Category: Integration

Question Number 31104 by abdo imad last updated on 02/Mar/18 $$find{\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}{e}^{-(x^2+2x-1)}dx.$$ Commented by abdo imad last updated on 03/Mar/18…

Question Number 96637 by 175 last updated on 03/Jun/20 Commented by bemath last updated on 03/Jun/20 $$\int \frac{\ln \left({\mathrm{x}}^{\mathrm{a}}\right)}{\mathrm{x}}\mathrm{dx}=\mathrm{a}\int \frac{\ln \left(\mathrm{x}\right)}{\mathrm{x}}\mathrm{dx}$$$$\mathrm{let}\mathrm{u}=\ln \left(\mathrm{x}\right)\Rightarrow \mathrm{du}=\frac{\mathrm{dx}}{\mathrm{x}}$$$$\Rightarrow \mathrm{a}\int \mathrm{u}\mathrm{du}=\frac{1}{2}\mathrm{a}{\mathrm{u}}^2+\mathrm{c}$$$$=\:\frac{\mathrm{a}}{\mathrm{2}}\:\left(\mathrm{ln}\left(\mathrm{x}\right)\right)^{\mathrm{2}}…

Question Number 31100 by abdo imad last updated on 02/Mar/18 $$find{\int }_0^{\mathrm{\infty }}\frac{cosx-cos\left(3x\right)}{x}{e}^{-2x}dx.$$ Commented by abdo imad last updated on 04/Mar/18 $${let}\:{introduce}\:{the}\:{function}\:{f}\left({t}\right)=\int_{\mathrm{0}}…

Question Number 31097 by abdo imad last updated on 02/Mar/18 $$calculateintermsofaandbtheintegral$$$${\int }_0^{\mathrm{\infty }}\frac{arctan\left(bt\right)-arctan\left(at\right)}{t}dtwithaandb>0.$$ Commented by abdo imad last updated on 05/Mar/18…

Question Number 31096 by abdo imad last updated on 02/Mar/18 $$find{\int }_0^{\pi }\frac{dx}{{(a+bcosx)}^2}witha>b>0thengivethe$$$$valueof{\int }_0^{\pi }\frac{dx}{{(2+cosx)}^2}$$ Commented by abdo imad…