搜搜做题作业网求不定积分∫[（1+1/x^2)(1-x^2)+xsinx]dx
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求不定积分∫[（1+1/x^2)(1-x^2)+xsinx]dx
![求不定积分∫[（1+1/x^2)(1-x^2)+xsinx]dx](/uploads/image/z/6016052-20-2.jpg?t=%E6%B1%82%E4%B8%8D%E5%AE%9A%E7%A7%AF%E5%88%86%E2%88%AB%5B%EF%BC%881%2B1%2Fx%5E2%29%281-x%5E2%29%2Bxsinx%5Ddx)
∫[（1+1/x^2)(1-x^2)+xsinx]dx
=∫(1/x^2-x^2 + xsinx) dx
= -1/x - 1/3*x^3 +∫xsinx dx
= -1/x - 1/3*x^3 -∫xdcosx
= -1/x - 1/3*x^3 -xcosx + ∫cosx dx
= -1/x - 1/3*x^3 -xcosx + sinx + C
=∫(1/x^2-x^2 + xsinx) dx
= -1/x - 1/3*x^3 +∫xsinx dx
= -1/x - 1/3*x^3 -∫xdcosx
= -1/x - 1/3*x^3 -xcosx + ∫cosx dx
= -1/x - 1/3*x^3 -xcosx + sinx + C
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