求∫(x^3+66)/x^2+7x+12)dx

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求∫(x^3+66)/x^2+7x+12)dx
求∫(x^3+66)/x^2+7x+12)dx

求∫(x^3+66)/x^2+7x+12)dx
(x³+66)÷(x²+7x+12)=x-7余37x+150
所以(x³+66)÷(x²+7x+12)=x-7+(37x+150)/(x+3)(x+4)
令(37x+150)/(x+3)(x+4)
=a/(x+3)+b/(x+4)
=(ax+bx+4a+3b)/(x+3)(x+4)
所以a=39,b=-2
所以原式=∫[x-7+39/(x+3)-2/(x+4)]dx
=x²/2-7x+39ln|x+3|-2ln|x+4|+C

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