Category: Integration

Question Number 63079 by mathmax by abdo last updated on 28/Jun/19 $$letf\left(z\right)=\frac{sin\left(2z\right)}{z^n}withnintegrnatural$$$$calculateRes(f,0)$$ Commented by mathmax by abdo last updated on…

Question Number 128610 by john_santu last updated on 08/Jan/21 $${\int }_{-\pi /4}^{\pi /4}\frac{\sec \mathrm{x}}{{\mathrm{e}}^{\mathrm{x}}+1}\mathrm{dx}$$ Commented by liberty last updated on 09/Jan/21 $$\mathrm{I}=−\int_{−\pi/\mathrm{4}} ^{\:\pi/\mathrm{4}} \frac{\mathrm{sec}\:\left(−\mathrm{x}\right)}{\mathrm{e}^{−\mathrm{x}}…

Question Number 128602 by Ahmed1hamouda last updated on 08/Jan/21 $${\int }_{-1}^1{\int }_0^{1-x}\sqrt{\frac{x^{\frac{2}{3}}y-x^{\frac{5}{3}}y-x^{\frac{2}{3}}{y}^2}{y^2}}dydx$$$$$$ Answered by…

Question Number 128575 by Study last updated on 08/Jan/21 $$\int \sqrt{x^2+4x+13}dx=??$$ Commented by MJS_new last updated on 08/Jan/21 $$\mathrm{use}\mathrm{formula}\mathrm{for}\int \sqrt{x^2+ax+b}dx!!!\mathrm{to}\mathrm{get}$$$$\frac{\left({x}+\mathrm{2}\right)\sqrt{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{13}}}{\mathrm{2}}+\frac{\mathrm{9}}{\mathrm{2}}\mathrm{ln}\:\left({x}+\mathrm{2}+\sqrt{{x}^{\mathrm{2}}…

Question Number 63032 by mathmax by abdo last updated on 28/Jun/19 $$letf\left(z\right)=\frac{1}{sin\left(\pi z\right)}calculateRes(f,n)withnintegr$$ Commented by mathmax by abdo last updated on 28/Jun/19 $${z}={n}\:{is}\:{simple}\:{pole}\:{for}\:{f}\:\Rightarrow{Res}\left({f},{n}\right)\:={lim}_{{z}\rightarrow{n}} \frac{{z}−{n}}{{sin}\left(\pi{z}\right)}…