Category: Integration

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…

Question Number 143545 by mathmax by abdo last updated on 15/Jun/21 $$\mathrm{calculate}{\int }_0^{\mathrm{\infty }}\frac{\mathrm{logx}}{{\mathrm{x}}^6+1}\mathrm{dx}$$ Answered by Pagnol last updated on 15/Jun/21 $$\mathrm{I}=\int_{\mathrm{0}}…

Question Number 12463 by tawa last updated on 23/Apr/17 $$\int \frac{\mathrm{x}+1}{{({\mathrm{x}}^2+2\mathrm{x}+3)}^{2/3}}\mathrm{dx}$$ Answered by ridwan balatif last updated on 23/Apr/17 $$\int\frac{\mathrm{x}+\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{2x}+\mathrm{3}\right)^{\mathrm{2}} }}\mathrm{dx}…

Question Number 77995 by mathmax by abdo last updated on 12/Jan/20 $$calculate{\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}\frac{arctan(2x+1)}{{(x^2+3)}^2}dx$$ Commented by msup trace by abdo last…