Question Number 142060 by iloveisrael last updated on 26/May/21 Answered by Ar Brandon last updated on 26/May/21 $$\mathrm{I}=\int\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }\mathrm{e}^{\frac{\mathrm{1}}{\mathrm{x}}} \mathrm{sec}\left(\mathrm{1}+\mathrm{e}^{\frac{\mathrm{1}}{\mathrm{x}}} \right)\mathrm{tan}\left(\mathrm{1}+\mathrm{e}^{\frac{\mathrm{1}}{\mathrm{x}}} \right)\mathrm{dx} \\ $$$${u}=\mathrm{1}+\mathrm{e}^{\frac{\mathrm{1}}{\mathrm{x}}} \Rightarrow\mathrm{d}{u}=−\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}}…
Question Number 142028 by mnjuly1970 last updated on 25/May/21 $$\:\:\:\:\:\:\:\:…………{Calculus}………\: \\ $$$$\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}\left({sin}\left({x}\right)\right).{e}^{{cos}\left({x}\right)} }{{x}}{dx}=??? \\ $$$$\:…………{m}.{n}….. \\ $$ Answered by mindispower last updated on…
Question Number 76468 by kaivan.ahmadi last updated on 27/Dec/19 $$\int\frac{\mathrm{1}−{x}^{\mathrm{2}} −\mathrm{8}{x}+\mathrm{1}}{{x}^{\mathrm{4}} −{x}^{\mathrm{3}} −{x}+\mathrm{1}}{dx} \\ $$ Commented by mr W last updated on 27/Dec/19 $${why}\:{did}\:{you}\:{write}\:\mathrm{1}−{x}^{\mathrm{2}} −\mathrm{8}{x}+\mathrm{1}…
Question Number 76467 by kaivan.ahmadi last updated on 27/Dec/19 $$\int\frac{{dx}}{\:\sqrt{{e}^{\mathrm{2}{x}} −\mathrm{4}}\left({sec}^{−\mathrm{1}} \left(\frac{{e}^{{x}} }{\mathrm{4}}\right)\right)} \\ $$ Answered by john santu last updated on 28/Dec/19 $${let}\::\mathrm{sec}\:{u}\:=\:\frac{{e}^{{x}} }{\mathrm{4}}\:\rightarrow\:{e}^{{x}}…
Question Number 76469 by kaivan.ahmadi last updated on 27/Dec/19 $$\int{cothx}\:{dx} \\ $$ Commented by mathmax by abdo last updated on 27/Dec/19 $$\int\:{coth}\left({x}\right){dx}\:=\int\:\frac{{ch}\left({x}\right)}{{sh}\left({x}\right)}{dx}\:=\int\:\:\frac{{e}^{{x}} \:+{e}^{−{x}} }{{e}^{{x}} −{e}^{−{x}}…
Question Number 76465 by kaivan.ahmadi last updated on 27/Dec/19 $$\int{e}^{−{x}} \left(−{e}^{−\mathrm{3}{x}} +\mathrm{5}{e}^{−\mathrm{2}{x}} −\mathrm{6}\right){sin}\left(\mathrm{2}{e}^{−{x}} \right){dx} \\ $$ Answered by john santu last updated on 28/Dec/19 $$\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{3}{e}^{−\mathrm{3}{x}}…
Question Number 141998 by iloveisrael last updated on 25/May/21 $$\:\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\frac{\mathrm{sin}\:\left(\mathrm{40}{x}\right)}{\mathrm{sin}\:\left(\mathrm{5}{x}\right)}\:{dx}\: \\ $$ Answered by EDWIN88 last updated on 25/May/21 $$\:\mathrm{I}\:=\:\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \:\frac{\mathrm{sin}\:\left(\mathrm{40x}\right)}{\mathrm{sin}\:\left(\mathrm{5x}\right)}\:\mathrm{dx}\: \\…
Question Number 76462 by kaivan.ahmadi last updated on 27/Dec/19 $$\int{cos}\mathrm{3}{x}\:{e}^{−\mathrm{2}{x}} {dx} \\ $$ Commented by mathmax by abdo last updated on 27/Dec/19 $${let}\:{A}\:=\int\:{cos}\left(\mathrm{3}{x}\right){e}^{−\mathrm{2}{x}} {dx}\:\Rightarrow{A}\:={Re}\left(\int\:{e}^{\mathrm{3}{ix}} \:{e}^{−\mathrm{2}{x}}…
Question Number 10913 by Saham last updated on 01/Mar/17 $$\int_{\:\mathrm{1}} ^{\:\mathrm{3}} \:\mathrm{x}^{\mathrm{x}} \:\:\mathrm{dx} \\ $$ Answered by FilupS last updated on 02/Mar/17 $${I}=\int_{\mathrm{1}} ^{\:\mathrm{3}} {x}^{{x}}…
Question Number 76442 by aliesam last updated on 27/Dec/19 Answered by Tanmay chaudhury last updated on 28/Dec/19 $${x}={tana}\:\:\:\:{dx}={sec}^{\mathrm{2}} {ada} \\ $$$${sec}^{−\mathrm{1}} \left(\frac{\mathrm{1}+{tan}^{\mathrm{2}} {a}}{\mathrm{1}−{tan}^{\mathrm{2}} {a}}\right)\rightarrow{sec}^{−\mathrm{1}} \left({sec}\mathrm{2}{a}\right)=\mathrm{2}{a}…