Tích phân \(\int\limits^2_{\frac{1}{2}}\dfrac{1}{x\left(x+1\right)}\text{d}x\) bằng
\(1\).\(2\).\(\ln2\).\(\ln3\).Hướng dẫn giải:\(\int\limits^2_{\frac{1}{2}}\dfrac{1}{x\left(x+1\right)}\text{d}x=\int\limits^2_{\frac{1}{2}}\left[\dfrac{1}{x}-\dfrac{1}{x+1}\right]\text{d}x\)
\(=\left[\ln x-\ln\left(x+1\right)\right]|^2_{\frac{1}{2}}=\ln\dfrac{x}{x+1}|^2_{\frac{1}{2}}\)
\(=\ln2\).