Category: Integration

Question Number 124922 by mathmax by abdo last updated on 07/Dec/20 $$\mathrm{let}\mathrm{f}\left(\mathrm{x}\right)=\frac{\ln (1+2\mathrm{x})}{{\mathrm{x}}^2+1}$$$$1)\mathrm{calculste}{\mathrm{f}}^{\left(\mathrm{n}\right)}\left(\mathrm{x}\right)\mathrm{and}{\mathrm{f}}^{\left(\mathrm{n}\right)}\left(0\right)$$$$2)\mathrm{develop}\mathrm{f}\mathrm{at}\mathrm{integr}\mathrm{serie}$$$$3)\mathrm{find}{\int }_0^1\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}$$…

Question Number 124921 by mathmax by abdo last updated on 07/Dec/20 $$\mathrm{calculate}{\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}{\mathrm{z}}^{-{\mathrm{x}}^2}\mathrm{dx}\mathrm{with}\mathrm{z}\mathrm{complex}$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 59381 by Karan last updated on 09/May/19 $$\int \frac{xdx}{\sin x}=?$$ Commented by Mr X pcx last updated on 11/May/19 $${let}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{{x}} \:\:\frac{{t}}{{sint}}{dt}\:{we}\:{have}\: \…

Question Number 124903 by Algoritm last updated on 06/Dec/20 Answered by MJS_new last updated on 06/Dec/20 $$\mathrm{just}\mathrm{decompose}\mathrm{and}\mathrm{solve},\mathrm{no}\mathrm{special}$$$$\mathrm{knowledge}\mathrm{necessary}.\mathrm{the}\mathrm{answer}\mathrm{is}:$$$$\frac{x-1}{2(x^2+1)}+\frac{1}{4}\ln (x^2+1)-\frac{1}{2}\ln \mid x+1\mid +C$$$$\mathrm{now}\:\mathrm{try}\:\mathrm{to}\:\mathrm{reach}\:\mathrm{this}\:\mathrm{for}\:\mathrm{yourself}…

Question Number 124887 by mnjuly1970 last updated on 06/Dec/20 $$\dots nicecalculus..$$$$evaluate:$$$$2{\int }_1^{\mathrm{\infty }}\left(\frac{\left\{x\right\}-\frac{1}{2}}{x}\right)dx-{\int }_0^{1}ln\left(\mathrm{\Gamma }\left(x\right)\right)dx=???$$$$\left\{x\right\}:fractionalpart\dots$$ Answered by Dwaipayan…