Question Number 215266 by depressiveshrek last updated on 02/Jan/25 $$\mathrm{Evaluate}\:\int_{{a}} ^{{b}} \frac{\mathrm{1}}{{x}}{dx}\:\mathrm{using}\:\mathrm{Riemann}\:\mathrm{sum} \\ $$$$\mathrm{0}<{a}<{b} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 215188 by MrGaster last updated on 31/Dec/24 $$\int_{\mathrm{0}} ^{\infty} \frac{{x}\:\mathrm{cos}\:\mathrm{2}\pi{x}}{{e}^{\mathrm{2}\pi\sqrt{{x}}} −\mathrm{1}}{dx} \\ $$ Answered by MathematicalUser2357 last updated on 31/Dec/24 $$\approx\mathrm{0}.\mathrm{000807442} \\ $$…
Question Number 215189 by MrGaster last updated on 31/Dec/24 $$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{ln}\left(\mathrm{1}+{x}^{\mathrm{12}} \right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$ Answered by MathematicalUser2357 last updated on 31/Dec/24 $$\mathrm{OMFG}\:\mathrm{Expression}\:\mathrm{too}\:\mathrm{long}. \\…
Question Number 215185 by MrGaster last updated on 31/Dec/24 $$\int_{−\infty} ^{\infty} \frac{\mathrm{exp}\left(\frac{{ax}}{\mathrm{1}+{x}^{\mathrm{2}} }\right)\mathrm{exp}\left(\frac{{a}}{\mathrm{1}+{x}^{\mathrm{2}} }\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx},{a}>\mathrm{0} \\ $$ Answered by MathematicalUser2357 last updated on 31/Dec/24 $$\mathrm{Oops}!\:\mathrm{Make}\:\mathrm{sure}\:\mathrm{you}\:\mathrm{typed}\:\mathrm{the}\:\mathrm{expression}\:\mathrm{made}\:\mathrm{of}\:{x}.…
Question Number 215190 by MrGaster last updated on 31/Dec/24 $$\int\frac{{x}^{{p}−\mathrm{1}} }{\mathrm{1}+{x}^{{n}} }\mathrm{lnln}\frac{\mathrm{1}}{{x}}{dx},{p},{n}>\mathrm{0} \\ $$ Answered by MathematicalUser2357 last updated on 31/Dec/24 $$\mathrm{No}\:\mathrm{result}\:\mathrm{found}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{standard}\:\mathrm{mathematical}\:\mathrm{functions} \\ $$ Answered…
Question Number 215187 by MrGaster last updated on 31/Dec/24 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}\boldsymbol{{K}}^{\mathrm{2}} \left({x}\right)}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{dx} \\ $$ Answered by MathematicalUser2357 last updated on 31/Dec/24 $$\approx\mathrm{8}.\mathrm{473967} \\…
Question Number 215186 by MrGaster last updated on 31/Dec/24 $$\int_{\mathrm{0}} ^{\infty} {Ei}\left(−{x}\right)\mathrm{ln}{xdx} \\ $$ Answered by MathematicalUser2357 last updated on 31/Dec/24 $$=\mathrm{1}+\boldsymbol{\gamma}\:\left(\approx\mathrm{1}.\mathrm{57722}\right) \\ $$ Terms…
Question Number 215161 by MrGaster last updated on 30/Dec/24 $$ \\ $$$$\:\:\:\:\:\:\int\frac{\left({x}^{\mathrm{8}} +\mathrm{16}{x}^{\mathrm{7}} −\mathrm{2}{x}^{\mathrm{4}} −\mathrm{3}\right){e}^{{x}} }{\left(\mathrm{1}+{x}^{\mathrm{4}} \right)^{\mathrm{2}/\mathrm{3}} }{dx} \\ $$$$ \\ $$ Commented by MathematicalUser2357…
Question Number 215134 by RoseAli last updated on 29/Dec/24 Answered by Ghisom last updated on 29/Dec/24 $$\int\sqrt{{x}−\sqrt{{x}^{\mathrm{2}} −\mathrm{4}}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\sqrt{{x}−\sqrt{{x}^{\mathrm{2}} −\mathrm{4}}}\:\rightarrow\:{dx}=−\frac{\mathrm{2}\sqrt{{x}^{\mathrm{2}} −\mathrm{4}}}{{t}}{dt}\right] \\ $$$$=\int\left({t}^{\mathrm{2}} −\frac{\mathrm{4}}{{t}^{\mathrm{2}}…
Question Number 215081 by MrGaster last updated on 28/Dec/24 $$ \\ $$$$\mathrm{prove}: \\ $$$$ \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{\left(\mathrm{ln}\left({x}/\left(\mathrm{1}+{x}\right)\right)^{\mathrm{4}} \mathrm{ln}\left({x}^{\mathrm{3}} \left(\mathrm{1}+{x}\right)^{\mathrm{17}} \right.\right.}{\mathrm{1}+{x}}{dx}=−\mathrm{240}\zeta\left(\mathrm{3}\right)^{\mathrm{2}} \\ $$$$ \\ $$…