Question Number 158596 by mnjuly1970 last updated on 06/Nov/21 $$ \\ $$$$\:\:\:\:\:{calculate}\:: \\ $$$$\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \frac{\:\mathrm{1}+\:{tan}^{\:\mathrm{4}} \left({x}\right)}{{cot}^{\:\mathrm{2}} \left({x}\right)}\:{dx}=? \\ $$$$ \\ $$ Answered by puissant…
Question Number 93061 by Ar Brandon last updated on 10/May/20 $$\int_{\mathrm{1}} ^{+\infty} \frac{\mathrm{sin}\:\mathrm{u}}{\mathrm{u}}\mathrm{du} \\ $$ Commented by mathmax by abdo last updated on 10/May/20 $${we}\:{have}\frac{\pi}{\mathrm{2}}\:=\int_{\mathrm{0}}…
Question Number 158591 by cortano last updated on 06/Nov/21 $$\:{I}=\int\:\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{6}} }\:=? \\ $$ Commented by tounghoungko last updated on 06/Nov/21 $${I}=\int\:\frac{{x}^{\mathrm{2}} +\mathrm{1}}{{x}^{\mathrm{6}} +\mathrm{1}}\:{dx}−\int\:\frac{{x}^{\mathrm{2}} }{{x}^{\mathrm{6}} +\mathrm{1}}\:{dx}…
Question Number 158590 by mnjuly1970 last updated on 06/Nov/21 $$ \\ $$$$\:\:\:{prove}\:{that}\: \\ $$$$\mathrm{1}.\:\mathrm{I}=\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{\:{sin}\left(\:{x}+{tan}\left({x}\right)\right)}{{sin}\left({x}\right)}{dx}\:=\frac{\pi}{\mathrm{2}} \\ $$$$\mathrm{2}.\:\mathrm{J}\:=\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{{sin}\left({x}−{tan}\left({x}\right)\right)}{{sin}\left({x}\right)}{dx}=\left(\frac{\mathrm{1}}{{e}}\:−\frac{\mathrm{1}}{\mathrm{2}}\right)\pi \\ $$$$ \\ $$ Answered…
Question Number 93045 by john santu last updated on 10/May/20 $$\int\:\mathrm{sin}^{−\mathrm{1}} \left(\sqrt{\frac{{x}}{\mathrm{2}}}\right)\:{dx}\: \\ $$ Commented by mathmax by abdo last updated on 10/May/20 $${I}\:=\int\:\:{arcsin}\left(\sqrt{\frac{{x}}{\mathrm{2}}}\right){dx}\:\:\:\:{changement}\:\sqrt{\frac{{x}}{\mathrm{2}}}={t}\:{give}\:\frac{{x}}{\mathrm{2}}={t}^{\mathrm{2}} \:\Rightarrow{x}=\mathrm{2}{t}^{\mathrm{2}}…
Question Number 93038 by i jagooll last updated on 10/May/20 $$\underset{\mathrm{1}} {\overset{\mathrm{5}} {\int}}\:\sqrt{\mathrm{x}^{\mathrm{3}} +\mathrm{1}}\:\mathrm{dx}\:=\:? \\ $$ Commented by abdomathmax last updated on 14/May/20 $${I}\:\:=\int_{\mathrm{1}} ^{\mathrm{5}}…
Question Number 27502 by abdo imad last updated on 07/Jan/18 $${find}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{ln}\left(\mathrm{1}+{xsin}^{\mathrm{2}} {t}\right)}{{sin}^{\mathrm{2}} {t}}{dt}\:{with}\:−\mathrm{1}<{x}<\mathrm{1}\:. \\ $$ Commented by abdo imad last updated on 09/Jan/18…
Question Number 27500 by abdo imad last updated on 07/Jan/18 $${find}\:\int\int_{\Delta} \sqrt{\mathrm{4}\:−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} \:}\:\:{dxdy}\:{with} \\ $$$$\Delta=\left\{\left({x},{y}\right)\:\in\mathbb{R}^{\mathrm{2}} /\:{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:\leqslant\mathrm{2}{x}\right\} \\ $$ Commented by abdo imad…
Question Number 27496 by abdo imad last updated on 07/Jan/18 $${let}\:{give}\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{\propto} \:\:\frac{\mathrm{1}}{\:\sqrt{{t}}}\:{e}^{−\left(\mathrm{1}+{ix}\right){t}} {dt} \\ $$$${calculate}\:{f}^{'} \left({x}\right)\:{prove}\:{that}\:\exists\lambda\in{R}/\left({x}+{i}\right)^{\mathrm{2}} \:\left({f}\left({x}\right)\right)^{\mathrm{2}} =\:\lambda \\ $$$${then}\:{find}\:\:\int_{\mathrm{0}} ^{\propto} \:\:{e}^{−{t}^{\mathrm{2}} } {dt}\:.…
Question Number 93031 by Power last updated on 10/May/20 Commented by Power last updated on 10/May/20 $$\mathrm{sir}\:\mathrm{indefinite}\:\mathrm{integration} \\ $$ Commented by prakash jain last updated…