Question Number 133027 by Engr_Jidda last updated on 18/Feb/21 $$\overset{\mathrm{2}} {\int}_{\mathrm{0}} {x}^{\mathrm{5}} \left(\mathrm{8}−{x}^{\mathrm{3}} \right)^{\frac{\mathrm{1}}{\mathrm{3}}} {dx} \\ $$ Answered by Olaf last updated on 18/Feb/21 $$\Omega\:=\:\int_{\mathrm{0}}…
Question Number 133016 by metamorfose last updated on 18/Feb/21 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \left({tan}\left({x}\right)\right)^{\frac{\mathrm{1}}{{n}}} {dx}\:… \\ $$ Answered by Ar Brandon last updated on 18/Feb/21 $$\mathcal{I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}}…
Question Number 133004 by liberty last updated on 18/Feb/21 $$\mathrm{If}\:\int\:\frac{\mathrm{tan}\:\mathrm{x}}{\mathrm{1}+\mathrm{tan}\:\mathrm{x}+\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}}\:\mathrm{dx}\:=\:\mathrm{x}−\frac{{k}}{\:\sqrt{{A}}}\:\mathrm{tan}^{−\mathrm{1}} \left(\frac{{k}\:\mathrm{tan}\:{x}+\mathrm{1}}{\:\sqrt{{A}}}\right)+\mathrm{C} \\ $$$$\mathrm{where}\:\mathrm{C}\:\mathrm{is}\:\mathrm{constant}\:\mathrm{of}\:\mathrm{integration}. \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{ordered}\:\mathrm{pair}\:\left({k},\mathrm{A}\right)\:\mathrm{is}\: \\ $$$$\mathrm{equal}\:\mathrm{to}\: \\ $$ Answered by EDWIN88 last updated…
Question Number 67467 by ~ À ® @ 237 ~ last updated on 27/Aug/19 $$ \\ $$$$ \\ $$$${Find}\:\:\:\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:\:\frac{\:{tlnt}}{\left(\mathrm{1}+{t}^{\mathrm{2}} \right)^{{x}} }\:{dt}\: \\ $$…
Question Number 67466 by ~ À ® @ 237 ~ last updated on 27/Aug/19 $$ \\ $$$$ \\ $$$${let}\:{consider}\:\:\:{for}\:{all}\:{n}\geqslant\mathrm{1}\:{the}\:{real}\:\left({t}\right)_{{n}} \:={t}\left({t}+\mathrm{1}\right)…..\left({t}+{n}−\mathrm{1}\right) \\ $$$${Find}\:\:\:{L}_{{n}} =\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\left({t}\right)_{\mathrm{1}}…
Question Number 133001 by Ahmed1hamouda last updated on 17/Feb/21 Commented by mr W last updated on 18/Feb/21 $$\infty \\ $$$${no}\:{closed}\:{volume}! \\ $$ Terms of Service…
Question Number 67463 by ~ À ® @ 237 ~ last updated on 27/Aug/19 $${Find} \\ $$$${Find}\:\:\:{K}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \sqrt{{tan}\theta}\:{d}\theta\: \\ $$ Commented by ~ À…
Question Number 67462 by ~ À ® @ 237 ~ last updated on 27/Aug/19 $$ \\ $$$$\:{Calculate}\:{when}\:{a},{b}\:{are}\:{positive}\:{reals}\:\:\:{f}\left({a},{b}\right)=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{t}^{{a}} −{t}^{{b}} }{{lnt}}\:{dt}\: \\ $$ Commented by…
Question Number 1925 by Yozzi last updated on 24/Oct/15 $${Evaluate}\:{the}\:{following}\:{integral}. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:{I}=\int_{\mathrm{5}} ^{\mathrm{6}} \frac{{ln}\left(\mathrm{11}{x}+\mathrm{12}\right)}{{x}^{\mathrm{2}} +\mathrm{42}}{dx} \\ $$ Commented by prakash jain last updated on 25/Oct/15…
Question Number 132987 by mnjuly1970 last updated on 17/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:….{mathematical}\:\:{analysis}… \\ $$$$\:{prove}\:\:{that}::\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}^{\mathrm{3}} \left({x}\right)}{{x}^{\mathrm{3}} }{dx}=\frac{\mathrm{3}\pi}{\mathrm{8}} \\ $$$$\:\:\:\:\ast\ast\ast\ast………. \\ $$$$ \\ $$ Answered by Dwaipayan…