Category: Integration

Question Number 53601 by maxmathsup by imad last updated on 23/Jan/19 $$calculate{\int }_0^{\mathrm{\infty }}\frac{e^{-x^2}-e^{-x}}{x}dx.$$ Answered by tanmay.chaudhury50@gmail.com last updated on…

Question Number 119070 by benjo_mathlover last updated on 22/Oct/20 $$\int \frac{x^2-x+6}{x^3+3x}dx$$$$\int \frac{5x^2+3x-2}{x^3+2x^2}dx$$ Answered by Olaf last updated on…

Question Number 119038 by MJS_new last updated on 21/Oct/20 $$\underset{-\pi /4}{\stackrel{+\pi /4}{\int }}\frac{\sqrt{1+\tan x}}{\sqrt{1-\tan x}}dx$$ Answered by mindispower last updated on 21/Oct/20 $$=\int_{−\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{4}}} \frac{\sqrt{\mathrm{1}−{tg}\left({x}\right)}}{\:\sqrt{\mathrm{1}+{tg}\left({x}\right)}}{dx},{I}=\int\frac{\sqrt{\mathrm{1}+{tg}\left({x}\right)}}{\:\sqrt{\mathrm{1}−{tg}\left({x}\right)}}{dx} \…

Question Number 119021 by A8;15: last updated on 21/Oct/20 Answered by MJS_new last updated on 21/Oct/20 $$\int \frac{\sqrt{\sin x}}{\sqrt{\sin x}+\sqrt{\cos x}}dx=\int \frac{\sqrt{\tan x}}{1+\sqrt{\tan x}}dx=$$$$[t=\sqrt{\tan x}\to dx=\frac{2t}{t^4+1}dt]$$$$=\mathrm{2}\int\frac{{t}^{\mathrm{2}} }{\left({t}+\mathrm{1}\right)\left({t}^{\mathrm{4}} +\mathrm{1}\right)}{dt} \…

Question Number 53477 by maxmathsup by imad last updated on 22/Jan/19 $$letf\left(a\right)={\int }_0^1\frac{dt}{\sqrt{x+a}+3}$$$$1)calculatef\left(a\right)$$$$2)findalso{\int }_0^1\frac{dt}{\sqrt{x+a}{(\sqrt{x+a}+3)}^2}$$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{values}\:{of}\:{integrals}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dt}}{\:\sqrt{{x}+\mathrm{1}}+\mathrm{3}}\:\:{and}\:\int_{\mathrm{0}}…