Category: Integration

Question Number 29854 by abdo imad last updated on 13/Feb/18 $$find{\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}\frac{(x^2+2)dx}{x^4+8x^2-16x+20}.$$ Commented by abdo imad last updated on…

Question Number 29853 by abdo imad last updated on 13/Feb/18 $$find{\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}\frac{dx}{x^2+2ix+2-4i}.$$ Commented by abdo imad last updated on 18/Feb/18 $${let}\:{put}\:{f}\left({z}\right)=\:\frac{\mathrm{1}}{{z}^{\mathrm{2}}…

Question Number 29849 by abdo imad last updated on 12/Feb/18 $$letgivea>0,b>0findthevslueof$$$${\int }_0^{+\mathrm{\infty }}\frac{e^{-at}-e^{-bt}}{t}cos\left(xt\right)dt.$$ Commented by abdo imad last updated…

Question Number 160902 by blackmamba last updated on 08/Dec/21 $$\int \frac{dx}{\sqrt{\sin {}^{3}x}\sqrt{\cos {}^{5}x}}=?$$ Answered by chhaythean last updated on 09/Dec/21 $$=\int\frac{\mathrm{dx}}{\:\sqrt{\frac{\mathrm{sin}^{\mathrm{3}} \mathrm{x}}{\mathrm{cos}^{\mathrm{3}} \mathrm{x}}×\mathrm{cos}^{\mathrm{8}} \mathrm{x}}}…

Question Number 160792 by cortano last updated on 06/Dec/21 $$\int \frac{\sec \mathrm{x}}{\sqrt{1+2\sec \mathrm{x}}}\sqrt{\frac{\mathrm{cosec}\mathrm{x}-\cot \mathrm{x}}{\mathrm{cosec}\mathrm{x}+\cot \mathrm{x}}}\mathrm{dx}=?$$ Answered by chhaythean last updated on 06/Dec/21 $$=\int \frac{\frac{1}{\mathrm{cosx}}}{\sqrt{\frac{\mathrm{cosx}+2}{\mathrm{cosx}}}}\times \sqrt{\frac{\frac{1-\mathrm{cosx}}{\mathrm{sinx}}}{\frac{1+\mathrm{cosx}}{\mathrm{sinx}}}}\mathrm{dx}$$$$=\int \frac{\frac{1}{\mathrm{cosx}}}{\sqrt{\frac{\mathrm{cosx}+2}{\mathrm{cosx}}}}\times \sqrt{\frac{1-\mathrm{cosx}}{1+\mathrm{cosx}}}\mathrm{dx}$$$$=\int\frac{\mathrm{sinx}}{\:\sqrt{\mathrm{cos}^{\mathrm{2}} \mathrm{x}+\mathrm{2cosx}}}×\frac{\mathrm{1}}{\mathrm{1}+\mathrm{cosx}}\mathrm{dx}…