Category: Integration

Question Number 157309 by cortano last updated on 22/Oct/21 $$\int \frac{dx}{\sqrt{x}+x\sqrt{x+1}}=?$$ Answered by MJS_new last updated on 22/Oct/21 $$\int \frac{dx}{\sqrt{x}+x\sqrt{x+1}}=$$$$=\int\frac{\sqrt{{x}+\mathrm{1}}}{{x}^{\mathrm{2}} +{x}−\mathrm{1}}{dx}−\int\frac{{dx}}{\left({x}^{\mathrm{2}} +{x}−\mathrm{1}\right)\sqrt{{x}}} \…

Question Number 91771 by  M±th+et+s last updated on 03/May/20 $${\int }_0^{\mathrm{\infty }}\frac{{sin}^3\left(x\right)}{x^2}dx$$ Commented by abdomathmax last updated on 03/May/20 $${let}\:{I}=\int_{\mathrm{0}} ^{\infty}…

Question Number 157268 by gsk2684 last updated on 21/Oct/21 $$provethat$$$$\int \frac{x^2}{{(x\sin x+\cos x)}^2}dx=-\frac{x\sec x}{x\sin x+\cos x}+\tan x+c$$ Answered by Ar Brandon last updated on 18/Nov/21 $${I}=\int\frac{{x}^{\mathrm{2}}…

Question Number 157257 by john_santu last updated on 21/Oct/21 $$\int \frac{\sin {}^{6}x+\cos {}^{5}x}{\sin {}^{2}x\cos {}^{2}x}dx$$ Answered by qaz last updated on 21/Oct/21 $$\int\frac{\mathrm{sin}\:^{\mathrm{6}} \mathrm{x}+\mathrm{cos}\:^{\mathrm{5}}…

Question Number 157254 by physicstutes last updated on 21/Oct/21 $$\mathrm{Show}\mathrm{that}{\int }_0^1\frac{1}{(x+1)(x+2)}dx=\ln \left(\frac{4}{3}\right)$$ Answered by puissant last updated on 21/Oct/21 $$\Omega=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)}{dx}\:=\:\int_{\mathrm{0}} ^{\mathrm{1}}…