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Category: Integration

x-3-x-2-1-3-dx-

Question Number 54995 by peter frank last updated on 15/Feb/19 $$\int\:\sqrt[{\mathrm{3}}]{{x}^{\mathrm{3}} +{x}^{\mathrm{2}} }\:{dx} \\ $$ Commented by MJS last updated on 16/Feb/19 $$\mathrm{I}\:\mathrm{can}\:\mathrm{solve}\:\mathrm{this}\:\mathrm{but}\:\mathrm{it}'\mathrm{s}\:\mathrm{a}\:\mathrm{lot}\:\mathrm{of}\:\mathrm{typing}\:\mathrm{work} \\ $$$$\mathrm{if}\:\mathrm{you}\:\mathrm{need}\:\mathrm{it}\:\mathrm{urgently}\:\mathrm{I}\:\mathrm{will}\:\mathrm{post}\:\mathrm{it}…

let-f-0-1-x-2-2-cos-x-1-dx-with-R-1-calculate-f-2-find-the-value-of-g-0-1-xsin-x-2-2cos-x-1-dx-

Question Number 54936 by maxmathsup by imad last updated on 14/Feb/19 $${let}\:{f}\left(\theta\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\sqrt{{x}^{\mathrm{2}} \:+\mathrm{2}\left({cos}\theta\right){x}\:+\mathrm{1}}{dx}\:\:\:{with}\:\theta\:\in\:{R}\:. \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left(\theta\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:{g}\left(\theta\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{xsin}\theta}{\:\sqrt{{x}^{\mathrm{2}} \:+\mathrm{2}{cos}\theta\:{x}\:+\mathrm{1}}}{dx} \\ $$ Commented…

dx-sin-x-1-cos-x-

Question Number 185985 by cortano1 last updated on 30/Jan/23 $$\:\:\:\int\:\frac{{dx}}{\:\sqrt{\mathrm{sin}\:{x}\left(\mathrm{1}+\mathrm{cos}\:{x}\right)}}\:=? \\ $$ Answered by ARUNG_Brandon_MBU last updated on 30/Jan/23 $${I}=\int\frac{{dx}}{\:\sqrt{\mathrm{sin}{x}\left(\mathrm{1}+\mathrm{cos}{x}\right)}}=\int\frac{{dx}}{\mathrm{2}\sqrt{\mathrm{sin}\frac{{x}}{\mathrm{2}}\mathrm{cos}^{\mathrm{3}} \frac{{x}}{\mathrm{2}}}} \\ $$$$\:\:=\int\frac{\frac{\mathrm{1}}{\mathrm{2}}\mathrm{sec}^{\mathrm{2}} \frac{{x}}{\mathrm{2}}}{\:\sqrt{\mathrm{tan}\frac{{x}}{\mathrm{2}}}}{dx}=\int\frac{{d}\left(\mathrm{tan}\frac{{x}}{\mathrm{2}}\right)}{\:\sqrt{\mathrm{tan}\frac{{x}}{\mathrm{2}}}}=\mathrm{2}\sqrt{\mathrm{tan}\frac{{x}}{\mathrm{2}}}+{C} \\…

x2-2x-2-

Question Number 54896 by yusufbode1996 last updated on 14/Feb/19 $$\int\sqrt{}\left({x}\mathrm{2}+\mathrm{2}{x}+\mathrm{2}\right) \\ $$ Commented by maxmathsup by imad last updated on 14/Feb/19 $${let}\:{I}\:=\int\:\sqrt{{x}^{\mathrm{2}} \:+\mathrm{2}{x}+\mathrm{2}}{dx}\:\Rightarrow{I}\:=\int\:\sqrt{\left({x}+\mathrm{1}\right)^{\mathrm{2}} \:+\mathrm{1}}{dx}\:\:{changement}\:{x}+\mathrm{1}\:={sh}\left({t}\right)\:{give} \\…