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 $$\int\sqrt{\mathrm{3}−\mathrm{2}{x}−\mathrm{2}{x}^{\mathrm{2}} }\:{dx} \\ $$$$=\sqrt{\mathrm{2}}\:\centerdot\:\int\sqrt{\left(\frac{\mathrm{3}}{\mathrm{2}}−{x}−{x}^{\mathrm{2}} \right)}\:{dx}…
Question Number 46 by surabhi last updated on 25/Jan/15 $$\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} \\ $$$$=\left(\mathrm{log}\:{x}\right)^{\mathrm{2}}…
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Question Number 65581 by aliesam last updated on 31/Jul/19 Commented by mathmax by abdo last updated on 31/Jul/19 $${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 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 $$\int{x}\:\mathrm{cos}^{\mathrm{2}} {x}\:{dx}\:=\int{x}\left(\frac{\mathrm{1}+\mathrm{cos}\:\mathrm{2}{x}}{\mathrm{2}}\right){dx} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\int{x}\:{dx}+\frac{\mathrm{1}}{\mathrm{2}}\int{x}\:\mathrm{cos}\:\mathrm{2}{x}\:{dx} \\…
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Question Number 35 by user2 last updated on 25/Jan/15 $$\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}= \\ $$$$={x}^{\mathrm{2}} \int\mathrm{sin}\:{x}\:{dx}−\int\left[\frac{{d}}{{dx}}\left({x}^{\mathrm{2}}…
Question Number 131104 by mnjuly1970 last updated on 01/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:…{advanced}\:\:{calculus}… \\ $$$$\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \frac{{x}^{{b}−\mathrm{1}} }{\left(\mathrm{1}+{x}^{{a}} \right)^{{s}} }{dx}\overset{???} {=}\frac{\Gamma\left(\frac{{b}}{{a}}\right)\Gamma\left({s}−\frac{{b}}{{a}}\right)}{{a}\Gamma\left({s}\right)} \\ $$ Answered by Ar Brandon last…
Question Number 131107 by ZiYangLee last updated on 01/Feb/21 $$\mathrm{Solve}\:\mathrm{sin}^{−\mathrm{1}} {x}+\mathrm{sin}^{−\mathrm{1}} \frac{{x}}{\mathrm{2}}=\frac{\mathrm{2}\pi}{\mathrm{3}} \\ $$ Answered by mr W last updated on 01/Feb/21 $${let}\:{t}=\frac{{x}}{\mathrm{2}}>\mathrm{0} \\ $$$$\mathrm{sin}^{−\mathrm{1}}…
Question Number 33 by user2 last updated on 25/Jan/15 $$\mathrm{Evaluate}\:\:\int\mathrm{sin}\:{x}\:\sqrt{\mathrm{1}−\mathrm{cos}\:\mathrm{2}{x}\:}{dx}. \\ $$ Answered by user2 last updated on 03/Nov/14 $$\int\mathrm{sin}\:{x}\:\sqrt{\mathrm{1}−\mathrm{cos}\:\mathrm{2}{x}}{dx} \\ $$$$=\int\mathrm{sin}\:{x}\centerdot\sqrt{\mathrm{2sin}^{\mathrm{2}} {x}\:}{dx}\: \\ $$$$=\sqrt{\mathrm{2}}\int\mathrm{sin}^{\mathrm{2}}…