那我手打多项式除法吧.
x^2 + x + 1
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x^3 + 0 - x + 0 √ x^5 + x^4 + 0 + 0 + 0 - 8
x^5 + 0 - x^3 + 0
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x^4 + x^3 + 0 + 0
x^4 + 0 - x^2 + 0
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x^3 + x^2 + 0 - 8
x^3 + 0 - x + 0
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x^2 + x - 8
所以(x⁵ + x⁴ - 8)/(x³ - x)
= x² + x + 1 + (x² + x - 8)/[x(x² - 1)]
= x² + x + 1 + 8/x - 4/(x + 1) - 3/(x - 1),部分分式方法,自己会设吧?
∫ (x⁵ + x⁴ - 8)/(x³ - x) dx
= x³/3 + x²/2 + x + 8ln|x| - 4ln|x + 1| - 3ln|x - 1| + C
