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Category: Integration

Question-45561

Question Number 45561 by Sanjarbek last updated on 14/Oct/18 Commented by tanmay.chaudhury50@gmail.com last updated on 14/Oct/18 $${x}={sin}\theta\:\:\:\:{dx}={cos}\theta{d}\theta \\ $$$$\int\frac{{cos}\theta{d}\theta}{\:\sqrt{{cos}\theta}} \\ $$$$\int\sqrt{{cos}\theta}\:{d}\theta \\ $$$${wait}… \\ $$…

0-JS-dx-0-pi-2-sin-x-4-sin-2-x-4-sin-2-x-2-dx-

Question Number 111082 by john santu last updated on 02/Sep/20 $$\:\:\:\left[\int_{\mathrm{0}} ^{\infty} {JS}\:{dx}\:\right] \\ $$$$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\frac{\mathrm{sin}\:\left({x}\right)\left(\mathrm{4}+\mathrm{sin}\:^{\mathrm{2}} \left({x}\right)\right)}{\left(\mathrm{4}−\mathrm{sin}\:^{\mathrm{2}} \left({x}\right)\right)^{\mathrm{2}} }\:{dx}\:? \\ $$ Commented by mathdave…

bemath-1-dx-3sin-x-sin-3-x-2-lim-x-x-5-1-x-1-3-find-the-asymptotes-x-2-a-2-y-2-b-2-1-

Question Number 111083 by bemath last updated on 02/Sep/20 $$\:\:\:\sqrt{\mathrm{bemath}} \\ $$$$\left(\mathrm{1}\right)\int\:\frac{\mathrm{dx}}{\mathrm{3sin}\:\mathrm{x}+\mathrm{sin}\:^{\mathrm{3}} \mathrm{x}} \\ $$$$\left(\mathrm{2}\right)\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{x}\left(\mathrm{5}^{\frac{\mathrm{1}}{\mathrm{x}}} \:−\mathrm{1}\right)\: \\ $$$$\left(\mathrm{3}\right)\:\mathrm{find}\:\mathrm{the}\:\mathrm{asymptotes}\:\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{a}^{\mathrm{2}} }\:−\:\frac{\mathrm{y}^{\mathrm{2}} }{\mathrm{b}^{\mathrm{2}} }\:=\:\mathrm{1}\: \\ $$…

let-a-gt-0-and-b-gt-0-calculate-acos-2-bsin-2-dpi-2-find-pi-4-pi-2-2cos-2-3-sin-2-d-

Question Number 45520 by maxmathsup by imad last updated on 14/Oct/18 $${let}\:{a}>\mathrm{0}\:{and}\:{b}>\mathrm{0}\:{calculate}\:\int\:\sqrt{{acos}^{\mathrm{2}} \theta\:+{bsin}^{\mathrm{2}} \theta}{d}\pi \\ $$$$\left.\mathrm{2}\right)\:{find}\:\int_{\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{2}}} \sqrt{\mathrm{2}{cos}^{\mathrm{2}} \theta\:+\mathrm{3}\:{sin}^{\mathrm{2}} \theta}{d}\theta\:. \\ $$ Commented by Meritguide1234…

0-1-tanh-1-x-2-1-x-2-dx-solution-note-tanh-1-x-1-2-ln-1-x-1-x-1-4-0-1-ln-2-1-x-1-x-

Question Number 176594 by mnjuly1970 last updated on 22/Sep/22 $$ \\ $$$$\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:\left(\:{tanh}^{\:−\mathrm{1}} \left({x}\right)\right)^{\mathrm{2}} }{\left(\mathrm{1}+{x}\:\right)^{\:\mathrm{2}} }\:{dx}\:=\:?\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\prec\:\:\:{solution}\:\:\succ \\ $$$$\:\:\:\:\:{note}\::\:\:{tanh}^{\:−\mathrm{1}} \left({x}\right)=−\:\frac{\mathrm{1}}{\mathrm{2}}\:{ln}\left(\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}\right) \\ $$$$\:\:\:\:\:\boldsymbol{\phi}=\:\frac{\mathrm{1}}{\mathrm{4}}\int_{\mathrm{0}} ^{\:\mathrm{1}}…

1-pi-2-pi-3-1-sinx-cosx-dx-

Question Number 176570 by mathlove last updated on 21/Sep/22 $$\left(\mathrm{1}\right)\:\:\underset{\frac{\pi}{\mathrm{3}}} {\int}^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{1}+{sinx}}{{cosx}}\:{dx}=? \\ $$ Answered by Peace last updated on 21/Sep/22 $$\int\frac{\mathrm{1}+{sin}\left({x}\right)}{{cos}\left({x}\right)}{dx}=\int\frac{{cos}\left({x}\right)}{{cos}^{\mathrm{2}} \left({x}\right)}+\int\frac{{sin}\left({x}\right)}{{cos}\left({x}\right)}{dx} \\ $$$$=\int\frac{{cos}\left({x}\right)}{\mathrm{1}−{sin}^{\mathrm{2}}…