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受欢迎的微积分 >

integral from 0 to 1 of (2x)/((x^2+5)^3)

解答

\int_{0}^{1} \frac{2 x}{( x ^{2} + 5 ) ^{3}} d x

解答

\frac{11}{1800}

+1

十进制

0.00611 \dots

求解步骤

\int_{0}^{1} \frac{2 x}{( x ^{2} + 5 ) ^{3}} d x

提出常数:

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

= 2 \cdot \int_{0}^{1} \frac{x}{( x ^{2} + 5 ) ^{3}} d x

使用换元积分法

= 2 \cdot \int_{5}^{6} \frac{1}{2 u ^{3}} d u

提出常数:

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

= 2 \cdot \frac{1}{2} \cdot \int_{5}^{6} \frac{1}{u ^{3}} d u

使用幂法则

= 2 \cdot \frac{1}{2} [- \frac{1}{2 u ^{2}}]_{5}^{6}

化简

2 \cdot \frac{1}{2} [- \frac{1}{2 u ^{2}}]_{5}^{6} : [- \frac{1}{2 u ^{2}}]_{5}^{6}

= [- \frac{1}{2 u ^{2}}]_{5}^{6}

带入上下限计算后得:

\frac{11}{1800}

= \frac{11}{1800}

作图

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