^{\mathrm{2}} −\mathrm{5}{x}\:+\mathrm{6}}\:{dx}\:\Rightarrow{I}\:=\:\int\:\:\frac{{x}\left({x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{6}\:\right)+\mathrm{5}{x}^{\mathrm{2}} −\mathrm{6}{x}\:+\mathrm{1}}{{x}^{\mathrm{2}} −\mathrm{5}{x}\:+\mathrm{6}}{dx}…
Question Number 109047 by Eric002 last updated on 20/Aug/20 $$\int_{−\mathrm{2}} ^{\infty} \left({x}+\mathrm{2}\right)^{\mathrm{5}} {e}^{−\left({x}+\mathrm{2}\right)} {dx} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{tan}\left({x}\right)}{{x}}{dx} \\ $$ Answered by Dwaipayan Shikari last…
Question Number 174560 by mnjuly1970 last updated on 04/Aug/22 $$ \\ $$$$\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:{dx}}{\:\sqrt{\mathrm{8}+\mathrm{3}{x}−\sqrt{\mathrm{1}+\left(\:{x}^{\:\mathrm{2}} +\mathrm{3}{x}\:+\mathrm{2}\right)\left({x}^{\:\mathrm{2}} +\mathrm{7}{x}+\mathrm{12}\right)}}} \\ $$$$ \\ $$ Answered by MJS_new last updated…