∫2x^4+2x^2+1/x^2+1dx的不定积分!分子是2x^4+2x^2+1,分母是x^2+1,后面加了个dx!
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![∫2x^4+2x^2+1/x^2+1dx的不定积分!分子是2x^4+2x^2+1,分母是x^2+1,后面加了个dx!](/uploads/image/z/2694180-12-0.jpg?t=%E2%88%AB2x%5E4%2B2x%5E2%2B1%2Fx%5E2%2B1dx%E7%9A%84%E4%B8%8D%E5%AE%9A%E7%A7%AF%E5%88%86%21%E5%88%86%E5%AD%90%E6%98%AF2x%5E4%2B2x%5E2%2B1%2C%E5%88%86%E6%AF%8D%E6%98%AFx%5E2%2B1%2C%E5%90%8E%E9%9D%A2%E5%8A%A0%E4%BA%86%E4%B8%AAdx%21)
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∫2x^4+2x^2+1/x^2+1dx的不定积分!分子是2x^4+2x^2+1,分母是x^2+1,后面加了个dx!
∫2x^4+2x^2+1/x^2+1dx的不定积分!分子是2x^4+2x^2+1,分母是x^2+1,后面加了个dx!
∫2x^4+2x^2+1/x^2+1dx的不定积分!分子是2x^4+2x^2+1,分母是x^2+1,后面加了个dx!
∫ (2x⁴ + 2x² + 1)/(x² + 1) dx
= ∫ [2x²(x² + 1) + 1]/(x² + 1) dx,将分子分裂为两项
= ∫ [2x² + 1/(x² + 1)] dx
= 2 · x³/3 + arctan(x) + C
= (2/3)x³ + arctan(x) + C
你把分子分为两项(2x^4+2x^2)+1,就可以了
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