∫(3x+2)/(x(x+1)^3)dx
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∫(3x+2)/(x(x+1)^3)dx
∫(3x+2)/(x(x+1)^3)dx
∫(3x+2)/(x(x+1)^3)dx
原式=∫[2/x-2/(x+1)-2/(x+1)²+1/(x+1)³]dx
=2ln│x│-2ln│x+1│+2/(x+1)-(1/2)/(x+1)²+C (C是积分常数)
=2ln│x/(x+1)│+2/(x+1)-(1/2)/(x+1)²+C.
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