求不定积分：∫sinx2dx\int\sin\dfrac{x}{2}dx∫sin2xdx.
设f(x)={x,−1≤x≤0x2,0<x≤1f(x)=\begin{cases}x, -1\leq x\leq 0\\x^{2}, 0< x\leq 1\end{cases}f(x)={x,−1≤x≤0x2,0<x≤1，求定积分∫−11f(x)dx\int_{-1}^{1}f(x)dx∫−11f(x)dx.
求极限：limx→0[2ln(1+x)−2x]\lim\limits_{x\to 0}[\dfrac{2}{\ln(1 + x)} - \dfrac{2}{x}]x→0lim[ln(1+x)2−x2].
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