Category: Integration

Question Number 38124 by maxmathsup by imad last updated on 22/Jun/18 $$provethat\int \frac{dx}{\sqrt{1+x^2}}=ln(x+\sqrt{1+x^2})+c$$$$2)find\int \frac{dx}{\sqrt{a+x^2}}witha>0$$ Answered by tanmay.chaudhury50@gmail.com last updated on…

Question Number 38122 by maxmathsup by imad last updated on 22/Jun/18 $$calculate{\int }_0^{\pi }\frac{sinx}{\sqrt{1+{cos}^{2}x}}dx$$ Answered by tanmay.chaudhury50@gmail.com last updated on 22/Jun/18 $${t}={cosx}\:\:\:{dt}=−{sinxdx}…

Question Number 38119 by maxmathsup by imad last updated on 22/Jun/18 $$calculate{\int }_1^{+\mathrm{\infty }}\frac{dx}{x^4\sqrt{x-1}}$$ Commented by math khazana by abdo last updated…

Question Number 38118 by maxmathsup by imad last updated on 21/Jun/18 $$provethat{\int }_0^1\frac{1}{1+\frac{t^a}{2}}dt=\sum _{n=0}^{\mathrm{\infty }}\frac{{(-1)}^n}{2^n(na+1)}$$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{2}^{{n}} \left(\mathrm{3}{n}+\mathrm{1}\right)}…

Question Number 38117 by maxmathsup by imad last updated on 21/Jun/18 $$letxandyfromRprovethat$$$$\mid cos(x+iy)\mid ={cos}^{2}x+{sh}^{2}y$$$$\mid sin(x+iy){\mid }^2={sin}^{2}x+{sh}^{2}y$$ Terms of…