help me !!!!!!

H

hanguyen445

[tex]I=\int\limit_{0}^{1}\frac{xdx}{x^3+1}=\int\limit_{0}^{1}\frac{dx}{x^2-x+1}-\int\limit_{0}^{1}\frac{xdx}{x^3+1}=\frac{2}{\sqrt{3}}\int\limit_{0}^{1}\frac{d(\frac{2}{\sqrt{3}}x)}{(\frac{2x+1}{\sqrt{3}})^2+1}-I\Rightarrow\[/tex]
[tex]2I=\frac{2}{\sqrt{3}}\int\limit_{\frac{1}{\sqrt{3}}}^{\sqrt{3}}\frac{dt}{t^2+1}[/tex]
[tex]=\frac{2}{\sqrt{3}}\int\limit_{\frac{\pi}{6}}^{\frac{\pi}{3}}dx=\frac{\pi}{3\sqrt{3}}\Rightarrow[/tex]
[tex]I=\frac{\pi}{6\sqrt{3}}[/tex]
 
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