Category: Integration

Question Number 211486 by mnjuly1970 last updated on 10/Sep/24 $$$$$$MathematicalAnalysis\dots$$$$$$$$f:\mathbb{R}\to \mathbb{R}isdiffrentiablefunction,$$$$fandf{}^{\prime },hasnocommonzero$$$$on\mathbb{R}.$$$$provethatthefollowingsetisfinite.$$$$ \…

Question Number 211400 by Spillover last updated on 08/Sep/24 $$$$$${\int }_0^1\frac{x^3-3x^2+3x-1}{x^4+4x^3+6x^2+4x+1}dx$$$$$$ Answered by…

Question Number 211344 by Nadirhashim last updated on 06/Sep/24 $$find\int \frac{\mathit{d}\mathit{x}}{{\mathit{s}\mathit{i}\mathit{n}}^3\left(\mathit{x}\right){\mathit{c}\mathit{o}\mathit{s}}^5\left(\mathit{x}\right)}.\mathit{d}\mathit{x}$$ Answered by Frix last updated on 06/Sep/24 $$\int\frac{{dx}}{\mathrm{cos}^{\mathrm{5}} \:{x}\:\mathrm{sin}^{\mathrm{3}} \:{x}}=\int\frac{\left(\mathrm{1}+\mathrm{tan}^{\mathrm{2}} \:{x}\right)^{\mathrm{4}}…

Question Number 211155 by Spillover last updated on 30/Aug/24 $$\int \frac{{(\sin {}^n\left(\theta \right)-\sin \left(\theta \right))}^{\frac{1}{n}}\cos \left(\theta \right)}{\sin {}^{n+1}\left(\theta \right)}d\theta$$$$$$ Answered by Frix last updated on 30/Aug/24 $$=\int\frac{{d}\theta}{\mathrm{sin}\:\theta}\:−\int\left(\mathrm{sin}\:\theta\right)^{\frac{\mathrm{1}−{n}−{n}^{\mathrm{2}}…

Question Number 211152 by Spillover last updated on 29/Aug/24 $$$$$$$$$$\int \frac{\sqrt{x}}{1+x+x^2+x^3}dx$$$$$$ Answered by Ghisom last updated…