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Category: Integration

dx-x-4-x-2-1-

Question Number 118010 by TANMAY PANACEA last updated on 14/Oct/20 dxx4+x2+1 Commented by mmmmmm1 last updated on 14/Oct/20 $$\:\:\frac{\boldsymbol{{d}}}{\boldsymbol{{dx}}}\left[\frac{\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)}{\boldsymbol{{g}}\left(\boldsymbol{{x}}\right)}\right]=\:\frac{\boldsymbol{{g}}\left(\boldsymbol{{x}}\right)\centerdot\frac{\boldsymbol{{d}}}{\boldsymbol{{dx}}}\left[\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)\right]\:−\:\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)\centerdot\frac{\boldsymbol{{d}}}{\boldsymbol{{dx}}}\left[\boldsymbol{{g}}\left(\boldsymbol{{x}}\right)\right]}{\boldsymbol{{g}}\left(\boldsymbol{{x}}\right)^{\mathrm{2}} } \

let-f-0-1-ln-1-i-x-1-x-2-dx-1-determine-a-explicit-form-of-f-2-calculate-0-1-ln-1-ix-1-x-2-dx-and-0-1-ln-1-2ix-1-x-2-dx-

Question Number 52459 by Abdo msup. last updated on 08/Jan/19 letf(α)=01ln(1+iαx)1+x2dx1)determineaexplicitformoff(α)$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}+{ix}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx}\:{and}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}+\mathrm{2}{ix}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx}. \