integral of (1-2x)^5

解答

\int (1 - 2 x)^{5} d x

- \frac{1}{12} (1 - 2 x)^{6} + C

求解步骤

\int (1 - 2 x)^{5} d x

使用换元积分法

= \int - \frac{u ^{5}}{2} d u

提出常数:

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

= - \frac{1}{2} \cdot \int u^{5} d u

使用幂法则

= - \frac{1}{2} \cdot \frac{u ^{6}}{6}

u = 1 - 2 x

代回

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

化简

- \frac{1}{2} \cdot \frac{( 1 - 2 x ) ^{6}}{6} : - \frac{1}{12} (1 - 2 x)^{6}

= - \frac{1}{12} (1 - 2 x)^{6}

解答补常数

= - \frac{1}{12} (1 - 2 x)^{6} + C

a re a y = e^{x}, y = 7 e^{- x}, x = 0

\int ln (x + x^{2} - 1) d x

y^{^{'}} = - 100 y + 101 cos (t) + 99 sin (t), y (0) = 1

\int (\frac{1}{x} - \frac{2}{9 x ^{2} + 1}) d x

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