Question Number 141333 by cesarL last updated on 17/May/21 $$\int{x}^{\mathrm{2}} \mathrm{cos}\:\left(\frac{{x}}{\mathrm{2}}\right){dx} \\ $$ Answered by qaz last updated on 17/May/21 $$\int{x}^{\mathrm{2}} \mathrm{cos}\:\frac{{x}}{\mathrm{2}}{dx} \\ $$$$=\mathrm{2}{x}^{\mathrm{2}} \mathrm{sin}\:\frac{{x}}{\mathrm{2}}−\mathrm{4}\int{x}\mathrm{sin}\:\frac{{x}}{\mathrm{2}}{dx}…
Question Number 141319 by mnjuly1970 last updated on 18/May/21 $$\:\:\: \\ $$$$\:\:\:\:\:{prove}:: \\ $$$$\:\:\:\:\:\:\:\Omega:=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}^{\mathrm{2}} \left({x}\right)}{\mathrm{1}−{x}^{\mathrm{4}} }{dx}\:=\frac{\pi^{\mathrm{3}} }{\mathrm{32}}+\frac{\mathrm{7}}{\mathrm{8}}\zeta\left(\mathrm{3}\right).. \\ $$ Answered by qaz last…
Question Number 141312 by qaz last updated on 17/May/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{n}} \frac{{Si}\left(\mathrm{2}\pi{n}\right)−\frac{\pi}{\mathrm{2}}}{{n}}=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 10241 by FilupSmith last updated on 31/Jan/17 $$\int_{{a}} ^{\:{a}+\delta} \frac{\mathrm{sin}\left({x}\right)}{\mathrm{cos}\left({x}+\delta\right)}{dx}\:=\:??? \\ $$ Commented by prakash jain last updated on 31/Jan/17 $$\frac{\mathrm{sin}\left({x}\right)}{\mathrm{cos}\left({x}+\delta\right)}=\frac{\mathrm{sin}\left({x}+\delta−\delta\right)}{\mathrm{cos}\left({x}+\delta\right)} \\ $$$$=\frac{\mathrm{sin}\:\left({x}+\delta\right)\mathrm{cos}\:\delta−\mathrm{cos}\:\left({x}+\delta\right)\mathrm{sin}\:\delta}{\mathrm{cos}\:\left({x}+\delta\right)}…
Question Number 75772 by Ajao yinka last updated on 16/Dec/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 75773 by Ajao yinka last updated on 16/Dec/19 Answered by mind is power last updated on 16/Dec/19 $$\mathrm{log}\left(\mathrm{1}+\mathrm{e}^{\mathrm{x}} \right)=\mathrm{x}+\mathrm{log}\left(\mathrm{1}+\mathrm{e}^{−\mathrm{x}} \right) \\ $$$$=\int_{\mathrm{0}} ^{+\infty}…
Question Number 75770 by Ajao yinka last updated on 16/Dec/19 Commented by ~blr237~ last updated on 17/Dec/19 $$\mathrm{A}=\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{dx}}{\mathrm{e}^{\mathrm{x}} \sqrt{\mathrm{sinh2x}}}\:=\sqrt{\mathrm{2}}\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{e}^{−\mathrm{x}} \mathrm{dx}}{\:\sqrt{\mathrm{e}^{\mathrm{2x}} −\mathrm{e}^{−\mathrm{2x}}…
Question Number 75769 by Ajao yinka last updated on 16/Dec/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 75768 by Ajao yinka last updated on 16/Dec/19 Answered by mind is power last updated on 17/Dec/19 $$\mathrm{not}\:\mathrm{Clear}\:\mathrm{sir} \\ $$ Commented by Ajao…
Question Number 75750 by rajesh4661kumar@gmail.com last updated on 16/Dec/19 Commented by MJS last updated on 16/Dec/19 $$\mathrm{this}\:\mathrm{cannot}\:\mathrm{be}\:\mathrm{solved}\:\mathrm{using}\:\mathrm{elementary} \\ $$$$\mathrm{calculus} \\ $$$$\mathrm{a}\:\mathrm{solution}\:\mathrm{was}\:\mathrm{posted}\:\mathrm{on}\:\mathrm{this}\:\mathrm{forum}\:\mathrm{some} \\ $$$$\mathrm{time}\:\mathrm{ago} \\ $$…