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Category: Integration

find-F-x-0-pi-ln-1-x-sin-2-t-dt-with-x-lt-1-2-calculate-0-pi-ln-1-1-2-sin-2-t-dt-

Question Number 35046 by math khazana by abdo last updated on 14/May/18 $${find}\:{F}\left({x}\right)=\:\int_{\mathrm{0}} ^{\pi} \:{ln}\left(\:\mathrm{1}+{x}\:{sin}^{\mathrm{2}} {t}\right){dt}\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\pi} \:\:{ln}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}{sin}^{\mathrm{2}} {t}\right){dt} \\ $$ Terms of…

x-2-1-x-3-2-dx-

Question Number 35015 by NECx last updated on 14/May/18 $$\int\frac{{x}^{\mathrm{2}} }{\left(\mathrm{1}+{x}^{\mathrm{3}} \right)^{\mathrm{2}} }{dx} \\ $$ Answered by ajfour last updated on 14/May/18 $${I}\:=\frac{\mathrm{1}}{\mathrm{3}}\int\frac{\mathrm{3}{x}^{\mathrm{2}} {dx}}{\left(\mathrm{1}+{x}^{\mathrm{3}} \right)^{\mathrm{2}}…