Category: Integration

Question Number 26952 by Femmy last updated on 31/Dec/17 Answered by prakash jain last updated on 31/Dec/17 $$\int \frac{{\sin }^{5}x}{{\cos }^{3}x}dx=\int \frac{{\sin }^{4}x}{{\cos }^{3}x}\sin xdx$$$$=\int\frac{\left(\mathrm{1}−\mathrm{cos}^{\mathrm{2}} {x}\right)^{\mathrm{2}}…

Question Number 26949 by Joel578 last updated on 31/Dec/17 $$\underset{0}{\stackrel{1}{\int }}\underset{0}{\stackrel{1}{\int }}\frac{1}{1+xy}dxdy$$ Commented by abdo imad last updated on 31/Dec/17 $$\left.{I}=\:\int_{\mathrm{0}^{}…

Question Number 158009 by zainaltanjung last updated on 30/Oct/21 $$$$$$$$ Answered by puissant last updated on 30/Oct/21 $$\Omega=\int_{\mathrm{2}} ^{\mathrm{4}} \frac{\mathrm{2}{x}−\mathrm{1}}{{x}^{\mathrm{2}} −{x}}{dx}=\left[{ln}\mid{x}^{\mathrm{2}}…

Question Number 157977 by tounghoungko last updated on 30/Oct/21 $$\int \frac{dx}{(1+\sqrt[4]{x})\sqrt{x}}=?$$ Answered by puissant last updated on 30/Oct/21 $$\mathrm{\Omega }=\int \frac{dx}{(1+\sqrt[4]{x})\sqrt{x}}$$$$u=\sqrt{x}\to du=\frac{1}{2\sqrt{x}}dx\to dx=2\sqrt{x}du$$$$\Rightarrow\:\Omega\:=\:\int\frac{\mathrm{2}\sqrt{{x}}{du}}{\left(\mathrm{1}+\sqrt{{u}}\right)\sqrt{{x}}}\:=\:\mathrm{2}\int\frac{{du}}{\left(\mathrm{1}+\sqrt{{u}}\right)} \…

Question Number 92420 by I want to learn more last updated on 06/May/20 Commented by mathmax by abdo last updated on 07/May/20 $${I}\:=\int\:\:\frac{{dx}}{{cos}^{\mathrm{6}} {x}\:+{sin}^{\mathrm{6}} {x}}\:\Rightarrow\:{I}\:=\int\:\:\:\frac{{dx}}{\left({cos}^{\mathrm{2}}…