Category: Integration

Question Number 75888 by abdomathmax last updated on 19/Dec/19 $$find{\int }_0^1\sqrt{1+x^4}dx$$ Commented by 21042004 last updated on 20/Dec/19 $$\mathrm{this}\mathrm{equation}\mathrm{is}\mathrm{so}\mathrm{long}$$$$\frac{\sqrt{\mathrm{2}}+\mathrm{2}\sqrt[{\mathrm{4}}]{−\mathrm{1}}\mathrm{F}\left(\mathrm{1}−\frac{{i}}{\mathrm{arcsinh}\left(\sqrt[{\mathrm{4}}]{−\mathrm{1}}\right)}\right)+\mathrm{2}\sqrt[{\mathrm{4}}]{−\mathrm{1}}{F}\left({i}\centerdot\mathrm{arcsinh}^{−\mathrm{1}}…

Question Number 141417 by mnjuly1970 last updated on 18/May/21 $$\dots \dots ..advanced\dots \dots \dots calculus\dots \dots .$$$$provethat::$$$$\mathcal{F}:={\int }_{-1}^0\frac{e^x+e^{\frac{1}{x}}-1}{x}dx\stackrel{??}{=}\gamma$$ Answered by mnjuly1970 last…

Question Number 75873 by Rio Michael last updated on 19/Dec/19 $$\int {xe}^{x}dx$$ Answered by MJS last updated on 19/Dec/19 $$u^{\prime }={\mathrm{e}}^x\Rightarrow u={\mathrm{e}}^x$$$${v}={x}\:\Rightarrow\:{v}'=\mathrm{1}…

Question Number 141388 by cesarL last updated on 18/May/21 $${\int }_0^{\pi /2}\sqrt{(senx\cdot cosx)}dx$$$$Help$$ Answered by Dwaipayan Shikari last updated on 18/May/21 $$\int_{\mathrm{0}}…

Question Number 141387 by cesarL last updated on 18/May/21 $${\int }_{-\pi /4}^{\pi /4}{({sec}^{2}x+tgx)}^{2}dx$$ Answered by MJS_new last updated on 18/May/21 $$\underset{−\pi/\mathrm{4}} {\overset{\pi/\mathrm{4}}…