Category: Integration

Question Number 125187 by bemath last updated on 08/Dec/20 $$\int \frac{dx}{\sqrt{\sin {}^{3}x}\sqrt{\cos {}^{5}x}}?$$ Answered by liberty last updated on 08/Dec/20 $${I}=\int\:\sqrt{\frac{\left(\frac{\mathrm{1}}{\mathrm{cos}\:^{\mathrm{3}} {x}}\right)}{\mathrm{tan}\:^{\mathrm{3}} {x}\:\mathrm{cos}\:^{\mathrm{5}} {x}}}\:{dx}\:=\:\int\frac{{dx}}{\:\sqrt{\mathrm{tan}\:^{\mathrm{3}}…

Question Number 190708 by mnjuly1970 last updated on 09/Apr/23 Answered by cortano12 last updated on 10/Apr/23 $$\mathrm{L}={\mathrm{e}}^{\underset{x\to 0}{\lim }(1+\sin 2\mathrm{x}-{\tan }^{-1}\left(2\mathrm{x}\right)-1).\frac{1}{{\mathrm{x}}^3}}$$$$\:\mathrm{L}=\mathrm{e}^{\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\mathrm{8}.\left(\frac{\mathrm{sin}\:\mathrm{2x}−\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{2x}\right)}{\left(\mathrm{2x}\right)^{\mathrm{3}} }\right)}…

Question Number 190700 by Rupesh123 last updated on 09/Apr/23 Answered by 07049753053 last updated on 09/Apr/23 $${\int }_0^{\mathrm{\infty }}\frac{sin\left(x\right)ln\left(x\right)}{x}dx$$$$\frac{\boldsymbol{\mathrm{d}}}{\boldsymbol{\mathrm{da}}}\mid_{\boldsymbol{\mathrm{a}}=\mathrm{1}} \int_{\mathrm{0}} ^{\infty} \frac{\boldsymbol{\mathrm{sin}}\left(\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{a}}} }{\boldsymbol{\mathrm{x}}}\boldsymbol{\mathrm{dx}}=\frac{\boldsymbol{\mathrm{d}}}{\boldsymbol{\mathrm{da}}}\mid_{\boldsymbol{\mathrm{a}}=\mathrm{1}}…

Question Number 125146 by mathmax by abdo last updated on 08/Dec/20 $$1)\mathrm{calculate}{\int }_0^{2\pi }\frac{\mathrm{d}\theta }{{\mathrm{x}}^2-2\mathrm{x}\cos \theta +1}$$$$2)\mathrm{calculate}{\int }_0^{2\pi }\frac{\cos \theta }{{({\mathrm{x}}^2-2\mathrm{xcos}\theta +1)}^2}\mathrm{d}\theta$$ Answered by…

Question Number 125125 by Study last updated on 08/Dec/20 $$\underset{\frac{\pi }{6}}{\int }\frac{\stackrel{\frac{\pi }{3}}{sinx}}{x}dx=?$$ Commented by Dwaipayan Shikari last updated on 08/Dec/20 $$Si\left(\frac{\pi }{3}\right)-Si\left(\frac{\pi }{6}\right)$$…