Category: Integration

Question Number 183761 by MikeH last updated on 29/Dec/22 $$\mathrm{Solve}\mathrm{the}\mathrm{differential}\mathrm{equation}\mathrm{for}\mathrm{the}\mathrm{function}$$$$\mathrm{given}\mathrm{by}U(x,t).$$$$\{\begin{array}{l}\frac{\partial U}{\partial t}=2\frac{{\partial }^{2}U}{\partial x^2},0<x<\pi \\ U(0,t)=0,U(\pi ,t)=0,t>0\end{array}$$$$U(x,0)=25x$$ Answered by leodera last updated…

Question Number 52683 by maxmathsup by imad last updated on 11/Jan/19 $$letf\left(\lambda \right)={\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}\frac{sin\left(\lambda x\right)}{{(x^2+2\lambda x+1)}^2}dxwith\mid \lambda \mid <1$$$$1)findthevalueoff\left(\lambda \right)$$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{sin}\left(\frac{{x}}{\mathrm{2}\:}\right)}{\left({x}^{\mathrm{2}} \:\:+{x}+\mathrm{1}\right)^{\mathrm{2}} }{dx} \…

Question Number 52667 by gunawan last updated on 11/Jan/19 $$\int \frac{x^4+1}{x^2\sqrt{x^4-1}}dx$$ Answered by tanmay.chaudhury50@gmail.com last updated on 11/Jan/19 $$\int\frac{{x}^{\mathrm{2}} +\frac{\mathrm{1}}{{x}^{\mathrm{2}} }}{\:\sqrt{{x}^{\mathrm{2}}…

Question Number 52649 by Tawa1 last updated on 10/Jan/19 $$\int \frac{{4\mathrm{x}}^2+3}{{({\mathrm{x}}^2+\mathrm{x}+1)}^2}\mathrm{dx}$$ Commented by maxmathsup by imad last updated on 10/Jan/19 $${et}\:{I}\:=\int\:\:\frac{\mathrm{4}{x}^{\mathrm{2}}…

Question Number 183706 by cortano1 last updated on 29/Dec/22 $$A=\int \frac{1+\cos {}^{2}x}{1+\sin {}^{4}x}dx$$ Answered by Ar Brandon last updated on 29/Dec/22 $${A}=\int\frac{\mathrm{1}+\mathrm{cos}^{\mathrm{2}} {x}}{\mathrm{1}+\mathrm{sin}^{\mathrm{4}} {x}}{dx}=\int\frac{\mathrm{sec}^{\mathrm{4}}…