Category: Integration

Question Number 119960 by mnjuly1970 last updated on 28/Oct/20 Answered by mathmax by abdo last updated on 28/Oct/20 $$\mathrm{A}\:=\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{arctanx}}{\left(\mathrm{1}+\mathrm{x}\right)\sqrt{\mathrm{x}}}\mathrm{dx}\:\Rightarrow\mathrm{A}\:=_{\sqrt{\mathrm{x}}=\mathrm{t}} \:\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{arctan}\left(\mathrm{t}^{\mathrm{2}} \right)}{\left(\mathrm{1}+\mathrm{t}^{\mathrm{2}}…

Question Number 185484 by Mingma last updated on 22/Jan/23 Answered by Ar Brandon last updated on 22/Jan/23 $${I}=\int_{\mathrm{0}} ^{\infty} \frac{{x}^{\mathrm{3}} }{{e}^{\mathrm{3}{x}} −\mathrm{1}}{dx}=\int_{\mathrm{0}} ^{\infty} \frac{{x}^{\mathrm{3}} {e}^{−\mathrm{3}{x}}…

Question Number 119930 by Lordose last updated on 28/Oct/20 Answered by mathmax by abdo last updated on 28/Oct/20 $$\mathrm{A}={\int }_0^1\arcsin \left(\tan \theta \right)\mathrm{d}\theta \mathrm{we}\mathrm{do}\mathrm{the}\mathrm{changement}$$$$\arcsin \left(\tan \theta \right)=\mathrm{x}\Rightarrow \tan \theta =\mathrm{sinx}\Rightarrow \theta =\mathrm{artan}\left(\mathrm{sinx}\right)\Rightarrow$$$$\mathrm{A}\:=\int_{\mathrm{0}}…

Question Number 185455 by cortano1 last updated on 22/Jan/23 $$\int \frac{x^3.e^{x^2}}{{(x^2+1)}^2}dx=?$$ Answered by SEKRET last updated on 22/Jan/23 $$\left.\:\:\mathrm{1}\right)\:\:\:\:\:\:\boldsymbol{\mathrm{x}}^{\mathrm{2}}…

Question Number 54376 by Abdo msup. last updated on 02/Feb/19 $$1)calculatef\left(a\right)={\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}\frac{dx}{x^2+ax+1}$$$$with\mid a\mid <2$$$$2)calculateg\left(a\right)={\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}\frac{x}{{(x^2+ax+1)}^2}$$$$\left.\mathrm{3}\right){find}\:{values}\:{of}\:{integrals}\:\int_{−\infty} ^{+\infty}…