Question Number 152140 by Ar Brandon last updated on 26/Aug/21 $${I}=\int_{\mathrm{0}} ^{\mathrm{2n}\pi} \mathrm{max}\left(\mathrm{sin}{x},\:\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{sin}{x}\right)\right){dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 152142 by Ar Brandon last updated on 26/Aug/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}}{\left(\mathrm{1}−{x}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} }\mathrm{ln}\left(\mathrm{ln}\frac{\mathrm{1}}{{x}}\right){dx}=−\frac{\gamma}{\mathrm{3}}−\frac{\mathrm{1}}{\mathrm{3}}\mathrm{ln}\frac{\mathrm{6}\sqrt{\mathrm{3}}}{\pi}+\frac{\pi\sqrt{\mathrm{3}}}{\mathrm{27}}\left(\mathrm{5ln2}\pi−\mathrm{6ln}\Gamma\left(\frac{\mathrm{1}}{\mathrm{6}}\right)\right) \\ $$ Answered by mindispower last updated on 28/Aug/21 $$\int_{\mathrm{0}}…
Question Number 86591 by M±th+et£s last updated on 29/Mar/20 $$\int_{−\mathrm{1}} ^{\mathrm{1}} \lfloor\:\mid{x}\mid+\sqrt[{\mathrm{3}}]{{x}}\:\rfloor\:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 152112 by peter frank last updated on 25/Aug/21 $$\mathrm{If}\:\mathrm{I}_{\mathrm{n}} =\int\frac{\mathrm{cos}\:\mathrm{nx}}{\mathrm{cos}\:\mathrm{x}}\mathrm{dx}\:\:\:\mathrm{then}\:\mathrm{1}_{\mathrm{n}} =? \\ $$ Answered by Olaf_Thorendsen last updated on 26/Aug/21 $$\mathrm{I}_{{n}} \:=\:\int\frac{\mathrm{cos}\left({nx}\right)}{\mathrm{cos}{x}}\:{dx} \\…
Question Number 86578 by Omer Alattas last updated on 29/Mar/20 Commented by john santu last updated on 29/Mar/20 $$\mathrm{let}\:\mathrm{F}\left(\mathrm{x}\right)\:\mathrm{antiderivative}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\int\underset{\mathrm{3}} {\overset{\:\mathrm{x}} {\:}}\:\frac{\mathrm{sin}\:\mathrm{t}\:\mathrm{dt}}{\mathrm{t}} \\ $$$$\mathrm{such}\:\mathrm{that}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{F}\left(\mathrm{x}\right)\:−\mathrm{F}\left(\mathrm{3}\right) \\ $$$$\mathrm{now}\:\underset{{x}\rightarrow\mathrm{3}}…
Question Number 152116 by peter frank last updated on 25/Aug/21 $$\int\frac{\mathrm{sin}\:\mathrm{x}}{\:\sqrt{\mathrm{1}+\mathrm{sin}\:\mathrm{x}}}\mathrm{dx} \\ $$ Commented by puissant last updated on 26/Aug/21 $${Q}=\int\frac{−{cos}\left(\frac{\pi}{\mathrm{2}}+{x}\right)}{\:\sqrt{\left({sin}\left(\frac{{x}}{\mathrm{2}}\right)+{cos}\left(\frac{{x}}{\mathrm{2}}\right)\right)^{\mathrm{2}} }}{dx} \\ $$$$=−\int\frac{{cos}\left(\frac{\pi}{\mathrm{2}}+{x}\right)}{{sin}\left(\frac{{x}}{\mathrm{2}}\right)+{cos}\left(\frac{{x}}{\mathrm{2}}\right)}{dx} \\…
Question Number 86576 by jagoll last updated on 29/Mar/20 $$\int\:\frac{\mathrm{ln}\:\left(\mathrm{1}+\mathrm{arc}\:\mathrm{sin}\:\left(\mathrm{x}^{\mathrm{2}} \right)\right)}{\mathrm{sin}\:\left(\mathrm{x}^{\mathrm{2}} \right)}\:\mathrm{dx}\:? \\ $$ Commented by M±th+et£s last updated on 29/Mar/20 $${sir}\:{you}\:{mean}\:{arcsin}\left({x}^{\mathrm{2}} \right)\:{or}\:\left({a}\right){sin}\left({x}^{\mathrm{2}} \right) \\…
Question Number 152115 by peter frank last updated on 25/Aug/21 $$\int\frac{\mathrm{dx}}{\mathrm{asin}\:\mathrm{x}+\mathrm{bcos}\:\mathrm{x}} \\ $$ Answered by aleks041103 last updated on 26/Aug/21 $$\int\frac{\mathrm{dx}}{\mathrm{asin}\:\mathrm{x}+\mathrm{bcos}\:\mathrm{x}}= \\ $$$$=\frac{\mathrm{1}}{\:\sqrt{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }}\int\frac{{dx}}{{sin}\left({x}+{r}\right)},\:{r}={atan}\left({b}/{a}\right)…
Question Number 152111 by peter frank last updated on 25/Aug/21 $$\int\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{sec}\:\mathrm{x}+\mathrm{tan}\:\mathrm{x}\right)\mathrm{dx} \\ $$ Answered by peter frank last updated on 26/Aug/21 $$\int\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}+\mathrm{sin}\:\mathrm{x}}{\mathrm{cos}\:\mathrm{x}}\right) \\…
Question Number 152106 by Tawa11 last updated on 25/Aug/21 $$\int\:\mathrm{x}^{\mathrm{n}} \:\mathrm{cos}\left(\mathrm{nx}\right)\:\mathrm{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com