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

解答

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

\frac{3}{22}

十进制

0.13636 \dots

求解步骤

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

使用换元积分法

= \int_{2}^{11} \frac{1}{3 u ^{2}} d u

提出常数:

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

= \frac{1}{3} \cdot \int_{2}^{11} \frac{1}{u ^{2}} d u

使用幂法则

= \frac{1}{3} [- \frac{1}{u}]_{2}^{11}

带入上下限计算后得:

\frac{9}{22}

= \frac{1}{3} \cdot \frac{9}{22}

化简

= \frac{3}{22}

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