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} \\ $$$${sec}^{−\mathrm{1}} \left(\frac{\mathrm{1}+{tan}^{\mathrm{2}} {a}}{\mathrm{1}−{tan}^{\mathrm{2}} {a}}\right)\rightarrow{sec}^{−\mathrm{1}} \left({sec}\mathrm{2}{a}\right)=\mathrm{2}{a}…
Question Number 10902 by Nayon last updated on 01/Mar/17 $$ \\ $$$$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\int\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }{dx}=? \\ $$$$ \\ $$$$ \\ $$$$ \\ $$…
Question Number 76424 by john santu last updated on 27/Dec/19 $${how}\:{to}\:{calculate}\:\int\sqrt{\frac{{x}}{\:\sqrt{\frac{{x}}{\:\sqrt{\frac{{x}}{\:\sqrt{…}}}}}}}\:\:{dx}\:? \\ $$ Commented by john santu last updated on 27/Dec/19 $${this}\:{the}\:{crazy}\:{integration} \\ $$ Answered…
Question Number 10876 by Saham last updated on 28/Feb/17 $$\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \int_{\:\mathrm{x}} ^{\:\sqrt{\mathrm{x}}} \:\left(\mathrm{x}\:+\:\mathrm{y}^{\mathrm{5}} \right)\:\mathrm{dy}\:\mathrm{dx} \\ $$ Answered by fariraihmudzengerere75@gmail.c last updated on 28/Feb/17 $${Answer}\:.\:\int_{\mathrm{0}}…
Question Number 10880 by Saham last updated on 28/Feb/17 $$\left.\int\:\left(\mathrm{x}\:+\:\mathrm{3}\right)\sqrt{\left(\mathrm{x}\:+\:\mathrm{4}\right.}\right)\:\mathrm{dx}\: \\ $$ Answered by geovane10math last updated on 28/Feb/17 $$\int\left({x}\:+\:\mathrm{3}\right)\sqrt{{x}\:+\:\mathrm{4}}\:\mathrm{dx}\:=\:\int{x}\sqrt{{x}\:+\:\mathrm{4}}\:\mathrm{dx}\:+\:\int\mathrm{3}\sqrt{{x}\:+\:\mathrm{4}}\:\mathrm{dx} \\ $$$$\mathrm{First}\:\mathrm{integral}: \\ $$$$\int{x}\sqrt{{x}\:+\:\mathrm{4}}\:\mathrm{dx}\:= \\…