integral from 0 to x of 1/((1-x)^{2.37)}

解答

\int_{0}^{x} \frac{1}{( 1 - x ) ^{2.37}} d x

\frac{0.72992 \dots}{( 1 - x ) ^{1.37}} - 0.72992 \dots

求解步骤

\int_{0}^{x} \frac{1}{( 1 - x ) ^{2.37}} d x

使用换元积分法

= \int_{1}^{1 - x} - \frac{1}{u ^{2.37}} d u

提出常数:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int_{1}^{1 - x} \frac{1}{u ^{2.37}} d u

使用幂法则

= - [- \frac{0.72992 \dots}{u ^{1.37}}]_{1}^{1 - x}

带入上下限计算后得:

- \frac{0.72992 \dots}{( 1 - x ) ^{1.37}} + 0.72992 \dots

= - (- \frac{0.72992 \dots}{( 1 - x ) ^{1.37}} + 0.72992 \dots)

化简

= \frac{0.72992 \dots}{( 1 - x ) ^{1.37}} - 0.72992 \dots

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