∫[1,-1]sin^3x+x^2/1+x^2dx=?

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∫[1,-1]sin^3x+x^2/1+x^2dx=?
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∫[1,-1]sin^3x+x^2/1+x^2dx=?
∫[1,-1]sin^3x+x^2/1+x^2dx=?

∫[1,-1]sin^3x+x^2/1+x^2dx=?
∫(-1-->1) (sin³x + x²)/(1 + x²) dx
= ∫(-1-->1) sin³x/(1 + x²) dx + ∫(-1-->1) x²/(1 + x²) dx,前面是奇函数,结果是0,后面是偶函数
= 0 + 2∫(0-->1) (x² + 1 - 1)/(1 + x²) dx
= 2∫(0-->1) [1 - 1/(1 + x²)] dx
= 2 · [x - arctan(x)] |(0-->1)
= 2 · (1 - π/4)
= 2 - π/2

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