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…
Question Number 89273 by Ar Brandon last updated on 16/Apr/20 $${Evaluate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{\mathrm{2}} }{\:\sqrt{\mathrm{1}+{x}^{\mathrm{3}} }}{dx}\:{and}\:{given}\:{that}\:{I}_{{n}\:} =\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{{n}} \left(\mathrm{1}+{x}^{\mathrm{3}} \right)^{−\frac{\mathrm{1}}{\mathrm{2}}} {dx} \\ $$$${show}\:{that}\:\left(\mathrm{2}{n}−\mathrm{1}\right){I}_{{n}} =\mathrm{2}\sqrt{\mathrm{2}}−\mathrm{2}\left({n}−\mathrm{1}\right)\:{for}\:{n}\geqslant\mathrm{3}. \\…
Question Number 154780 by talminator2856791 last updated on 21/Sep/21 $$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\int_{−\infty} ^{\:\infty} \:\frac{\mathrm{1}}{{x}^{\mathrm{4}} +{x}^{\mathrm{3}} +{x}^{\mathrm{2}} +\mathrm{1}}\:{dx} \\ $$$$\: \\ $$ Answered by phanphuoc last…
Question Number 89240 by Ar Brandon last updated on 16/Apr/20 $${If}\:{I}_{{n}} =\int_{\mathrm{0}} ^{\pi} {e}^{{x}} {sin}^{{n}} {xdx},\:{show}\:{that}\: \\ $$$$\left({n}^{\mathrm{2}} +\mathrm{1}\right){I}_{{n}} ={n}\left({n}−\mathrm{1}\right){I}_{{n}−\mathrm{2}} \\ $$ Terms of Service…
Question Number 89237 by cindiaulia last updated on 16/Apr/20 $$\int_{\mathrm{2}} ^{\mathrm{1}} \left(\mathrm{x}+\mathrm{1}\right)\left(\sqrt{\left.\mathrm{x}+\mathrm{3}\right)}\right. \\ $$ Commented by niroj last updated on 16/Apr/20 $$=\:\int_{\mathrm{2}} ^{\mathrm{1}} \left(\mathrm{x}+\mathrm{1}\right)\sqrt{\mathrm{x}+\mathrm{3}}\:\:\mathrm{dx} \\…
Question Number 89228 by cindiaulia last updated on 16/Apr/20 $$\underset{\mathrm{4}} {\overset{\mathrm{5}} {\int}}\mathrm{x}^{\mathrm{2}} \sqrt{\mathrm{x}−\mathrm{4}} \\ $$ Commented by jagoll last updated on 16/Apr/20 $$\sqrt{{x}−\mathrm{4}}\:=\:{t}\:\Rightarrow{x}={t}^{\mathrm{2}} +\mathrm{4} \\…
Question Number 89226 by cindiaulia last updated on 16/Apr/20 $$\int\left(\frac{\mathrm{x}^{\mathrm{3}} +\mathrm{2}}{\mathrm{x}^{\mathrm{3}} }\right)\sqrt{\mathrm{x}−\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }} \\ $$ Commented by jagoll last updated on 16/Apr/20 $$\int\:\left(\mathrm{1}+\frac{\mathrm{2}}{{x}^{\mathrm{3}} }\right)\:\sqrt{{x}−\frac{\mathrm{1}}{{x}^{\mathrm{2}} }}\:{dx}\:…