∫(x^2-1)/(x^2+1)dx 求它的积分?
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∫(x^2-1)/(x^2+1)dx 求它的积分?
![∫(x^2-1)/(x^2+1)dx 求它的积分?](/uploads/image/z/5082898-58-8.jpg?t=%E2%88%AB%EF%BC%88x%5E2-1%29%2F%28x%5E2%2B1%29dx+%E6%B1%82%E5%AE%83%E7%9A%84%E7%A7%AF%E5%88%86%3F)
答:
∫ (x²-1) /(x²+1) dx
=∫ (x²+1-2) /(x²+1) dx
=∫ 1 -2/(x²+1) dx
=x-2arctanx+C
∫ (x²-1) /(x²+1) dx
=∫ (x²+1-2) /(x²+1) dx
=∫ 1 -2/(x²+1) dx
=x-2arctanx+C