Question Number 89317 by abdomathmax last updated on 16/Apr/20 $${find}\:\int\:\:\:\:\:\frac{{dx}}{\left({x}+\sqrt{{x}−\mathrm{1}}\right)^{\mathrm{2}} } \\ $$ Commented by mathmax by abdo last updated on 17/Apr/20 $${parametric}\:{method}\:{let}\:{f}\left({a}\right)\:=\int\:\frac{{dx}}{{a}+{x}+\sqrt{{x}−\mathrm{1}}} \\ $$$${we}\:{have}\:{f}^{'}…
Question Number 89314 by abdomathmax last updated on 16/Apr/20 $${calculate}\:\int\int_{{D}} \:{x}^{\mathrm{2}} \sqrt{{x}+{y}}{dxdy}\:{with}\:{D}\:{is}\:{the}\:{triangle} \\ $$$$\mathrm{0}\:{A}\:{B}\:\:\:\left(\mathrm{0}\:{origin}\right)\:\:\:{A}\left(\mathrm{1},\mathrm{0}\right)\:\:\:{B}\left(\mathrm{0},\mathrm{1}\right) \\ $$ Commented by abdomathmax last updated on 18/Apr/20 $${the}\:{equation}\:{of}\:{line}\:\left({AB}\right)\:{is}\:{x}+{y}=\mathrm{1}\:\Rightarrow{y}=\mathrm{1}−{x}\:\Rightarrow \\…
Question Number 89315 by abdomathmax last updated on 16/Apr/20 $${calculate}\:\int\int_{\left[\mathrm{0},\mathrm{1}\right]^{\mathrm{2}} } \:\:\:\frac{{arctan}\left({xy}\right)}{\left({x}+{y}\right)^{\mathrm{2}} }{dxdy} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 89312 by abdomathmax last updated on 16/Apr/20 $${calculate}\:\int\int_{{D}} \:{xe}^{−{x}} {siny}\:{dy}\:{with}\:{D}\:{is}\:{the}\:{triangle} \\ $$$${OAB}\:\:\:\:{O}\left(\mathrm{0},\mathrm{0}\right)\:\:{A}\left(\mathrm{1},\mathrm{0}\right)\:{B}\left(\mathrm{0},\mathrm{1}\right) \\ $$ Commented by mathmax by abdo last updated on 17/Apr/20…
Question Number 89311 by nimnim last updated on 16/Apr/20 $$\:\:{Show}\:{that} \\ $$$$\underset{\:\:\:\mathrm{0}} {\overset{\:\:\:\:\:\:\:\mathrm{1}} {\int}}\left\{\underset{\:\:\:\:\mathrm{0}} {\overset{\:\:\:\mathrm{1}} {\int}}\frac{{x}−{y}}{\left({x}+{y}\right)^{\mathrm{2}} }{dy}\right\}{dx}=\underset{\:\:\mathrm{0}} {\overset{\:\:\:\:\:\:\:\mathrm{1}} {\int}}\left\{\underset{\:\:\:\mathrm{0}} {\overset{\:\:\:\:\:\:\mathrm{1}} {\int}}\frac{{x}−{y}}{\left({x}+{y}\right)^{\mathrm{2}} }{dx}\right\}{dy} \\ $$$$ \\…
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Question Number 89302 by M±th+et£s last updated on 16/Apr/20 $$\int\frac{\mathrm{1}+{cos}\left({x}\right)+{sin}\left({x}\right)}{{x}^{\mathrm{3}} }{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 89286 by M±th+et£s last updated on 16/Apr/20 $${show}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\left({x}^{\mathrm{2}} +\mathrm{1}\right){ln}\left(\mathrm{1}+{x}\right)}{{x}^{\mathrm{4}} −{x}^{\mathrm{2}} +\mathrm{1}}{dx}=\frac{\pi}{\mathrm{6}}{ln}\left(\mathrm{2}+\sqrt{\mathrm{3}}\right) \\ $$ Answered by TANMAY PANACEA. last updated…
Question Number 154824 by talminator2856791 last updated on 21/Sep/21 $$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{\mathrm{4}^{−{k}} \Gamma\left({k}\right)}{{k}!} \\ $$$$\: \\ $$ Answered by Ar Brandon last updated…
Question Number 154823 by talminator2856791 last updated on 21/Sep/21 $$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \:\frac{{e}^{−{x}} }{\:{x}^{\frac{\mathrm{3}}{\mathrm{4}}} \:}\:{dx} \\ $$$$\: \\ $$ Answered by Jonathanwaweh last updated…