[tex] \int\limits^1_0{\frac{x^2}{x+1} \, dx =\int\limits^1_0 {\frac{x^2-1+1}{x+1} \, dx =\int\limits^1_0 {\frac{(x-1)(x+1)+1}{x+1}} \,dx=[tex] \int\limits^1_0 { \frac{(x-1)(x+1)}{x+1} } \, dx + \int\limits^1_0 { \frac{1}{x+1} } \, dx [/tex]
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