Category: Integration

Question Number 143638 by mnjuly1970 last updated on 16/Jun/21 $$\dots \dots Calculus\dots .$$$$\mathit{\varphi }:\stackrel{?}{=}{\int }_0^1\frac{ln(1-x)ln\left(x\right)\left(ln\left(\frac{1-x}{x}\right)\right)}{x}dx$$$$m.n\dots .$$$$$$ Commented by TheHoneyCat last…

Question Number 143622 by ArielVyny last updated on 16/Jun/21 $${\int }_0^{\propto }{e}^{2arctg\left(t^2\right)}dt$$ Answered by TheHoneyCat last updated on 17/Jun/21 $$\mathrm{arctan}\left({t}\right)\underset{{t}\rightarrow+\infty} {\rightarrow}\frac{\pi}{\mathrm{2}}>\mathrm{0}…

Question Number 12535 by tawa last updated on 24/Apr/17 $$\mathrm{Use}\mathrm{the}\mathrm{reduction}\mathrm{formular}.$$$${\mathrm{I}}_{\mathrm{n}}=\int {\sin }^{\mathrm{n}}\left(\mathrm{x}\right)\mathrm{dx}=-\frac{1}{\mathrm{n}}{\sin }^{\mathrm{n}-1}\left(\mathrm{x}\right)\cos \left(\mathrm{x}\right)+\frac{\mathrm{n}-1}{\mathrm{n}}{\mathrm{I}}_{\mathrm{n}}-2,\mathrm{to}\mathrm{evaluate}$$$${\mathrm{I}}_{\mathrm{n}}=\int {\sin }^6\left(\mathrm{x}\right)\mathrm{dx}$$ Answered by mrW1…

Question Number 143588 by bobhans last updated on 16/Jun/21 Answered by EDWIN88 last updated on 16/Jun/21 $$\mathrm{F}\left(\mathrm{x}\right)=\underset{4}{\stackrel{8\mathrm{x}}{\int }}\mathrm{f}\left(\mathrm{t}\right)\mathrm{dt}=\sqrt{2+{\mathrm{x}}^2}+\mathrm{c}$$$$\mathrm{F}{}^{\prime }\left(\mathrm{x}\right)=8\mathrm{f}\left(8\mathrm{x}\right)=\frac{\mathrm{x}}{\sqrt{2+{\mathrm{x}}^2}}$$$$\mathrm{F}'\left(\mathrm{x}\right)=\mathrm{f}\left(\mathrm{8x}\right)=\frac{\mathrm{x}}{\mathrm{8}\sqrt{\mathrm{2}+\mathrm{x}^{\mathrm{2}}…

Question Number 12500 by FilupS last updated on 24/Apr/17 $$\mathrm{Please}\mathrm{help}\mathrm{explain}\mathrm{how}\mathrm{to}\mathrm{solve}$$$$\int e^{\frac{1}{x}}dx$$ Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 24/Apr/17 $${e}^{\frac{\mathrm{1}}{{x}}} ={t}\Rightarrow\frac{\mathrm{1}}{{x}}={lnt}\Rightarrow\left({lnx}+{c}\right)^{'} ={lnt}\Rightarrow…