Category: Integration

Question Number 207382 by efronzo1 last updated on 13/May/24 Answered by sniper237 last updated on 13/May/24 $$\overset{{X}=^{\mathrm{3}} \sqrt{{x}−\mathrm{2}}} {=}\underset{{X}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{X}^{\mathrm{6}} +\mathrm{2}{X}^{\mathrm{3}} +{X}}{\:^{\mathrm{3}} \sqrt{\mathrm{4}−\mathrm{2}\sqrt{\mathrm{3}{X}^{\mathrm{3}} +\mathrm{4}}−{X}^{\mathrm{3}} \sqrt{\mathrm{3}{X}^{\mathrm{3}}…

Question Number 207359 by Shrodinger last updated on 12/May/24 $$\int \frac{ln(x^2+sin\left(sin\left(e^x\right)\right))}{\sqrt{x+tan\left(ln\left(x\right)\right)}}dx$$ Answered by Berbere last updated on 12/May/24 $$itsemmsnoncloseforme$$ Commented…

Question Number 207099 by tri26112004 last updated on 06/May/24 Answered by Berbere last updated on 06/May/24 $$={\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}\frac{e^{i\pi ax}}{{(x^2+{\beta }^2)}^{n+1}}dx;a\in {\mathbb{R}}_{+}$$$${if}\:{Imx}\geqslant\mathrm{0}\:\mid{e}^{{i}\pi{ax}}…

Question Number 206962 by Ghisom last updated on 01/May/24 $$\underset{0}{\stackrel{1}{\int }}\frac{\sqrt{1-x}}{\sqrt{1-\sqrt{1-x}}+\sqrt{1+\sqrt{1-x}}}dx=?$$ Answered by lepuissantcedricjunior last updated on 02/May/24 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\sqrt{\mathrm{1}−\boldsymbol{{x}}}}{\:\sqrt{\mathrm{1}−\sqrt{\mathrm{1}−\boldsymbol{{x}}}}+\sqrt{\mathrm{1}+\sqrt{\mathrm{1}−\boldsymbol{{x}}}}}\boldsymbol{{dx}}=\boldsymbol{{k}} \…

Question Number 206890 by mathzup last updated on 29/Apr/24 $$cansomeonefindtheexactvalueof$$$$\sum _{n=0}^{\mathrm{\infty }}\frac{1}{{(n!)}^2}$$ Commented by Frix last updated on 30/Apr/24 $$\mathrm{This}\:\mathrm{is}\:\mathrm{a}\:\mathrm{Modified}\:\mathrm{Bressel}\:\mathrm{Function}\:\mathrm{of}\:\mathrm{the}…