Category: Integration

Question Number 124251 by bramlexs22 last updated on 02/Dec/20 $$\underset{0}{\stackrel{\mathrm{\infty }}{\int }}\frac{x^2}{\cosh x}dx?$$ Commented by Dwaipayan Shikari last updated on 02/Dec/20 $$\mathrm{2}\underset{{n}=\mathrm{1}} {\overset{\infty}…

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Question Number 124217 by bramlexs22 last updated on 01/Dec/20 $$\underset{0}{\stackrel{\mathrm{\infty }}{\int }}\frac{dx}{x\sqrt{1+x^2}}?$$ Answered by Dwaipayan Shikari last updated on 01/Dec/20 $$\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\:={t}\Rightarrow\frac{{x}}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}}…

Question Number 124201 by mnjuly1970 last updated on 01/Dec/20 $$:::nicecalculus:::$$$$pleaseprove:::$$$$\mathrm{\Omega }={\int }_0^{\mathrm{\infty }}\frac{x^{\frac{1}{2}}}{x^2+2x+5}dx=\frac{\pi }{\sqrt{\phi }}$$$$where\phi isGoldenratio\dots$$ Answered by ajfour…

Question Number 58639 by rahul 19 last updated on 26/Apr/19 Answered by tanmay last updated on 27/Apr/19 $$F\left(x\right)={\int }_0^{x}tf\left(t\right)dt$$$$\frac{{dF}}{{dx}}=\int_{\mathrm{0}} ^{{x}} \frac{\partial}{\partial{x}\:}\left({tf}\left({t}\right){dt}\:+{xf}\left({x}\right)\frac{{dx}}{{dx}}−\mathrm{0}×{f}\left(\mathrm{0}\right)×\frac{{d}\mathrm{0}}{{dx}}\right. \…