Question Number 141848 by iloveisrael last updated on 24/May/21 $$\:\mathscr{I}\:=\:\int\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }−\mathrm{1}}\:{dx}\: \\ $$ Answered by ArielVyny last updated on 24/May/21 $${we}\:{know}\:{that}\:\:{cos}^{\mathrm{2}} {x}+{sin}^{\mathrm{2}} {x}=\mathrm{1} \\ $$$${let}\:{us}\:{consider}\:{that}\:\:{x}={sint}…
Question Number 141847 by iloveisrael last updated on 24/May/21 $$\:\mathcal{I}\:=\:\int\:\frac{\mathrm{sec}\:{x}}{\mathrm{1}+\mathrm{csc}\:{x}}\:{dx}\: \\ $$ Answered by MJS_new last updated on 24/May/21 $$\int\frac{\mathrm{sec}\:{x}}{\mathrm{1}+\mathrm{csc}\:{x}}= \\ $$$$\:\:\:\:\:\left[{t}=\mathrm{tan}\:\frac{{x}}{\mathrm{2}}\:\rightarrow\:{dx}=\mathrm{2cos}^{\mathrm{2}} \:\frac{{x}}{\mathrm{2}}\:{dt}\right] \\ $$$$=−\mathrm{4}\int\frac{{t}}{\left({t}−\mathrm{1}\right)\left({t}+\mathrm{1}\right)^{\mathrm{3}}…
Question Number 76298 by benjo last updated on 26/Dec/19 $$\int\sqrt{\:\mathrm{tanx}+\mathrm{cotxdx}} \\ $$ Commented by benjo last updated on 26/Dec/19 Commented by john santuy last updated…
Question Number 10761 by 2525 last updated on 24/Feb/17 $$\mathrm{Express}\:\mathrm{the}\:\mathrm{following}\:\Gamma\:\mathrm{function}\:\mathrm{using}\:\mathrm{tables} \\ $$$$\mathrm{and}\:\mathrm{evaluate}\:\mathrm{them}\:\mathrm{using}\:\mathrm{a}\:\mathrm{table}\:\mathrm{or}\:\Gamma\:\mathrm{functions}. \\ $$$$ \\ $$$$\int_{\mathrm{0}} ^{\infty} {x}^{−\mathrm{1}/\mathrm{3}} {e}^{−\mathrm{8}{x}\:} {dx} \\ $$ Terms of Service…
Question Number 141811 by mnjuly1970 last updated on 23/May/21 $$\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\Theta:=\left(\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{{n}^{\mathrm{4}} }{\mathrm{2}^{{n}} \:.\:{n}!}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} =? \\ $$ Answered by qaz last updated on…
Question Number 141757 by Ndala last updated on 23/May/21 $$\Gamma\left(\mathrm{n}+\frac{\mathrm{1}}{\mathrm{2}}\right)=\frac{\sqrt{\pi}\centerdot\Gamma\left(\mathrm{2n}+\mathrm{1}\right)}{\mathrm{2}^{\mathrm{2n}} \Gamma\left(\mathrm{n}+\mathrm{1}\right)} \\ $$ Commented by Ndala last updated on 23/May/21 $$\mathrm{someone}\:\mathrm{to}\:\mathrm{help}\:\mathrm{me}\:\mathrm{with}\:\mathrm{the}\:\mathrm{proof}.\:\mathrm{Please} \\ $$ Terms of…
Question Number 76220 by Master last updated on 25/Dec/19 Commented by benjo last updated on 25/Dec/19 $$\mathrm{waw}..\mathrm{this}\:\mathrm{problem}\:\mathrm{very}\:\mathrm{nice} \\ $$ Answered by MJS last updated on…
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Question Number 10669 by mrW1 last updated on 22/Feb/17 $$\int\sqrt{{a}^{\mathrm{2}} −\mathrm{cos}^{\mathrm{2}} \:{x}\:}{dx}=?\:\:\:\left({a}\geqslant\mathrm{1}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 76194 by abdomathmax last updated on 25/Dec/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{cos}\left({x}^{\mathrm{2}} \right)}{{x}^{\mathrm{4}} −{x}^{\mathrm{2}} \:+\mathrm{1}}{dx} \\ $$ Commented by abdomathmax last updated on 25/Dec/19 $${let}\:{A}\:=\int_{\mathrm{0}}…