求不定积分x^3/(x+2)dx

Question

求不定积分x^3/(x+2)dx

Answer 1

∫ x³/(x+2) dx
=∫ (x³+8-8)/(x+2) dx
=∫ (x³+8)/(x+2) dx - 8∫ 1/(x+2) dx
=∫ (x²-2x+4) dx - 8ln|x+2|
=(1/3)x³ - x² + 4x - 8ln|x+2| + C
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