Category: Integration

Question Number 94718 by john santu last updated on 20/May/20 $$\int \sqrt{\tan \mathrm{x}}\mathrm{dx}=$$$$\int \frac{\sqrt{\tan \mathrm{x}}+\sqrt{\cot \mathrm{x}}}{2}\mathrm{dx}+\int \frac{\sqrt{\tan \mathrm{x}}-\sqrt{\cot \mathrm{x}}}{2}\mathrm{dx}$$$$=\frac{1}{\sqrt{2}}\int \frac{\sin \mathrm{x}+\cos \mathrm{x}}{\sqrt{\sin 2\mathrm{x}}}\mathrm{dx}+\frac{1}{\sqrt{2}}\int \frac{\sin \mathrm{x}-\cos \mathrm{x}}{\sqrt{\sin 2\mathrm{x}}}\mathrm{dx}$$$$=\frac{1}{\sqrt{2}}\int \frac{\sin \mathrm{x}+\cos \mathrm{x}}{\sqrt{1-{(\sin \mathrm{x}-\cos \mathrm{x})}^2}}\mathrm{dx}+$$$$\frac{1}{\sqrt{2}}\int \frac{\sin \mathrm{x}-\cos \mathrm{x}}{\sqrt{{(\sin \mathrm{x}+\cos \mathrm{x})}^2-1}}\mathrm{dx}$$$$=\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}\:}\int\:\frac{\mathrm{dt}}{\:\sqrt{\mathrm{1}−\mathrm{t}^{\mathrm{2}} }}\:+\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}\:}\int\:\frac{−\mathrm{du}}{\:\sqrt{\mathrm{u}^{\mathrm{2}} −\mathrm{1}}}…

Question Number 29162 by abdo imad last updated on 04/Feb/18 $$findfindI={\int }_1^3\frac{\mid x-2\mid }{{(x^2-4x)}^2}dx.$$ Commented by abdo imad last updated on 06/Feb/18…

Question Number 94662 by i jagooll last updated on 20/May/20 $$\int \sqrt{\tan \mathrm{x}+\cot \mathrm{x}}\mathrm{dx}=?$$ Commented by i jagooll last updated on 20/May/20 $$\int\:\frac{\mathrm{sec}\:^{\mathrm{2}} \mathrm{x}\:\mathrm{dx}}{\:\sqrt{\mathrm{1}+\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}}\:.\sqrt{\mathrm{tan}\:\mathrm{x}}}\:=\: \…

Question Number 94649 by msup by abdo last updated on 20/May/20 $$calculate{\int }_0^{\mathrm{\infty }}{e}^{-x}lnxdx$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 94625 by i jagooll last updated on 20/May/20 $$\underset{0}{\stackrel{1}{\int }}\ln (\mathrm{\Gamma }\left(x\right)dx=?$$$$note\mathrm{\Gamma }\left(x\right):\mathrm{Gamma}\mathrm{function}$$ Commented by turbo msup by abdo last updated…