integral of sin(1-2x)

解答

\int sin (1 - 2 x) d x

\frac{1}{2} cos (1 - 2 x) + C

求解步骤

\int sin (1 - 2 x) d x

使用换元积分法

= \int - \frac{1}{2} sin (u) 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 sin (u) d u

使用积分常见定则:

\int sin (u) d u = - cos (u)

= - \frac{1}{2} (- cos (u))

u = 1 - 2 x

代回

= - \frac{1}{2} (- cos (1 - 2 x))

化简

= \frac{1}{2} cos (1 - 2 x)

解答补常数

= \frac{1}{2} cos (1 - 2 x) + C

x \to - 2 lim (\frac{2 x ^{2}}{2 x + 2})

s l o p e in t erce pt (0.5) (7.9)

\int 9 e^{5 x + e^{5 x}} d x

\int x (4 x - 1)^{4} d x

d er i v a t i v e y = ln (8 x)