Category: Integration

Question Number 37343 by math khazana by abdo last updated on 12/Jun/18 $$letf\left(x\right)={\int }_0^{1}ln(1+{xt}^2)dtwith\mid x\mid <1$$$$1)findf\left(x\right)$$$$2)calculate{\int }_0^{1}ln(2+t^2)dt.$$…

Question Number 37337 by math khazana by abdo last updated on 12/Jun/18 $$calculate{A}_n={\int }_0^1{ch}^{n}xdx.$$ Commented by math khazana by abdo…

Question Number 37316 by rahul 19 last updated on 11/Jun/18 $$\int \frac{x^2}{{(x\sin x+\cos x)}^2}dx=?$$ Answered by ajfour last updated on 11/Jun/18 $${let}\:{x}\mathrm{sin}\:{x}+\mathrm{cos}\:{x}=\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\mathrm{sin}\:\left({x}+\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{1}}{{x}}\right)…

Question Number 37307 by math khazana by abdo last updated on 11/Jun/18 $$calculate{\int }_{\gamma }\frac{dz}{z}with\gamma =\{z\in C/\mid z\mid =1\}.$$ Commented by prof Abdo imad last updated on 15/Jun/18…

Question Number 37306 by math khazana by abdo last updated on 11/Jun/18 $$calculate{\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}{e}^{ix}\frac{x-i}{(x+i)(x^2+3)}dx.$$$$$$ Commented by prof Abdo…