Question Number 158159 by cortano last updated on 31/Oct/21 $$\:\:\:\:\:\:\int\:\frac{{dx}}{\mathrm{3}−\mathrm{tan}\:{x}}\:=? \\ $$ Answered by peter frank last updated on 31/Oct/21 $$\int\frac{\mathrm{cos}\:\mathrm{x}}{\mathrm{3cos}\:\mathrm{x}−\mathrm{sin}\:\mathrm{x}}\mathrm{dx} \\ $$$$\mathrm{t}−\mathrm{substitution} \\ $$$$\mathrm{t}=\mathrm{tan}\:\frac{\mathrm{x}}{\mathrm{2}}…
Question Number 158142 by alcohol last updated on 31/Oct/21 $${f}\left({x}\right)={x}−\left[{x}\right]\:{where}\:\left[{x}\right]\:{is}\:{the}\:{greatest} \\ $$$${integer}\:{function}\:{and}\:−\mathrm{3}\leqslant{x}\leqslant\mathrm{3} \\ $$$$\left.{a}\right)\:{sketch}\:{f}\left({x}\right) \\ $$$$\left.{b}\right)\:{state}\:{the}\:{domain}\:{of}\:{f}\left({x}\right) \\ $$$$\left.{c}\right)\:{study}\:{the}\:{continuity}\:{of}\:{f}\left({x}\right)\:{on}\:{its}\:{domain} \\ $$$$\left.{d}\right)\:{state}\:{the}\:{range}\:{of}\:{f}\left({x}\right) \\ $$ Terms of Service…
Question Number 27045 by abdo imad last updated on 01/Jan/18 $${find}\:{the}\:{value}\:{of}\:\int_{\frac{\mathrm{2}}{\pi}} ^{\frac{\mathrm{6}}{\pi}} \:{x}^{\mathrm{3}} \:{cos}\left(\left[\frac{\mathrm{1}}{{x}}\right]\right){dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 27032 by cmaxamuud98 @gmail.com last updated on 01/Jan/18 $${xy}=\left(\mathrm{1}−{x}^{\mathrm{2}} \right)\frac{{dy}}{{dx}}\:\:\:\:{x}=\mathrm{0}\:{y}=\mathrm{1} \\ $$ Commented by abdo imad last updated on 01/Jan/18 $${e}.{d}\Rightarrow\:\:\left(\mathrm{1}−{x}^{\mathrm{2}} \right){y}^{'} \:−{xy}\:=\mathrm{0}\:{with}\:{y}\left(\mathrm{0}\right)=\mathrm{1}…
Question Number 27031 by cmaxamuud98 @gmail.com last updated on 01/Jan/18 $${xy}=\left(\mathrm{1}−{x}^{\mathrm{2}} \right)\frac{{dy}}{{dx}}\:\:\:\:{x}=\mathrm{0}\:{y}=\mathrm{1} \\ $$ Answered by mrW1 last updated on 01/Jan/18 $$\frac{{dy}}{{y}}=\frac{{xdx}}{\mathrm{1}−{x}^{\mathrm{2}} }=−\frac{\mathrm{1}}{\mathrm{2}}×\frac{{d}\left(\mathrm{1}−{x}^{\mathrm{2}} \right)}{\mathrm{1}−{x}^{\mathrm{2}} }…
Question Number 92539 by mathmax by abdo last updated on 07/May/20 $$\left.\mathrm{1}\right)\:{find}\:\int\:\:\:\:\:\frac{{dx}}{\left({x}+\mathrm{2}\right)^{\mathrm{3}} \left({x}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{2}} ^{+\infty} \:\frac{{dx}}{\left({x}+\mathrm{2}\right)^{\mathrm{3}} \left({x}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{2}} } \\ $$ Terms…
Question Number 27003 by Joel578 last updated on 01/Jan/18 $$\underset{\mathrm{1}/\mathrm{8}} {\overset{\mathrm{1}/\mathrm{2}} {\int}}\:\lfloor\mathrm{ln}\:\lceil\frac{\mathrm{1}}{{x}}\rceil\rfloor\:{dx} \\ $$ Commented by abdo imad last updated on 01/Jan/18 $$\:{if}\:{you}\:{mean}\:{the}\:{integral}\:{I}=\:\int_{\frac{\mathrm{1}}{\mathrm{8}}} ^{\frac{\mathrm{1}}{\mathrm{2}}} {ln}\left[\:\frac{\mathrm{1}}{{x}}\right]{dx}\:{we}\:{do}\:{the}\:{changement}…
Question Number 26993 by abdo imad last updated on 31/Dec/17 Commented by prakash jain last updated on 01/Jan/18 $$\mathrm{Happy}\:\mathrm{new}\:\mathrm{year} \\ $$ Commented by Rasheed.Sindhi last…
Question Number 158053 by Ar Brandon last updated on 30/Oct/21 $$\int\frac{{dx}}{\mathrm{sin}^{\mathrm{4}} {x}} \\ $$ Answered by ajfour last updated on 30/Oct/21 $$\int\frac{{dx}}{\left[\mathrm{1}−\mathrm{cos}\:^{\mathrm{2}} {x}\right]^{\mathrm{2}} }=\int\frac{\left(\mathrm{1}+{t}^{\mathrm{2}} \right){dt}}{{t}^{\mathrm{4}}…
Question Number 26952 by Femmy last updated on 31/Dec/17 Answered by prakash jain last updated on 31/Dec/17 $$\int\frac{\mathrm{sin}^{\mathrm{5}} {x}}{\mathrm{cos}^{\mathrm{3}} {x}}{dx}=\int\frac{\mathrm{sin}^{\mathrm{4}} {x}}{\mathrm{cos}^{\mathrm{3}} {x}}\mathrm{sin}\:{xdx} \\ $$$$=\int\frac{\left(\mathrm{1}−\mathrm{cos}^{\mathrm{2}} {x}\right)^{\mathrm{2}}…