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求(x^2+2)/(x+1)^3的不定积分.
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求(x^2+2)/(x+1)^3的不定积分.
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答案和解析
原式=∫[(x+1)^2-2x-2+3]/(x+1)^3dx
=∫[1/(x+1) -2/(x+1)^2+3/(x+1)^3]dx
=ln|x+1|+2/(x+1)-3/[2 (x+1)^2]+c
=∫[1/(x+1) -2/(x+1)^2+3/(x+1)^3]dx
=ln|x+1|+2/(x+1)-3/[2 (x+1)^2]+c
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