Category: Integration

Question Number 154143 by mnjuly1970 last updated on 14/Sep/21 Answered by phanphuoc last updated on 14/Sep/21 $$u=-lnx\to e^{-u}=x\to -e^{-u}du=dx$$$$\Omega=\int_{\infty} ^{\mathrm{0}} \frac{{e}^{−{x}} {sinx}}{\mathrm{1}+{e}^{−\mathrm{2}{x}} }\left(−{e}^{−{x}}…

Question Number 154142 by EDWIN88 last updated on 14/Sep/21 Answered by mr W last updated on 14/Sep/21 $$y=a(x-4){(x+2)}^2$$$$8=a(-4){(+2)}^2\Rightarrow a=-\frac{1}{2}$$$$y=-\frac{1}{2}(x-4){(x+2)}^2$$$$\frac{{dy}}{{dx}}=−\frac{\mathrm{1}}{\mathrm{2}}\left[\left({x}+\mathrm{2}\right)^{\mathrm{2}}…

Question Number 88586 by M±th+et£s last updated on 11/Apr/20 $$\int \frac{\sqrt{cos\left(2x\right)+3}}{cos\left(x\right)}dx$$ Answered by TANMAY PANACEA. last updated on 11/Apr/20 $$\int \frac{cos2x+3}{cosx\sqrt{3+cos2x}}dx$$$$\int\frac{\mathrm{2}{cos}^{\mathrm{2}} {x}+\mathrm{2}}{{cosx}\sqrt{\mathrm{2}{cos}^{\mathrm{2}} {x}+\mathrm{2}}}…

Question Number 88555 by M±th+et£s last updated on 11/Apr/20 $$slove$$$$\lceil \frac{x}{a}\rceil <a$$$$whena>1$$$$\lceil \dots \rceil isceilfunction$$ Answered by mr W last updated on…

Question Number 88547 by ajfour last updated on 11/Apr/20 $$provefor(0<a<2)$$$${\int }_0^{\mathrm{\infty }}\frac{x^{a-1}dx}{1+x+x^2}=\frac{2\pi }{\sqrt{3}}\cos \left(\frac{2\pi a+\pi }{6}\right)\mathrm{cosec}\pi a.$$ Answered by mind is power last updated…