Category: Integration

Question Number 42489 by maxmathsup by imad last updated on 26/Aug/18 $$calculateL\left({sinxe}^{-ax}\right)witha>0Lmeanslaplacetransform.$$ Commented by maxmathsup by imad last updated on 27/Aug/18 $${L}\left({sinx}\:{e}^{−{ax}}…

Question Number 42487 by maxmathsup by imad last updated on 26/Aug/18 $$letf\left(x\right)={\int }_0^1\frac{dt}{x+ch\left(t\right)}$$$$1)findaexpliciteformoff\left(x\right)$$$$2)calculate{\int }_0^1\frac{dt}{{(x+ch\left(t\right))}^2}$$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\:\frac{{dt}}{\mathrm{1}+{ch}\left({t}\right)}\:{and}\:\:\int_{\mathrm{0}}…

Question Number 173523 by Physicien last updated on 13/Jul/22 Answered by Mathspace last updated on 13/Jul/22 $$I=\int \frac{1+\sqrt{x}-\sqrt{1+x}}{{(1+\sqrt{x})}^2-1-x}dx$$$$=\int \frac{1+\sqrt{x}-\sqrt{1+x}}{1+2\sqrt{x}+x-1-x}dx$$$$=\frac{1}{2}\int \frac{1+\sqrt{x}}{\sqrt{x}}dx-\frac{1}{2}\int \frac{\sqrt{1+x}}{\sqrt{x}}dx$$$${we}\:{have}\:\int\frac{\mathrm{1}+\sqrt{{x}}}{\:\sqrt{{x}}}{dx}=\int\frac{{dx}}{\:\sqrt{{x}}}\:+\int{dx} \…

Question Number 42435 by maxmathsup by imad last updated on 25/Aug/18 $$find{\int }_0^1\frac{dx}{\sqrt{x}+\sqrt{1-x}}$$ Commented by maxmathsup by imad last updated on 25/Aug/18…

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] \…