Category: Integration

Question Number 107965 by bemath last updated on 13/Aug/20 $$\frac{⊚\mathcal{B}e\mathcal{M}ath⊚}{}$$$$\int x\sqrt{\frac{x}{2a-x}}dx?$$ Answered by bobhans last updated on 13/Aug/20 $$\frac{\ddots \mathcal{BOBHANS}\text{iddots}}{\mathrm{\Pi }}$$$$\:\mathrm{I}=\:\int\:\mathrm{x}\:\sqrt{\frac{\mathrm{x}}{\mathrm{2a}−\mathrm{x}}}\:\mathrm{dx}\:\:\left[\:\mathrm{set}\:\mathrm{x}\:=\:\mathrm{a}−\mathrm{acos}\:\mathrm{2t}\:\right] \…

Question Number 42407 by Tawa1 last updated on 25/Aug/18 $$\int \frac{1}{1+\mathrm{tanx}}\mathrm{dx}$$ Commented by maxmathsup by imad last updated on 25/Aug/18 $$letI=\int \frac{dx}{1+tanx}changementtanx=tgive$$$${I}\:\:=\:\int\:\:\:\:\:\frac{\mathrm{1}}{\left(\mathrm{1}+{t}\right)\left({t}^{\mathrm{2}} \:+\mathrm{1}\right)}{dt}\:\:{let}\:{decompose}\:{F}\left({t}\right)\:=\:\:\frac{\mathrm{1}}{\left({t}+\mathrm{1}\right)\left({t}^{\mathrm{2}}…

Question Number 42395 by abdo.msup.com last updated on 24/Aug/18 $$calculate\int {\int }_D\frac{xy}{(1+x^2+y^2)}dxdywith$$$$D=\{(x,y)\in R^2/0⩽x⩽1,0⩽y⩽1,x^2+y^2⩽1\}$$ Commented by maxmathsup by imad…

Question Number 42392 by abdo.msup.com last updated on 24/Aug/18 $$calculate\int \frac{lnx}{x+x{\left(lnx\right)}^2}dx$$ Commented by maxmathsup by imad last updated on 25/Aug/18 $$changementln\left(x\right)=tgive$$$${I}\:\:=\:\int\:\:\:\:\:\:\:\frac{{t}}{{e}^{{t}}…

Question Number 42370 by Raj Singh last updated on 24/Aug/18 Commented by maxmathsup by imad last updated on 24/Aug/18 $$letA=\int \frac{dx}{sin\left(2x\right)+sinx}$$$${A}\:=\:\int\:\:\:\:\:\frac{{dx}}{\mathrm{2}{sinx}\:{cosx}\:+{sinx}}\:=\:\int\:\:\:\:\:\:\frac{{sinx}}{\mathrm{2}{sin}^{\mathrm{2}} {xcosx}\:+{sin}^{\mathrm{2}} {x}}\:{dx} \…