Question Number 57324 by turbo msup by abdo last updated on 02/Apr/19
![we want to find the vslue of I =∫_0 ^1 ((ln(1+x))/(1+x^2 )) dx let A=∫∫_W (x/((1+x^2 )(1+xy)))dxdy with W=[0,1]^2 calculate A by two method and conclude the value of I .](Q57324.png)
$${we}\:{want}\:{to}\:{find}\:{the}\:{vslue}\:{of} \\ $$$${I}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}+{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx}\:{let} \\ $$$${A}=\int\int_{{W}} \frac{{x}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{xy}\right)}{dxdy} \\ $$$${with}\:{W}=\left[\mathrm{0},\mathrm{1}\right]^{\mathrm{2}} \\ $$$${calculate}\:{A}\:{by}\:{two}\:{method}\:{and} \\ $$$${conclude}\:{the}\:{value}\:{of}\:{I}\:. \\ $$