Category: Integration

Question Number 116815 by bemath last updated on 07/Oct/20 $$\int \frac{\mathrm{dx}}{(\mathrm{x}-2)({\mathrm{x}}^2+4)}=?$$ Answered by john santu last updated on 07/Oct/20 $$\Rightarrow\:\frac{\mathrm{1}}{\left({x}−\mathrm{2}\right)\left({x}^{\mathrm{2}} +\mathrm{4}\right)}\:=\:\frac{{A}}{{x}−\mathrm{2}}\:+\:\frac{{Bx}+{C}}{{x}^{\mathrm{2}} +\mathrm{4}} \…

Question Number 116806 by Backer last updated on 07/Oct/20 $$\mathrm{Hi}$$$$\mathrm{Prove}\mathrm{that}:$$$${\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}-{\mathrm{e}}^{-{\mathrm{x}}^2}\mathrm{dx}=\sqrt{\pi }$$$$\mathrm{Thanks}\mathrm{beforehand}$$$$$$ Answered…

Question Number 116796 by mnjuly1970 last updated on 08/Oct/20 $$\dots calculus\dots$$$$$$$$provethat::$$$$$$$$\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\left(\mathrm{1}−{x}^{{p}} \right)\left(\mathrm{1}−{x}^{{q}} \right){x}^{{r}−\mathrm{1}} }{{log}\left({x}\right)}{dx}\overset{???} {=}{log}\left(\:\frac{\left({p}+{q}+{r}+\mathrm{1}\right){r}}{\left({p}+{r}\right)\left({q}+{r}\right)}\:\right) \…

Question Number 182295 by universe last updated on 07/Dec/22 Answered by SEKRET last updated on 07/Dec/22 $$\mathbf{d}?$$ Commented by universe last updated on…

Question Number 51215 by gunawan last updated on 25/Dec/18 $${\int }_0^{\pi }{e}^{(1+i)x}dx=\dots$$ Answered by tanmay.chaudhury50@gmail.com last updated on 25/Dec/18 $$a=1+i$$$$\int_{\mathrm{0}}…