求不定积分x^5/(x^2+1)dx

题目详情

求不定积分x^5/(x^2+1)dx

▼优质解答

答案和解析

x^5/(x²+1)
=(x^5-x+x)/(x²+1)
=x(x²+1)(x²-1)/(x²+1)+x/(x²+1)
=x³-x+x/(x²+1)
原式=∫(x³-x)dx+∫x/(x²+1) dx
=∫(x³-x)dx+1/2∫d(x²+1)/(x²+1)
=x^4/4-x²/2+1/2*ln(x²+1)+C

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