題目 Problem Compute the following integrals: (a) ∫0∞2x−3(x−1)(x2+4) dx=(12)‾\displaystyle\int_0^\infty \frac{2x-3}{(x-1)(x^2+4)}\,dx = \underline{\quad(12)\quad}∫0∞(x−1)(x2+4)2x−3dx=(12). (b) ∫dxx2−6x=(13)‾\displaystyle\int \frac{dx}{\sqrt{x^2-6x}} = \underline{\quad(13)\quad}∫x2−6xdx=(13). (c) ∫sin−1(x) dx=(14)‾\displaystyle\int \sin^{-1}(\sqrt{x})\,dx = \underline{\quad(14)\quad}∫sin−1(x)dx=(14). 解答
