Question Number 164163 by Zaynal last updated on 15/Jan/22 $$\mathrm{Prove}\:\mathrm{the}; \\ $$$$\int_{−\infty} ^{\infty} \:\frac{\mathrm{1}}{\mathrm{1}\:+\:\boldsymbol{{x}}^{\mathrm{2}} }\:\boldsymbol{{dx}}\:=\:\boldsymbol{\pi} \\ $$$$\:^{\left\{\mathrm{Z}.\mathrm{A}\right\}} \\ $$ Answered by mathmax by abdo last…
Question Number 164162 by Zaynal last updated on 15/Jan/22 $$\mathrm{Prove}\:\mathrm{the}; \\ $$$$\left(\boldsymbol{{tan}}\:\boldsymbol{\alpha}\:+\:\frac{\boldsymbol{{cos}}\:\boldsymbol{\alpha}}{\mathrm{1}\:+\:\boldsymbol{{sin}}\:\boldsymbol{\alpha}}\right)\:\boldsymbol{{sin}}\:\boldsymbol{\alpha}\:=\:\boldsymbol{\alpha} \\ $$$$\:^{\left[\mathrm{Z}.\mathrm{A}\right]} \\ $$ Commented by som(math1967) last updated on 15/Jan/22 $$\left\{\boldsymbol{{tan}\alpha}\:+\frac{\boldsymbol{{cos}\alpha}\left(\mathrm{1}−\boldsymbol{{sin}\alpha}\right)}{\mathrm{1}−\boldsymbol{{sin}}^{\mathrm{2}} \boldsymbol{\alpha}}\right\}×{sin}\alpha…
Question Number 98623 by hardylanes last updated on 15/Jun/20 $${evaluate}\: \\ $$$$\int_{\frac{\mathrm{2}}{\:\sqrt{\mathrm{3}}}} ^{\mathrm{2}} \frac{\mathrm{1}}{{x}^{\mathrm{2}} \sqrt{\mathrm{4}+{x}^{\mathrm{2}} }}{dx}\:{using}\:{the}\:{substitution}\:{x}=\mathrm{2tan}\theta \\ $$$$ \\ $$ Answered by Kunal12588 last updated…
Question Number 33069 by abdo imad last updated on 09/Apr/18 $${by}\:\:{using}\:{residus}\:{theorem}\:{prove}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{t}^{{a}−\mathrm{1}} }{\mathrm{1}+{t}}\:{dt}\:=\:\frac{\pi}{{sin}\left(\pi{a}\right)}\:{with}\:\:\mathrm{0}<{a}<\mathrm{1}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 164129 by mnjuly1970 last updated on 14/Jan/22 $$ \\ $$$$\:\:\:{prove} \\ $$$$ \\ $$$$\:\:\:\:\:\boldsymbol{\phi}=\:\mathscr{R}{e}\:\left(\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\mathrm{Li}_{\:\mathrm{2}} \:\left(\:\frac{\mathrm{1}}{{x}}\:\right)\:\right){dx}\:=\:\zeta\:\left(\mathrm{2}\right) \\ $$$$\:\:\:\:\:\:−−−{m}.{n}−−− \\ $$ Answered by…
Question Number 98594 by bemath last updated on 15/Jun/20 Answered by bobhans last updated on 15/Jun/20 $$\int\:\mathrm{e}^{\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{2}}} \:\left(\mathrm{x}^{\mathrm{2}} +\mathrm{2x}+\mathrm{1}\right)\:\mathrm{dx}\:=\:\int\:\mathrm{e}^{\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{2}}} \:\mathrm{x}^{\mathrm{2}} \:\mathrm{dx}\:+\:\int\:\mathrm{2x}\:\mathrm{e}^{\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{2}}} \:\mathrm{dx}\:+\:\int\:\mathrm{e}^{\frac{\mathrm{x}^{\mathrm{2}}…
Question Number 98589 by mathmax by abdo last updated on 14/Jun/20 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{sin}\left(\alpha\mathrm{x}^{\mathrm{2}} \right)}{\mathrm{x}^{\mathrm{2}} \:+\mathrm{4}}\mathrm{dx}\:\:\mathrm{with}\:\alpha\:\mathrm{real} \\ $$ Answered by mathmax by abdo last updated…
Question Number 98588 by mathmax by abdo last updated on 14/Jun/20 $$\mathrm{calculate}\:\int_{−\infty} ^{\infty} \:\frac{\mathrm{xsin}\left(\mathrm{x}\right)}{\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} }\mathrm{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 164120 by Zaynal last updated on 14/Jan/22 $$\mathrm{How}\:\mathrm{do}\:\mathrm{you}\:\mathrm{all}\:\mathrm{to}\:\mathrm{prove}\:\mathrm{Integral}; \\ $$$$\:\boldsymbol{{Prove}}\:\boldsymbol{{the}}; \\ $$$$\:\int\:\frac{\left(\boldsymbol{{In}}\:\boldsymbol{{x}}\right)\mathrm{2}}{\boldsymbol{{x}}}\:\boldsymbol{{dx}}\:=\:\frac{\mathrm{1}}{\mathrm{3}}\:\left(\boldsymbol{{In}}\:\boldsymbol{{x}}\right)^{\mathrm{3}} \\ $$ Commented by som(math1967) last updated on 14/Jan/22 $$\int\left({lnx}\right)^{\mathrm{2}} {d}\left({lnx}\right)=\frac{\mathrm{1}}{\mathrm{3}}\left({lnx}\right)^{\mathrm{3}}…
Question Number 164123 by Zaynal last updated on 14/Jan/22 $$\mathrm{very}\:\mathrm{nice}\:\mathrm{to}\:\mathrm{problem}: \\ $$$$\boldsymbol{{find}}\:\boldsymbol{{in}}\:\boldsymbol{{closed}}\:\boldsymbol{{form}}; \\ $$$$\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\boldsymbol{{log}}\:\left(\mathrm{1}−\boldsymbol{{x}}^{\mathrm{2}} \right)\:\boldsymbol{{log}}\:^{\boldsymbol{{n}}\:} \:\left(\mathrm{1}−\boldsymbol{{x}}\right)\:\boldsymbol{{dx}}; \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{n}}\:\in\:\:\mathbb{N}^{+} \\ $$$$\:^{\mathrm{z}.} \\ $$ Terms…