Question Number 134828 by liberty last updated on 09/Mar/21 $$\underset{\mathrm{0}} {\int}^{\:\frac{\pi}{\mathrm{2}}} \frac{\mathrm{sin}\:\left(\frac{\mathrm{2}{x}}{\mathrm{3}}\right)}{\mathrm{tan}\:\left({x}\right)}\:{dx}\:=?\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 134820 by 0731619177 last updated on 07/Mar/21 Answered by Ar Brandon last updated on 07/Mar/21 $$\mathcal{I}=\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{xyz}}{\left(\mathrm{x}+\mathrm{y}\right)\left(\mathrm{x}+\mathrm{z}\right)\left(\mathrm{z}+\mathrm{y}\right)}\mathrm{dxdydz} \\…
Question Number 134811 by bramlexs22 last updated on 07/Mar/21 $$\int_{\mathrm{0}} ^{\:\pi/\mathrm{2}} \:\frac{\mathrm{sin}\:\left(\frac{\mathrm{3x}}{\mathrm{2}}\right)}{\mathrm{tan}\:\left(\mathrm{3x}\right)}\:\mathrm{dx} \\ $$ Answered by EDWIN88 last updated on 07/Mar/21 $$\mathrm{set}\:\frac{\mathrm{3x}}{\mathrm{2}}\:=\:\mathrm{t}\:\Rightarrow\:\mathrm{3x}\:=\:\mathrm{2t}\:,\:\begin{array}{|c|c|}{\mathrm{x}=\frac{\pi}{\mathrm{2}}\rightarrow\mathrm{t}=\frac{\mathrm{3}\pi}{\mathrm{4}}}\\{\mathrm{x}=\mathrm{0}\:\rightarrow\mathrm{t}=\mathrm{0}}\\\hline\end{array} \\ $$$$\mathbb{L}\:=\:\int_{\mathrm{0}} ^{\:\mathrm{3}\pi/\mathrm{4}}…
Question Number 134795 by 0731619177 last updated on 07/Mar/21 Answered by EDWIN88 last updated on 07/Mar/21 $$\:\mathrm{noting}\:\mathrm{that}\:\mathrm{the}\:\mathrm{integrand}\:\mathrm{is}\:\mathrm{even}\:\mathrm{function} \\ $$$$\mathrm{I}=\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{sin}\:\left(\pi\mathrm{x}\right)}{\mathrm{x}\left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)}\:\mathrm{dx}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\int_{−\infty} ^{\infty} \frac{\mathrm{sin}\:\left(\pi\mathrm{x}\right)}{\mathrm{x}\left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)}\:\mathrm{dx}…
Question Number 69261 by mathmax by abdo last updated on 22/Sep/19 $${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{xtanx}\:{dx} \\ $$ Answered by mind is power last updated on 23/Sep/19…
Question Number 69257 by Henri Boucatchou last updated on 21/Sep/19 $$\int_{−\mathrm{2}} ^{\:\:\mathrm{4}} \mid\boldsymbol{{x}}\mid^{\mathrm{2}\boldsymbol{{x}}^{\mathrm{3}} } \boldsymbol{{dx}}\:=\:? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 69246 by ~ À ® @ 237 ~ last updated on 21/Sep/19 $$\:\:\:{Explicit}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{Si}\left({ax}\right)}{{x}+{b}}\:{dx}\:\:\:{with}\:\:{Si}\left({u}\right)=\int_{\mathrm{0}} ^{{u}} \:\frac{{sinx}}{{x}}{dx} \\ $$ Terms of Service Privacy…
Question Number 69241 by ~ À ® @ 237 ~ last updated on 21/Sep/19 $$\:{Let}\:{consider}\:{K}=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\left(\mathrm{1}−{x}^{{a}} \right)\left(\mathrm{1}−{x}^{{b}} \right)\left(\mathrm{1}−{x}^{{c}} \right)}{\left({x}−\mathrm{1}\right){lnx}}{dx}\: \\ $$$${prove}\:{that}\: \\ $$$${e}^{{K}} =\:\frac{\left({a}+{b}\right)!\left({a}+{c}\right)!\left({b}+{c}\right)!}{{a}!{b}!{c}!\left({a}+{b}+{c}\right)!}\:\:…
Question Number 69238 by ~ À ® @ 237 ~ last updated on 21/Sep/19 $${Use}\:{Residus}\:{Theorem}\:{to}\:{explicit}\: \\ $$$${f}\left({a}\right)=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\left(−\mathrm{1}\right)^{{n}} {sin}\left({na}\right)}{{n}^{\mathrm{3}} }\:\: \\ $$ Commented by…
Question Number 69233 by ~ À ® @ 237 ~ last updated on 21/Sep/19 $${Prove}\:{that}\:\:{B}=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\left[{ln}\left(−{lnu}\right)\right]^{\mathrm{2}} \:{du}\:=\:\gamma^{\mathrm{2}} +\:\zeta\left(\mathrm{2}\right)\:\: \\ $$ Commented by mathmax by…