Category: Integration

Question Number 185455 by cortano1 last updated on 22/Jan/23 $$\int \frac{x^3.e^{x^2}}{{(x^2+1)}^2}dx=?$$ Answered by SEKRET last updated on 22/Jan/23 $$\left.\:\:\mathrm{1}\right)\:\:\:\:\:\:\boldsymbol{\mathrm{x}}^{\mathrm{2}}…

Question Number 54376 by Abdo msup. last updated on 02/Feb/19 $$1)calculatef\left(a\right)={\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}\frac{dx}{x^2+ax+1}$$$$with\mid a\mid <2$$$$2)calculateg\left(a\right)={\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}\frac{x}{{(x^2+ax+1)}^2}$$$$\left.\mathrm{3}\right){find}\:{values}\:{of}\:{integrals}\:\int_{−\infty} ^{+\infty}…

Question Number 54372 by maxmathsup by imad last updated on 02/Feb/19 $$letf\left(x\right)={\int }_0^{2\pi }\frac{sint}{x+sint}dt$$$$1)calculatef\left(x\right)$$$$2)calculateg\left(x\right)={\int }_0^{2\pi }\frac{sint}{{(x+sint)}^2}dt$$$$\left.\mathrm{3}\right)\:{calculste}\:{for}\:{n}\in{N}\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\frac{{sint}}{\left({x}+{sint}\right)^{{n}}…

Question Number 54367 by maxmathsup by imad last updated on 02/Feb/19 $$find{\int }_1^{+\mathrm{\infty }}\frac{\left[t\right]}{t}{t}^{-p}dtintermsof\xi \left(p\right)withp>0.$$ Commented by maxmathsup by imad last updated on…

Question Number 119821 by bemath last updated on 27/Oct/20 $$\underset{-3}{\stackrel{0}{\int }}\frac{6x-6}{\sqrt{x^2-2x+1}}dx=?$$ Answered by bobhans last updated on 27/Oct/20 $$\:\underset{−\mathrm{3}} {\overset{\mathrm{0}} {\int}}\:\frac{\mathrm{6}\left({x}−\mathrm{1}\right)}{\:\sqrt{\left({x}−\mathrm{1}\right)^{\mathrm{2}}…