integral of 14(x-5)^6

解答

\int 14 (x - 5)^{6} d x

2 (x - 5)^{7} + C

求解步骤

\int 14 (x - 5)^{6} d x

提出常数:

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

= 14 \cdot \int (x - 5)^{6} d x

使用换元积分法

= 14 \cdot \int u^{6} d u

使用幂法则

= 14 \cdot \frac{u ^{7}}{7}

u = x - 5

代回

= 14 \cdot \frac{( x - 5 ) ^{7}}{7}

化简

14 \cdot \frac{( x - 5 ) ^{7}}{7} : 2 (x - 5)^{7}

= 2 (x - 5)^{7}

解答补常数

= 2 (x - 5)^{7} + C

\frac{\partial}{\partial θ} (z)

\frac{d}{d x} ((2 x - 5)^{- 1} \cdot (4 x + 3)^{- 1})

in v erse l a pl a ce f (s 0) = s - 3 (s 2 + 4 s + 13)

\int \frac{1}{x ^{5} + 16 x ^{3} + 64 x} d x

t an g e n t 3 x + 7, at x = 3