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x/(x的平方+2x+3)dx的不定积分是多少?
人气:103 ℃ 时间:2020-05-27 05:46:23
解答
∫x/(x的平方+2x+3)dx
=∫x/[(x+1)²+2] dx
=∫[(x+1)-1]/[(x+1)²+2] dx
=∫[(x+1)/[(x+1)²+2] dx-∫1/[(x+1)²+2] dx
=1/2∫1/(x的平方+2x+3) d(x的平方+2x+3) -1/√2 arctan(x+1)/√2+c
=1/2ln(x的平方+2x+3)-√2/2 arctan(x+1)/√2+c1/2∫1/(x的平方+2x+3) d(x的平方+2x+3) -1/√2 arctan(x+1)/√2+c这步怎么来的啊,请详解
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