Category: Integration

Question Number 212023 by Spillover last updated on 27/Sep/24 Answered by Frix last updated on 27/Sep/24 $$\int \frac{(x+1)\tan x}{{(1+\tan x)}^2}dx=$$$$=\frac{1}{2}\int (x+1-\frac{1}{\underset{[t=\tan x]}{\underbrace{1+\sin 2x}}}-\frac{x}{\underset{\left[\mathrm{by}\mathrm{parts}\right]}{\underbrace{1+\sin 2x}}})dx=$$$$… \…

Question Number 212007 by Nadirhashim last updated on 26/Sep/24 $$\int \mathit{s}\mathit{i}\mathit{n}\left(\mathit{x}\right)\sqrt[3]{\mathit{t}\mathit{a}\mathit{n}\left(\mathit{x}\right)}.\mathit{d}\mathit{x}$$ Answered by Ghisom last updated on 26/Sep/24 $$=\int {\left(\cos x\right)}^{-1/3}{\left(\sin x\right)}^{4/3}dx=$$$$=\frac{\mathrm{3}}{\mathrm{7}}\:_{\mathrm{2}} {F}_{\mathrm{1}}…

Question Number 211857 by Frix last updated on 22/Sep/24 $$\underset{1}{\stackrel{\mathrm{\infty }}{\int }}\left(\frac{{\tan }^{-1}x}{x}\times \frac{\ln x}{x}\right)dx=?$$ Answered by Berbere last updated on 23/Sep/24 $$\int_{\mathrm{1}} ^{\infty} \frac{\mathrm{tan}^{−\mathrm{1}}…

Question Number 211749 by universe last updated on 19/Sep/24 $$volumeboundedbythecurve$$$$z=\sqrt{3x^2+3y^2}and{x}^2+y^2+z^2=6^2$$ Answered by mr W last updated…

Question Number 211696 by mnjuly1970 last updated on 16/Sep/24 $$$$$${\underset{0}{\int }}^1\frac{1}{{(2+2x+x^2)}^3}dx=?$$$$\underbrace{\underset{\stackrel{\mathrm{Improper}\mathrm{integral}}{}}{}}$$$$---------$$ Answered…