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Category: Integration

5cos-2-x-4-dx-

Question Number 116237 by bobhans last updated on 02/Oct/20 $$\int\:\sqrt{\mathrm{5cos}\:^{\mathrm{2}} \mathrm{x}+\mathrm{4}}\:\mathrm{dx}\:? \\ $$ Answered by Lordose last updated on 02/Oct/20 $$\int\sqrt{\mathrm{5}\left(\mathrm{1}−\mathrm{sin}^{\mathrm{2}} \mathrm{x}\right)+\mathrm{4}}\:\mathrm{dx} \\ $$$$\int\sqrt{\mathrm{9}−\mathrm{5sin}^{\mathrm{2}} \mathrm{x}}\:\mathrm{dx}…

sec-x-tan-x-tan-2-x-3-dx-

Question Number 116231 by bemath last updated on 02/Oct/20 $$\int\:\mathrm{sec}\:\mathrm{x}\:\mathrm{tan}\:\mathrm{x}\:\sqrt{\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}−\mathrm{3}}\:\mathrm{dx}\:? \\ $$ Answered by john santu last updated on 02/Oct/20 $$\int\:\mathrm{sec}\:{x}\:\mathrm{tan}\:{x}\:\sqrt{\mathrm{sec}\:^{\mathrm{2}} \:{x}−\mathrm{4}}\:{dx} \\ $$$$\left[\:{let}\:{u}\:=\:\mathrm{sec}\:{x}\:\rightarrow{du}\:=\:\mathrm{sec}\:{x}\:\mathrm{tan}\:{x}\:{dx}\:\right]…

If-c-is-the-line-segement-from-0-0-0-to-1-2-3-find-x-e-yz-ds-

Question Number 50689 by Tawa1 last updated on 18/Dec/18 $$\mathrm{If}\:\:\mathrm{c}\:\mathrm{is}\:\mathrm{the}\:\mathrm{line}\:\mathrm{segement}\:\mathrm{from}\:\:\left(\mathrm{0},\:\mathrm{0},\:\mathrm{0}\right)\:\mathrm{to}\:\left(\mathrm{1},\:\mathrm{2},\:\mathrm{3}\right) \\ $$$$\mathrm{find}\:\:\:\int\:\mathrm{x}\:\mathrm{e}^{\mathrm{yz}} \:\:\mathrm{ds} \\ $$ Answered by mr W last updated on 19/Dec/18 $$\frac{{x}−\mathrm{1}}{\mathrm{1}}=\frac{{y}−\mathrm{2}}{\mathrm{2}}=\frac{{z}−\mathrm{3}}{\mathrm{3}} \\…

0-pi-ln-1-1-2-cos-x-cos-x-dx-

Question Number 116216 by bemath last updated on 02/Oct/20 $$\underset{\mathrm{0}} {\overset{\pi} {\int}}\:\frac{\mathrm{ln}\:\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}\:\mathrm{x}\right)}{\mathrm{cos}\:\mathrm{x}}\:\mathrm{dx}\:? \\ $$ Answered by Bird last updated on 02/Oct/20 $${let}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\pi} \:\frac{{ln}\left(\mathrm{1}+{acosx}\right)}{{cosx}}{dx}\:{with}−\mathrm{1}<{a}<\mathrm{1} \\…

please-help-integrate-x-sin-x-1-cos-x-dx-

Question Number 50633 by Necxx last updated on 18/Dec/18 $${please}\:{help}\:{integrate}\:\frac{{x}+\mathrm{sin}\:{x}}{\mathrm{1}+\mathrm{cos}\:{x}}{dx} \\ $$ Commented by maxmathsup by imad last updated on 18/Dec/18 $${let}\:{I}\:=\:\int\:\:\frac{{x}+{sinx}}{\mathrm{1}+{cosx}}{dx}\:\:{we}\:{have}\:{I}\:=\int\:\:\frac{{x}}{\mathrm{1}+{cosx}}{dx}\:+\int\:\:\frac{{sinx}}{\mathrm{1}+{cosx}}{dx}\:{but} \\ $$$$\int\:\:\frac{{sinx}}{\mathrm{1}+{cosx}}{dx}\:=\int\:\frac{−{d}\left({cosx}\right)}{\mathrm{1}+{cosx}}\:{dx}=−{ln}\mid\mathrm{1}+{cosx}\mid\:+{c}_{\mathrm{1}} \\…