An automatic integration scheme is proposed for evaluating the indefinite integral of function having algebraic singularity: I(x, y, c)=∫^y_x|t-c|^αf(t)dt, a≤x, y, c≤b, -1<α within a finite range [a, b] for a given smooth function f(t), for which the Chebyshev series expansion over [a, b] converges rapidly. The Fast Fourier Transform (FFT) and recurrence relations are used to efficiently compute the Chebyshev coefficients of f(t) and to expand the indefinite integral I(x, y, c) in the Chebyshev series, respectively. Numerical examples are also included to illustrate the performance of the present method.
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