求不定积分,∫x^4/x+1dx

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求不定积分,∫x^4/x+1dx
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求不定积分,∫x^4/x+1dx
求不定积分,∫x^4/x+1dx

求不定积分,∫x^4/x+1dx
∫(x^4-1+1)/(x+1)dx
=∫(x^2-1)(x^2+1)/(x+1)dx+∫1/(x+1)dx
=∫(x-1)(x^2+1)dx+∫1/(x+1)dx
=∫(x^3-x^2+x-1)dx+∫1/(x+1)dx
=x^4/4-x^3/3+x^2/2-x+ln|x+1|+C