integral of sin(8-x)

解答

\int sin (8 - x) d x

cos (8 - x) + C

求解步骤

\int sin (8 - x) d x

使用换元积分法

= \int - sin (u) d u

提出常数:

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

= - \int sin (u) d u

使用积分常见定则:

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

= - (- cos (u))

u = 8 - x

代回

= - (- cos (8 - x))

化简

= cos (8 - x)

解答补常数

= cos (8 - x) + C

\int_{- 1}^{0} x^{2} d x

\int e^{c o s (8 x)} sin (8 x) d x

x \to 1 lim ((x - 1) (x + 1))

\frac{d}{d x} (\frac{1}{cos ( x )})

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