作业帮求 (x^5+x^4-8)/(x^3-x)的积分
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求 (x^5+x^4-8)/(x^3-x)的积分
求 (x^5+x^4-8)/(x^3-x)的积分
求 (x^5+x^4-8)/(x^3-x)的积分
原式=∫{x²+x+1+(x²+x-8)/[x(x²-1)]}dx
=x³/3+x²/2+x+∫[8/x-3/(x-1)-4/(x+1)]dx
=x³/3+x²/2+x+8ln│x│-3ln│x-1│-4ln│x+1│+C (C是积分常数)
=x³/3+x²/2+x+ln│x^8/[(x-1)³(x+1)^4]│+C.
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