求∫dx/x(x²+1)积分?
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求∫dx/x(x²+1)积分?
![求∫dx/x(x²+1)积分?](/uploads/image/z/6917785-25-5.jpg?t=%E6%B1%82%E2%88%ABdx%2Fx%28x%26%23178%3B%2B1%29%E7%A7%AF%E5%88%86%3F)
∫dx/x(x²+1)
=∫xdx/ x²(x²+1)
=0.5∫dx²/ x²(x²+1)
=0.5∫1/x² -1/(x²+1) dx²
=0.5lnx² - 0.5ln(x²+1) +C,C为常数
=∫xdx/ x²(x²+1)
=0.5∫dx²/ x²(x²+1)
=0.5∫1/x² -1/(x²+1) dx²
=0.5lnx² - 0.5ln(x²+1) +C,C为常数