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Category: Integration

tan3x-sec3x-dx-

Question Number 93959 by mashallah last updated on 16/May/20 $$\int\left(\mathrm{tan3x}+\mathrm{sec3x}\right)\mathrm{dx}= \\ $$ Answered by john santu last updated on 16/May/20 $$\int\:\frac{\mathrm{sin}\:\mathrm{3x}}{\mathrm{cos}\:\mathrm{3x}}\:\mathrm{dx}\:=\:−\frac{\mathrm{1}}{\mathrm{3}}\int\:\frac{\mathrm{d}\left(\mathrm{cos}\:\mathrm{3x}\right)}{\mathrm{cos}\:\mathrm{3x}} \\ $$$$=\:−\frac{\mathrm{1}}{\mathrm{3}}\mathrm{ln}\:\mid\mathrm{cos}\:\mathrm{3x}\mid\: \\ $$$$\int\:\mathrm{sec}\:\mathrm{3x}\:\mathrm{dx}\:=\:\frac{\mathrm{1}}{\mathrm{3}}\int\:\mathrm{sec}\:\mathrm{3x}\:\mathrm{d}\left(\mathrm{3x}\right)…

sinx-cosx-sinx-cosx-dx-

Question Number 93958 by mashallah last updated on 16/May/20 $$\int\frac{\mathrm{sinx}−\mathrm{cosx}}{\mathrm{sinx}+\mathrm{cosx}}\mathrm{dx}= \\ $$ Commented by mathmax by abdo last updated on 17/May/20 $${I}\:=\int\:\frac{{sinx}−{cosx}}{{sinx}\:+{cosx}}{dx}\:\Rightarrow{I}\:=\int\frac{{tanx}−\mathrm{1}}{{tanx}\:+\mathrm{1}}{dx}\:=_{{tanx}\:={t}} \\ $$$$=\int\frac{{t}−\mathrm{1}}{{t}+\mathrm{1}}×\frac{{dt}}{\mathrm{1}+{t}^{\mathrm{2}} }\:=\int\:\:\:\:\frac{{t}−\mathrm{1}}{\left({t}+\mathrm{1}\right)\left({t}^{\mathrm{2}}…

Show-that-the-function-f-x-e-x-is-of-Reimann-within-x-1-5-hence-calculate-1-5-e-x-dx-

Question Number 93941 by Ar Brandon last updated on 16/May/20 $$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{function}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{e}^{\mathrm{x}\:} \:\mathrm{is}\:\mathrm{of}\:\mathrm{Reimann}\:\mathrm{within} \\ $$$$\mathrm{x}\in\left[\mathrm{1};\mathrm{5}\right]\:\mathrm{hence}\:\mathrm{calculate}\:\int_{\mathrm{1}} ^{\mathrm{5}} \mathrm{e}^{\mathrm{x}} \mathrm{dx} \\ $$ Commented by mathmax by abdo last…

1-tan-x-dx-

Question Number 93937 by seedhamaieng@gmail.com last updated on 16/May/20 $$\int\frac{\mathrm{1}}{\:\sqrt{\mathrm{tan}\:{x}}}{dx}=? \\ $$ Commented by i jagooll last updated on 16/May/20 $$\int\:\frac{\mathrm{sec}\:^{\mathrm{2}} \mathrm{x}}{\mathrm{sec}\:^{\mathrm{2}} \mathrm{x}\:\sqrt{\mathrm{tan}\:\mathrm{x}}}\:\mathrm{dx}\:= \\ $$$$\int\:\frac{\mathrm{du}}{\left(\mathrm{1}+\mathrm{u}^{\mathrm{2}}…

1-calculate-A-n-0-pi-2-cos-n-x-dx-2-calculate-dx-x-2-x-1-n-n-integr-natural-

Question Number 93907 by abdomathmax last updated on 16/May/20 $$\left.\mathrm{1}\right)\:{calculate}\:\:{A}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{cos}^{{n}} {x}\:{dx} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{−\infty} ^{+\infty} \:\frac{{dx}}{\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)^{{n}} } \\ $$$${n}\:{integr}\:{natural} \\ $$ Commented…

let-f-x-2-3-x-and-g-x-x-2-2x-5-1-calculate-fog-x-and-determine-D-fog-2-calculate-fog-x-dx-3-calculate-f-1-x-f-x-dx-and-f-1-og-x-fog-x-dx-

Question Number 93898 by mathmax by abdo last updated on 16/May/20 $${let}\:{f}\left({x}\right)=\mathrm{2}\sqrt{\mathrm{3}−{x}}\:{and}\:{g}\left({x}\right)\:={x}^{\mathrm{2}} −\mathrm{2}{x}\:+\mathrm{5} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{fog}\left({x}\right)\:{and}\:{determine}\:{D}_{{fog}} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int\:{fog}\left({x}\right){dx} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int\:\frac{{f}^{−\mathrm{1}} \left({x}\right)}{{f}\left({x}\right)}{dx}\:\:{and}\:\:\int\:\frac{{f}^{−\mathrm{1}} {og}\left({x}\right)}{{fog}\left({x}\right)}{dx} \\ $$ Commented by…