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Category: Integration

find-U-n-0-e-nx-2-x-2-n-2-dx-n-1-nature-of-U-n-and-nU-n-

Question Number 147203 by mathmax by abdo last updated on 18/Jul/21 $$\mathrm{find}\:\mathrm{U}_{\mathrm{n}} =\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{e}^{−\mathrm{nx}^{\mathrm{2}} } }{\mathrm{x}^{\mathrm{2}} \:+\mathrm{n}^{\mathrm{2}} }\mathrm{dx}\:\:\:\:\:\left(\mathrm{n}\geqslant\mathrm{1}\right) \\ $$$$\mathrm{nature}\:\mathrm{of}\:\Sigma\mathrm{U}_{\mathrm{n}} \:\mathrm{and}\:\Sigma\:\mathrm{nU}_{\mathrm{n}} \\ $$ Answered…

x-5-2-x-3-dx-

Question Number 16061 by Joel577 last updated on 17/Jun/17 $$\int\:{x}^{\mathrm{5}} \sqrt{\mathrm{2}\:−\:{x}^{\mathrm{3}} }\:{dx} \\ $$ Answered by Tinkutara last updated on 17/Jun/17 $$\mathrm{Let}\:\mathrm{2}\:−\:{x}^{\mathrm{3}} \:=\:{t} \\ $$$$\mathrm{Then}\:−\mathrm{3}{x}^{\mathrm{2}}…