Question Number 131138 by liberty last updated on 02/Feb/21 $$\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{arctan}\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{2}}}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{2}}}\:\mathrm{dx}\:=? \\ $$ Answered by EDWIN88 last updated on 02/Feb/21 $$=\frac{\mathrm{5}\pi^{\mathrm{2}}…
Question Number 131135 by LYKA last updated on 01/Feb/21 Commented by LYKA last updated on 01/Feb/21 $${if}\:{anyone}\:{knows}\:{this}\:{question}\: \\ $$$${please}\:{help}\:{me} \\ $$ Terms of Service Privacy…
Question Number 53 by surabhi last updated on 25/Jan/15 $$\mathrm{Evaluate}\:\int_{\mathrm{1}} ^{\mathrm{4}} \frac{\left({x}^{\mathrm{2}} +{x}\right)}{\:\sqrt{\mathrm{2}{x}+\mathrm{1}}}{dx} \\ $$ Answered by surabhi last updated on 04/Nov/14 $$\left[\left({x}^{\mathrm{2}} +{x}\right)\centerdot\sqrt{\mathrm{2}{x}+\mathrm{1}}\right]_{\mathrm{2}} ^{\mathrm{4}}…
Question Number 51 by surabhi last updated on 25/Jan/15 $$\mathrm{Evaluate}\:\int_{\mathrm{0}} ^{\pi/\mathrm{2}} {x}\mathrm{cos}\:{x}\:{dx} \\ $$ Answered by surabhi last updated on 04/Nov/14 $$\int_{\mathrm{0}} ^{\pi/\mathrm{2}} {x}\mathrm{cos}\:{x}\:{dx}=\left[{x}\mathrm{sin}\:{x}\right]_{\mathrm{0}} ^{\pi/\mathrm{2}}…
Question Number 46 by surabhi last updated on 25/Jan/15 $$\int\left(\mathrm{log}\:{x}\right)^{\mathrm{2}} {dx} \\ $$ Answered by surabhi last updated on 04/Nov/14 $$\int\left(\mathrm{log}\:{x}\right)^{\mathrm{2}} {dx}=\int\mid\left(\mathrm{log}\:{x}\right)^{\mathrm{2}} \centerdot\mathrm{1}\mid{dx} \\ $$$$=\left(\mathrm{log}\:{x}\right)^{\mathrm{2}}…
Question Number 48 by surabhi last updated on 25/Jan/15 $$\mathrm{Evaluate}\:\:\:\int\sqrt{\mathrm{3}−\mathrm{2}{x}−\mathrm{2}{x}^{\mathrm{2}} \:}{dx}. \\ $$ Answered by surabhi last updated on 04/Nov/14 $$\int\sqrt{\mathrm{3}−\mathrm{2}{x}−\mathrm{2}{x}^{\mathrm{2}} }\:{dx} \\ $$$$=\sqrt{\mathrm{2}}\:\centerdot\:\int\sqrt{\left(\frac{\mathrm{3}}{\mathrm{2}}−{x}−{x}^{\mathrm{2}} \right)}\:{dx}…
Question Number 50 by surabhi last updated on 25/Jan/15 $$\mathrm{Evaluate}\:\:\:\int\left({x}+\mathrm{1}\right)\sqrt{\mathrm{1}−{x}−{x}^{\mathrm{2}} }{dx}. \\ $$ Commented by 123456 last updated on 13/Dec/14 $$\mathrm{tente}?\mathrm{completar}\:\mathrm{quadrados}\:\mathrm{e}\:\mathrm{fca}\:\mathrm{uma}\:\mathrm{substutuico} \\ $$ Answered by…
Question Number 40 by user3 last updated on 25/Jan/15 $$\mathrm{Evaluate}\:\:\:\int{x}\:\mathrm{cos}\:^{\mathrm{2}} {x}\:{dx}. \\ $$ Answered by user3 last updated on 03/Nov/14 $$\int{x}\:\mathrm{cos}^{\mathrm{2}} {x}\:{dx}\:=\int{x}\left(\frac{\mathrm{1}+\mathrm{cos}\:\mathrm{2}{x}}{\mathrm{2}}\right){dx} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\int{x}\:{dx}+\frac{\mathrm{1}}{\mathrm{2}}\int{x}\:\mathrm{cos}\:\mathrm{2}{x}\:{dx} \\…
Question Number 65581 by aliesam last updated on 31/Jul/19 Commented by mathmax by abdo last updated on 31/Jul/19 $${let}\:{A}\:=\int\:{e}^{\left(\frac{\mathrm{1}}{{x}}−{x}\right)} \:{dx}\:\:\:{we}\:{have}\:{e}^{{u}} \:=\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{{u}^{{n}} }{{n}!}\:\:{with}\:{radius}\:{infinite}\Rightarrow \\…
Question Number 35 by user2 last updated on 25/Jan/15 $$\mathrm{Evaluate}\:\:\int{x}^{\mathrm{2}} \mathrm{sin}\:{x}\:{dx} \\ $$ Answered by surabhi last updated on 04/Nov/14 $$\int{x}^{\mathrm{2}} \mathrm{sin}\:{xdx}= \\ $$$$={x}^{\mathrm{2}} \int\mathrm{sin}\:{x}\:{dx}−\int\left[\frac{{d}}{{dx}}\left({x}^{\mathrm{2}}…