Category: Integration

Question Number 162298 by mathmax by abdo last updated on 28/Dec/21 $$\mathrm{find}{\int }_0^1\mathrm{lnx}\ln (1-{\mathrm{x}}^3)\mathrm{dx}$$ Answered by Ar Brandon last updated on 28/Dec/21…

Question Number 96748 by MJS last updated on 04/Jun/20 $$\mathrm{nobody}\mathrm{tried}\mathrm{question}94184\dots$$ Commented by bemath last updated on 04/Jun/20 how did mister solve this integral? Terms of Service Privacy Policy…

Question Number 96705 by bemath last updated on 04/Jun/20 $$\int \ln (\sqrt{1-\mathrm{x}}+\sqrt{1+\mathrm{x}})\mathrm{dx}=?$$ Answered by john santu last updated on 04/Jun/20 $$\mathrm{D}.\mathrm{I}\mathrm{method}$$$$\mathrm{I}=x\ln (\sqrt{1-x}+\sqrt{1+x})-\int \frac{x(\frac{-1}{2\sqrt{1-x}}+\frac{1}{2\sqrt{1+x}})}{\sqrt{1-x}+\sqrt{1+x}}dx$$$$\mathrm{I}\:=\:{x}\:\mathrm{ln}\left(\sqrt{\mathrm{1}−{x}}+\sqrt{\mathrm{1}+{x}}\right)−\frac{\mathrm{1}}{\mathrm{2}}\int\:{x}\left(\frac{\sqrt{\mathrm{1}−{x}^{\mathrm{2}}…

Question Number 96699 by Rio Michael last updated on 04/Jun/20 $$\int \frac{{\tan }^3\left(\ln x\right)}{x}dx=??$$ Commented by bobhans last updated on 04/Jun/20 $$\mathrm{u}=\mathrm{ln}\left(\mathrm{x}\right)\:\Rightarrow\:\int\:\mathrm{tan}\:^{\mathrm{3}} \mathrm{u}\:\mathrm{du}\:=\:\int\left(\mathrm{sec}\:^{\mathrm{2}} \mathrm{u}−\mathrm{1}\right)\mathrm{tan}\:\mathrm{u}\:\mathrm{du} \…

Question Number 96693 by 175 last updated on 03/Jun/20 Answered by abdomathmax last updated on 04/Jun/20 $${\mathrm{A}}_{\mathrm{n}}=\int \frac{\mathrm{dx}}{1+{\tan }^{\mathrm{n}}\mathrm{x}}{=}_{\mathrm{tanx}=\mathrm{t}}\int \frac{\mathrm{dt}}{(1+{\mathrm{t}}^2)(1+{\mathrm{t}}^{\mathrm{n}})}$$$$\mathrm{let}\:\mathrm{decompose}\:\mathrm{F}\left(\mathrm{t}\right)\:=\frac{\mathrm{1}}{\left(\mathrm{t}^{\mathrm{2}} +\mathrm{1}\right)\left(\mathrm{t}^{\mathrm{n}}…