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 $$\int{x}^{\mathrm{2}} \mathrm{sin}\:{xdx}= \\ $$$$={x}^{\mathrm{2}} \int\mathrm{sin}\:{x}\:{dx}−\int\left[\frac{{d}}{{dx}}\left({x}^{\mathrm{2}}…
Question Number 33 by user2 last updated on 25/Jan/15 $$\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} \\ $$$$=\int\mathrm{sin}\:{x}\centerdot\sqrt{\mathrm{2sin}^{\mathrm{2}} {x}\:}{dx}\: \\ $$$$=\sqrt{\mathrm{2}}\int\mathrm{sin}^{\mathrm{2}}…
Question Number 31 by user2 last updated on 25/Jan/15 $$\mathrm{Evaluate}\:\int\sqrt{\mathrm{1}+\mathrm{sin}\:{x}}{dx}. \\ $$ Answered by user2 last updated on 03/Nov/14 $$\int\sqrt{\mathrm{1}+\mathrm{sin}\:{x}}\:{dx}=\int\sqrt{\mathrm{sin}^{\mathrm{2}} \frac{{x}}{\mathrm{2}}+\mathrm{cos}^{\mathrm{2}} \frac{{x}}{\mathrm{2}}+\mathrm{2sin}\frac{{x}}{\mathrm{2}}\mathrm{cos}\frac{{x}}{\mathrm{2}}\:}{dx} \\ $$$$=\int\left(\mathrm{sin}\frac{{x}}{\mathrm{2}}+\mathrm{cos}\frac{{x}}{\mathrm{2}}\right){dx} \\…
Question Number 131073 by Algoritm last updated on 01/Feb/21 Answered by mr W last updated on 01/Feb/21 $${F}\:'\left({x}\right)={e}^{\left(\mathrm{ln}\:{x}\right)^{\mathrm{100}} } \frac{\mathrm{1}}{{x}} \\ $$$${F}\:'\left({e}\right)={e}^{\left(\mathrm{ln}\:{e}\right)^{\mathrm{100}} } \frac{\mathrm{1}}{{e}}={e}×\frac{\mathrm{1}}{{e}}=\mathrm{1} \\…
Question Number 78549 by aliesam last updated on 18/Jan/20 Answered by ~blr237~ last updated on 18/Jan/20 $$\mathrm{let}\:\mathrm{named}\:\mathrm{it}\:\mathrm{A} \\ $$$$\mathrm{state}\:\mathrm{u}=\frac{\mathrm{x}}{\mathrm{2}}\:\:,\:\mathrm{A}=\mathrm{2}\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \frac{\sqrt{\mathrm{tan2u}}}{\mathrm{1}+\mathrm{sinu}}\:\mathrm{du} \\ $$$$\frac{\mathrm{A}}{\mathrm{2}}=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \frac{\sqrt{\mathrm{tan2u}}}{\mathrm{cos}^{\mathrm{2}}…
Question Number 13004 by Nayon last updated on 10/May/17 $${If}\:\int{f}\left({x}\right){dx}={g}\left({x}\right)\:,{then}\:{why} \\ $$$$\int_{{b}} ^{{a}} {f}\left({x}\right){dx}={g}\left({a}\right)−{g}\left({b}\right)??? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 13000 by Joel577 last updated on 10/May/17 $$\int\:\mathrm{sin}^{\mathrm{4}} \:{x}\:\mathrm{cos}^{\mathrm{3}} \:{x}\:{dx} \\ $$ Commented by Joel577 last updated on 10/May/17 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{idea}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{that}\:\mathrm{problem}? \\ $$ Commented…
Question Number 144064 by 0731619 last updated on 21/Jun/21 Answered by MJS_new last updated on 21/Jun/21 $$\mathrm{simply}\:\mathrm{let}\:{t}=\mathrm{tan}\:{x} \\ $$$$\Rightarrow\:\mathrm{answer}\:\mathrm{is} \\ $$$$−\frac{{x}}{{b}^{\mathrm{2}} }+\frac{\sqrt{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }}{{ab}^{\mathrm{2}} }\mathrm{arctan}\:\frac{{a}\mathrm{tan}\:{x}}{\:\sqrt{{a}^{\mathrm{2}}…