Category: Integration

Question Number 213216 by Spillover last updated on 01/Nov/24 Answered by MrGaster last updated on 01/Nov/24 $$=\int_{\mathrm{0}} ^{\infty} \frac{{x}^{\mathrm{3}} }{\left({x}+\mathrm{1}\right)^{\mathrm{2}} \left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}^{\mathrm{3}} +\mathrm{1}\right)}{dx}+\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{log}^{\mathrm{2}}…

Question Number 213138 by Spillover last updated on 31/Oct/24 Commented by Frix last updated on 31/Oct/24 $$\mathrm{We}\mathrm{must}\mathrm{first}\mathrm{solve}\int \sin t^{3}dt\mathrm{which}\mathrm{might}$$$$\mathrm{be}\mathrm{possible}\mathrm{using}$$$$\mathrm{sin}\:{t}^{\mathrm{3}} \:=\frac{\mathrm{e}^{\mathrm{i}{t}^{\mathrm{3}} } −\mathrm{e}^{−\mathrm{i}{t}^{\mathrm{3}}…

Question Number 213114 by efronzo1 last updated on 30/Oct/24 $$\underset{―}{\mathbf{÷}}$$ Answered by issac last updated on 30/Oct/24 $$f\left(x\right)=-C(x-1)+\frac{\mathit{i}}{\pi }{(x-1)}^{5000}\ln (x-1)$$$$(\mathrm{thx}\mathrm{wolfram}\mathrm{alpha}!!)$$$${f}\left(\mathrm{1}\right)=\mathrm{0}\:,\:\mathrm{cus}\:\:{f}\left(\mathrm{1}+\mathrm{0}\right)+{f}\left(\mathrm{1}−\mathrm{0}\right)=\mathrm{0}^{\mathrm{5000}}…

Question Number 213098 by MathematicalUser2357 last updated on 30/Oct/24 $$\int \frac{3x+2}{5x^2+2x+3}\mathrm{d}x=?$$ Answered by issac last updated on 30/Oct/24 $$\mathrm{Hmmmmm}\dots ..$$$$\frac{\mathrm{3}{x}+\mathrm{2}}{\mathrm{5}{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{3}}=\frac{\mathrm{3}\left(\mathrm{10}{x}+\mathrm{2}\right)}{\mathrm{10}\left(\mathrm{5}{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{3}\right)}+\frac{\mathrm{7}}{\mathrm{5}\left(\mathrm{5}{x}^{\mathrm{2}}…

Question Number 212899 by vasil92 last updated on 26/Oct/24 Answered by MrGaster last updated on 02/Nov/24 $$\underset{n\to \mathrm{\infty }}{\lim }{\int }_0^1\sqrt{1-x^n}dx=1$$$$=\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left[{x}−\frac{{x}^{{n}−\mathrm{1}} }{\left({n}+\mathrm{1}\right)\centerdot^{\mathrm{2}}…