Question Number 186347 by normans last updated on 03/Feb/23 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\underset{−\mathrm{2}} {\overset{\mathrm{2}} {\int}}\:\:\:\:\frac{\boldsymbol{{x}}^{\mathrm{5}} \:−\:\:\mathrm{1}\:\:+\:\:\mathrm{2}}{\boldsymbol{{x}}^{\mathrm{4}} \:\:+\:\:\boldsymbol{{x}}\:\:−\mathrm{2}}\:\:\:\:\boldsymbol{{dx}}\:\:\:\:\:\:\: \\ $$$$ \\ $$ Commented by Frix last updated…
Question Number 186346 by test1234 last updated on 03/Feb/23 $${if}\:{S}_{{a}} =\mathrm{cos}\left({a}\right)+\mathrm{sin}\left({x}+{a}\right) \\ $$$${then}\:\int\frac{{S}_{\mathrm{1}} }{{S}_{\mathrm{2}} }−\frac{{x}+{S}_{\mathrm{1}} }{{x}−{S}_{\mathrm{3}} }=? \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 55271 by maxmathsup by imad last updated on 20/Feb/19 $$\left.\mathrm{1}\right)\:{let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\frac{{cost}}{\mathrm{3}\:+{sin}\left({xt}\right)}{dt} \\ $$$${find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\frac{{tcos}\left({xt}\right){cost}}{\left(\mathrm{3}\:+{sin}\left({xt}\right)\right)^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{{cost}}{\mathrm{3}+{sint}}\:\:{and}\:\:\:\int_{\mathrm{0}}…
Question Number 55267 by maxmathsup by imad last updated on 25/Feb/19 $$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:{ln}\left(\mathrm{1}+{xtan}\theta\right){d}\theta \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{values}\:{of}\:{integrals}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:{ln}\left(\mathrm{1}+{tan}\theta\right)\:\:{and}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {ln}\left(\mathrm{1}+\mathrm{2}{tan}\theta\right){d}\theta\:. \\ $$$$\left.\mathrm{1}\right)\:{we}\:{have}\:{f}^{'} \left({x}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\:\frac{{tan}\theta}{\mathrm{1}+{xtan}\theta}\:{d}\theta\:=\int_{\mathrm{0}}…
Question Number 186321 by Mingma last updated on 03/Feb/23 Answered by normans last updated on 03/Feb/23 $$\int_{\mathrm{1}} ^{{e}^{\left(\boldsymbol{{n}}+\mathrm{1}\right)} } \boldsymbol{{log}}\:\left(\boldsymbol{{x}}\right)=\boldsymbol{{e}}^{\boldsymbol{{n}}+\mathrm{1}} \left(\boldsymbol{{log}}\left(\boldsymbol{{e}}^{\boldsymbol{{n}}+\mathrm{1}} \right)−\mathrm{1}+\mathrm{1}\right. \\ $$$$\boldsymbol{{for}}\:\boldsymbol{{e}}^{\boldsymbol{{n}}} \geqslant\mathrm{0}\wedge\left(\boldsymbol{{e}}^{\boldsymbol{{n}}+\mathrm{1}}…
Question Number 120774 by mnjuly1970 last updated on 02/Nov/20 $$\:\:\:\:\:\:\:\:\:\:…{advanced}\:\:{calculus}… \\ $$$$\:\:\:\:\:\:\:{prove}\:\:{that}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}\left({x}\right)}{\:\sqrt[{\mathrm{3}}]{\mathrm{1}−{x}^{\mathrm{3}} }}{dx}\overset{???} {=}−\frac{\pi}{\mathrm{3}\sqrt{\mathrm{3}}}\left({ln}\left(\mathrm{3}\right)+\frac{\pi}{\mathrm{3}\sqrt{\mathrm{3}}}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{m}.{n}.\mathrm{1970}… \\ $$ Answered by mindispower…
Question Number 55237 by peter frank last updated on 19/Feb/19 $$\int_{\mathrm{0}} ^{\mathrm{3}} \int_{\mathrm{1}} ^{\mathrm{2}} \left(\mathrm{x}^{\mathrm{3}} +\mathrm{y}^{\mathrm{2}} \right)\mathrm{dxdy} \\ $$ Commented by Abdo msup. last updated…
Question Number 120775 by mnjuly1970 last updated on 02/Nov/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{advanced}\:\:{calculus}… \\ $$$$\:\:\:\:{evaluate}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Phi\overset{???} {=}\int_{\mathrm{0}} ^{\:\mathrm{1}} {ln}\left({x}\right){tan}^{−\mathrm{1}} \left({x}\right){dx} \\ $$$$\:\:\:\:\:\:\:\:\:…{m}.{n}.\mathrm{1970}… \\ $$ Answered by Dwaipayan…
Question Number 186310 by normans last updated on 03/Feb/23 $$ \\ $$$$\:\:\:\frac{\int\boldsymbol{{x}}\left(\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{5}\right)^{\mathrm{1}/\mathrm{2}} \boldsymbol{{dx}}\:−\:\mathrm{3}\int\boldsymbol{{x}}\left(\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{5}\right)^{−\mathrm{1}/\mathrm{2}} \:\boldsymbol{{dx}}}{\int\:\:\frac{\boldsymbol{{x}}\left[\left(\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{5}\right)−\mathrm{3}\right]}{\:\sqrt{\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{5}\:\:}}\:\boldsymbol{{dx}}}\:=??\:\:\:\: \\ $$$$ \\ $$ Answered by Frix…
Question Number 186306 by MikeH last updated on 03/Feb/23 $$\mathrm{Evaluate}\:\int\frac{\mathrm{ln}\left(\mathrm{sin}\:{x}\right)}{\mathrm{ln}\left(\mathrm{tan}\:{x}\right)+\mathrm{1}}\:{dx} \\ $$ Commented by MJS_new last updated on 03/Feb/23 $$\mathrm{indefinite}\:\mathrm{integral}\:\mathrm{not}\:\mathrm{possible} \\ $$ Commented by normans…