Category: Integration

Question Number 33704 by math khazana by abdo last updated on 22/Apr/18 $$letf\left(t\right)=\frac{1}{a^2+t^2}witha>0givethefourier$$$$transformforf.$$$$$$ Commented by prof Abdo…

Question Number 99234 by abdomathmax last updated on 19/Jun/20 $$\mathrm{calculate}{\int }_0^{\mathrm{\infty }}{\mathrm{e}}^{-\mathrm{x}}\mathrm{lnx}\mathrm{dx}$$ Answered by maths mind last updated on 19/Jun/20 $$\Gamma\left({x}\right)=\int_{\mathrm{0}} ^{\infty}…

Question Number 99228 by  M±th+et+s last updated on 19/Jun/20 $$$$$${\int }_0^{\mathrm{\infty }}\frac{sin\left(x\right)ln\left(x\right)}{x}dx=\frac{-\gamma \pi }{2}$$ Answered by maths mind last updated on 20/Jun/20 $$\frac{{ln}\left({x}\right)}{{x}}=\frac{\partial}{\partial{a}}{x}^{{a}−\mathrm{1}}…

Question Number 33689 by NECx last updated on 22/Apr/18 $$\int \frac{x}{x^3+1}dx$$ Commented by mondodotto@gmail.com last updated on 22/Apr/18 $$\mathbf{let}\mathbf{u}={\mathbf{x}}^3+1$$$$\frac{\boldsymbol{\mathrm{du}}}{\boldsymbol{\mathrm{dx}}}=\mathrm{3}\boldsymbol{\mathrm{x}}^{\mathrm{2}} \Rightarrow\boldsymbol{\mathrm{dx}}=\frac{\boldsymbol{\mathrm{du}}}{\mathrm{3}\boldsymbol{\mathrm{x}}^{\mathrm{2}}…

Question Number 99205 by bemath last updated on 19/Jun/20 Commented by bramlex last updated on 19/Jun/20 $$let\sqrt{4-\sqrt{x}}=t,4-\sqrt{x}=t^2$$$${(4-t^2)}^2=x;dx=-4t(4-t^2)dt$$$$\mathrm{I}\:=\:\int\:{t}\:\left(−\mathrm{4}{t}\left(\mathrm{4}−{t}^{\mathrm{2}} \right)\right)\:{dt}\:…