Category: Integration

Question Number 48757 by sandeepkeshari0797@gmail.com last updated on 28/Nov/18 Commented by maxmathsup by imad last updated on 28/Nov/18 $$methodwithoneparametrletf\left(x\right)={\int }_0^{\mathrm{\infty }}\frac{sint}{t}{e}^{-tx}dtwithx⩾0wehave$$$${f}^{'} \left({x}\right)=−\int_{\mathrm{0}}…

Question Number 48719 by Abdo msup. last updated on 27/Nov/18 $$find\int \frac{x-2}{\sqrt{x^2+4x-3}}dx$$ Commented by Abdo msup. last updated on 27/Nov/18 $${I}=\int\:\:\frac{{x}−\mathrm{2}}{\:\sqrt{{x}^{\mathrm{2}} \:+\mathrm{4}{x}+\mathrm{4}−\mathrm{7}}}\:=\int\:\:\frac{{x}−\mathrm{2}}{\:\sqrt{\left({x}+\mathrm{2}\right)^{\mathrm{2}} −\mathrm{7}}}{dx}…

Question Number 48717 by Abdo msup. last updated on 27/Nov/18 $$letf\left(x\right)={\int }_0^{\frac{\pi }{4}}ln(1+xtant)dt$$$$1)findf\left(x\right)atasimpleform$$$$2)calculate{\int }_0^{\frac{\pi }{4}}ln(1+2tan\left(t\right))dt$$ Commented by maxmathsup by…

Question Number 48715 by Abdo msup. last updated on 27/Nov/18 $$1)findf\left(\lambda \right)={\int }_0^1\frac{dx}{2+e^{-\lambda x}}with\lambda >0$$$$2)calculate{\int }_0^1\frac{x}{{(2+e^{-\lambda x})}^2}dx$$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\frac{{dx}}{\mathrm{2}\:+{e}^{−{x}\sqrt{\mathrm{3}}} }{dx}\:{and}\:\int_{\mathrm{0}}…

Question Number 48667 by maxmathsup by imad last updated on 26/Nov/18 $$find{\int }_0^1\frac{arctan\left(x\right)}{\sqrt{1+x^2}}dx.$$ Commented by Abdo msup. last updated on 02/Dec/18…