用牛顿莱布尼兹公式求微积分
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用牛顿莱布尼兹公式求微积分
∫(下限为1,上限为2)(1+x^3)/(x^2+x^3)dx
请写出具体过程
∫(下限为1,上限为2)(1+x^3)/(x^2+x^3)dx
请写出具体过程
![用牛顿莱布尼兹公式求微积分](/uploads/image/z/16287045-69-5.jpg?t=%E7%94%A8%E7%89%9B%E9%A1%BF%E8%8E%B1%E5%B8%83%E5%B0%BC%E5%85%B9%E5%85%AC%E5%BC%8F%E6%B1%82%E5%BE%AE%E7%A7%AF%E5%88%86)
∫(下限为1,上限为2)(1+x^3)/(x^2+x^3)dx
=∫(下限为1,上限为2)(x^3+x^2-x^2+1)/(x^2+x^3)dx
=∫(下限为1,上限为2)(x^3+x^2-x^2+1)/(x^2+x^3)dx
=∫(下限为1,上限为2)[1+(-x^2+1)/(x^2+x^3)]dx
=∫(下限为1,上限为2)[1+(1-x)/x^2]dx
=∫(下限为1,上限为2)[1+1/x^2-1/x]dx
=x-1/x-lnx |(下限为1,上限为2)
=1-ln2
=∫(下限为1,上限为2)(x^3+x^2-x^2+1)/(x^2+x^3)dx
=∫(下限为1,上限为2)(x^3+x^2-x^2+1)/(x^2+x^3)dx
=∫(下限为1,上限为2)[1+(-x^2+1)/(x^2+x^3)]dx
=∫(下限为1,上限为2)[1+(1-x)/x^2]dx
=∫(下限为1,上限为2)[1+1/x^2-1/x]dx
=x-1/x-lnx |(下限为1,上限为2)
=1-ln2