Category: Integration

Question Number 192933 by mnjuly1970 last updated on 31/May/23 Answered by MM42 last updated on 01/Jun/23 $$ln(1-x)=u\Rightarrow \frac{-1}{1-x}dx=du\mathrm{\&}i{x}^{n-1}dx=dv\Rightarrow \frac{x^n}{n}=v$$$$\Rightarrow{I}_{{n}} =\int{x}^{{n}−\mathrm{1}} {ln}\left(\mathrm{1}−{x}\right){dx}=\frac{{x}^{{n}} {ln}\left(\mathrm{1}−{x}\right)}{{n}}\:+\frac{\mathrm{1}}{{n}}\int\:\frac{{x}^{{n}} }{\mathrm{1}−{x}}{dx}…

Question Number 192916 by Mingma last updated on 31/May/23 Answered by ARUNG_Brandon_MBU last updated on 31/May/23 $$I={\int }_0^{\frac{\pi }{2}}(\frac{1-\sin 2x}{1+\cos x}+\frac{1-\cos 2x}{1+\sin x})dx$$$$\:\:\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{dx}}{\mathrm{1}+\mathrm{cos}{x}}+\mathrm{2}\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{cos}{x}}{\mathrm{1}+\mathrm{cos}{x}}\left(\mathrm{sin}{xdx}\right)+\mathrm{2}\int_{\mathrm{0}}…

Question Number 127377 by I want to learn more last updated on 29/Dec/20 Commented by zdf last updated on 29/Dec/20 $$$$ Commented by…

Question Number 127368 by I want to learn more last updated on 29/Dec/20 $$\int \frac{\sqrt{\tan \mathrm{x}}}{\sqrt{{\tan }^2\mathrm{x}-1}}\mathrm{dx}$$ Answered by liberty last updated on 29/Dec/20 $$\:{let}\:\rightarrow\begin{cases}{\mathrm{tan}\:{x}\:\geqslant\mathrm{0}}\{\mathrm{tan}^{\mathrm{2}}…

Question Number 127350 by bobhans last updated on 29/Dec/20 $$\int \frac{x^2}{{(x^2-1)}^{\frac{5}{2}}}dx?$$ Answered by bemath last updated on 29/Dec/20 Terms of Service…