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Category: Integration

2sin-x-3cos-x-3sin-x-4cos-x-dx-

Question Number 62266 by aliesam last updated on 18/Jun/19 $$\int\frac{\mathrm{2}{sin}\left({x}\right)+\mathrm{3}{cos}\left({x}\right)}{\mathrm{3}{sin}\left({x}\right)+\mathrm{4}{cos}\left({x}\right)}{dx} \\ $$ Commented by maxmathsup by imad last updated on 19/Jun/19 $${let}\:{A}\:=\int\:\:\:\frac{\mathrm{2}{sinx}\:+\mathrm{3}{cosx}}{\mathrm{3}{sinx}\:+\mathrm{4}{cosx}}\:{dx}\:{changement}\:{tan}\left(\frac{{x}}{\mathrm{2}}\right)={t}\:{give} \\ $$$${A}\:=\int\:\:\:\frac{\frac{\mathrm{4}{t}}{\mathrm{1}+{t}^{\mathrm{2}} }+\mathrm{3}\frac{\mathrm{1}−{t}^{\mathrm{2}}…

find-the-value-of-I-0-e-t-sint-t-dt-and-J-0-e-t-cos-t-t-dt-study-first-the-convergence-

Question Number 62262 by maxmathsup by imad last updated on 18/Jun/19 $${find}\:{the}\:{value}\:{of}\: \\ $$$${I}\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{−{t}} {sint}}{\:\sqrt{{t}}}{dt}\:\:{and}\:{J}\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{−{t}} {cos}\left({t}\right)}{\:\sqrt{{t}}}{dt}\:\:,{study}\:{first}\:{the}\:{convergence}. \\ $$ Commented by maxmathsup…