integral from 6 to 8 of (14)/((x-6)^3)

解答

\int_{6}^{8} \frac{14}{( x - 6 ) ^{3}} d x

发散

求解步骤

\int_{6}^{8} \frac{14}{( x - 6 ) ^{3}} d x

提出常数:

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

= 14 \cdot \int_{6}^{8} \frac{1}{( x - 6 ) ^{3}} d x

使用换元积分法

= 14 \cdot \int_{0}^{2} \frac{1}{u ^{3}} d u

使用幂法则

= 14 [- \frac{1}{2 u ^{2}}]_{0}^{2}

带入上下限计算后得:

发散

= 发散

x \to a lim ((\frac{sin ( x )}{sin ( a )})^{\frac{1}{x + a}})

\int \frac{2 x + 1}{3 x ^{2} + 3 x + 4} d x

a re a 3 x + 3, 4 x + 4, - 1, 3

\frac{\partial}{\partial x} (ln (2 x y + 4))

\frac{\partial}{\partial y} (arctan (x + 6 y))