Category: Integration

Question Number 87540 by Power last updated on 04/Apr/20 Commented by abdomathmax last updated on 05/Apr/20 $$letI={\int }_0^{\mathrm{\infty }}\frac{dx}{{(x+\sqrt{1+x^2})}^2}changementx=sh\left(t\right)give$$$${I}\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{ch}\left({t}\right)\:{dt}}{\left({sh}\left({t}\right)+{cht}\right)^{\mathrm{2}}…

Question Number 87526 by mathmax by abdo last updated on 04/Apr/20 $$calculate{\int }_0^{\mathrm{\infty }}{e}^{-\left[nx\right]}dx$$ Commented by mathmax by abdo last updated on…

Question Number 153063 by talminator2856791 last updated on 04/Sep/21 $$$$$$\mathrm{show}\mathrm{that}$$$$$$$${\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}\frac{1}{\sqrt{x^2+1}}dx$$$$$$$$\mathrm{is}\mathrm{unsolvable}$$$$\:…

Question Number 21970 by j.masanja06@gmail.com last updated on 07/Oct/17 $$integrate$$$$\int {sec}^{3}xdx$$ Answered by Tikufly last updated on 07/Oct/17 $$\:\int\mathrm{sec}^{\mathrm{3}} {xdx}=\int\:\left(\mathrm{sec}{x}\right)\left(\mathrm{sec}^{\mathrm{2}} {x}\right){dx}…

Question Number 87503 by M±th+et£s last updated on 04/Apr/20 $$\int \frac{x^2}{1+x^5}dx$$ Commented by MJS last updated on 04/Apr/20 $${x}^{\mathrm{5}} +\mathrm{1}=\left({x}+\mathrm{1}\right)\left({x}^{\mathrm{2}} −\frac{\mathrm{1}−\sqrt{\mathrm{5}}}{\mathrm{2}}{x}+\mathrm{1}\right)\left({x}^{\mathrm{2}} −\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}+\mathrm{1}\right)…