integral of 2*(x-6)^3

解答

\int 2 \cdot (x - 6)^{3} d x

\frac{1}{2} (x - 6)^{4} + C

求解步骤

\int 2 (x - 6)^{3} d x

提出常数:

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

= 2 \cdot \int (x - 6)^{3} d x

使用换元积分法

= 2 \cdot \int u^{3} d u

使用幂法则

= 2 \cdot \frac{u ^{4}}{4}

u = x - 6

代回

= 2 \cdot \frac{( x - 6 ) ^{4}}{4}

化简

2 \cdot \frac{( x - 6 ) ^{4}}{4} : \frac{1}{2} (x - 6)^{4}

= \frac{1}{2} (x - 6)^{4}

解答补常数

= \frac{1}{2} (x - 6)^{4} + C

t an g e n t f (x) = 7 + 4 x^{2} - 2 x^{3}, at x = a

d er i v a t i v e 4 e^{x^{- 3}}

x \to 0 lim (9 x^{2} - 4 x + 8)

\int sec^{2} (x) d x

y^{^{''}} + 1.5 y^{^{'}} + 0.037 y = 0, y (0) = 2, y^{^{'}} (0) = 1