Category: Integration

Question Number 84894 by Power last updated on 17/Mar/20 Commented by abdomathmax last updated on 18/Mar/20 $$I=\int \sqrt{\frac{ax+b}{cx+d}}dxwedothechangement\sqrt{\frac{ax+b}{cx+d}}=t\Rightarrow$$$$\frac{{ax}+{b}}{{cx}+{d}}={t}^{\mathrm{2}} \:\Rightarrow{ax}+{b}={ct}^{\mathrm{2}} {x}\:+{dt}^{\mathrm{2}} \:\Rightarrow\left({a}−{ct}^{\mathrm{2}} \right){x}={dt}^{\mathrm{2}} −{b}\:\Rightarrow \…

Question Number 84859 by M±th+et£s last updated on 16/Mar/20 $$showthat$$$$\underset{{n}\rightarrow\infty} {{lim}}\int_{\mathrm{0}} ^{\mathrm{1}} …\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{n}}{{x}_{\mathrm{1}} +{x}_{\mathrm{2}} +{x}_{\mathrm{3}} +…+{x}_{{n}} }{dx}_{\mathrm{1}} {dx}_{\mathrm{2}} …{dx}_{{n}} =\mathrm{2}\: \…

Question Number 150366 by SLVR last updated on 11/Aug/21 Commented by SLVR last updated on 11/Aug/21 $$kindlyprovidesolution..already$$$$giveningroup$$ Terms of Service Privacy…

Question Number 84809 by M±th+et£s last updated on 16/Mar/20 $$\int \frac{x}{{(x^2+1)}^{\frac{3}{2}}arctan\left(x\right)}dx$$ Commented by abdomathmax last updated on 18/Mar/20 $${A}\:=\int\:\:\:\:\frac{{x}}{\left({x}^{\mathrm{2}\:} +\mathrm{1}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} \:{arctanx}}\:{changement}\:{arctanx}={t} \…

Question Number 84766 by jagoll last updated on 15/Mar/20 $$\int \frac{\mathrm{dx}}{{(16+9\sin \mathrm{x})}^2}$$$$$$ Commented by jagoll last updated on 16/Mar/20 $$\int\:\mathrm{sec}\:\:\mathrm{x}\:\left[\:\frac{\mathrm{cos}\:\:\mathrm{x}}{\left(\mathrm{16}+\mathrm{9sin}\:\mathrm{x}\right)^{\mathrm{2}} }\right]\:\mathrm{dx}\:= \…