integral from 6 to 8 of (20)/((x-6)^3)

解答

\int_{6}^{8} \frac{20}{( x - 6 ) ^{3}} d x

发散

求解步骤

\int_{6}^{8} \frac{20}{( x - 6 ) ^{3}} d x

提出常数:

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

= 20 \cdot \int_{6}^{8} \frac{1}{( x - 6 ) ^{3}} d x

使用换元积分法

= 20 \cdot \int_{0}^{2} \frac{1}{u ^{3}} d u

使用幂法则

= 20 [- \frac{1}{2 u ^{2}}]_{0}^{2}

带入上下限计算后得:

发散

= 发散

\frac{d}{d x} (f (x) (e^{x}))

n = 0 \sum \infty 3 (- \frac{1}{3})^{n}

t an g e n t y = x^{3} - 2 x + 1, (4, 57)

y^{^{'}} = \frac{x}{6 y}

\frac{d y}{d t} = 0.12 - \frac{6 y}{50 - 2 t}