Category: Integration

Question Number 76467 by kaivan.ahmadi last updated on 27/Dec/19 $$\int \frac{dx}{\sqrt{e^{2x}-4}\left({sec}^{-1}\left(\frac{e^x}{4}\right)\right)}$$ Answered by john santu last updated on 28/Dec/19 $${let}\::\mathrm{sec}\:{u}\:=\:\frac{{e}^{{x}} }{\mathrm{4}}\:\rightarrow\:{e}^{{x}}…

Question Number 76465 by kaivan.ahmadi last updated on 27/Dec/19 $$\int e^{-x}(-e^{-3x}+5e^{-2x}-6)sin\left(2e^{-x}\right)dx$$ Answered by john santu last updated on 28/Dec/19 $$\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{3}{e}^{−\mathrm{3}{x}}…

Question Number 76462 by kaivan.ahmadi last updated on 27/Dec/19 $$\int cos3x{e}^{-2x}dx$$ 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 76442 by aliesam last updated on 27/Dec/19 Answered by Tanmay chaudhury last updated on 28/Dec/19 $$x=tanadx={sec}^{2}ada$$$${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 76424 by john santu last updated on 27/Dec/19 $$howtocalculate\int \sqrt{\frac{x}{\sqrt{\frac{x}{\sqrt{\frac{x}{\sqrt{\dots }}}}}}}dx?$$ Commented by john santu last updated on 27/Dec/19 $$thisthecrazyintegration$$ Answered…