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受欢迎的微积分 >

integral of (10sin(5x))

解答

\int (10 sin (5 x)) d x

解答

- 2 cos (5 x) + C

求解步骤

\int 10 sin (5 x) d x

提出常数:

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

= 10 \cdot \int sin (5 x) d x

使用换元积分法

= 10 \cdot \int sin (u) \frac{1}{5} d u

提出常数:

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

= 10 \cdot \frac{1}{5} \cdot \int sin (u) d u

使用积分常见定则:

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

= 10 \cdot \frac{1}{5} (- cos (u))

u = 5 x

代回

= 10 \cdot \frac{1}{5} (- cos (5 x))

化简

10 \cdot \frac{1}{5} (- cos (5 x)) : - 2 cos (5 x)

= - 2 cos (5 x)

解答补常数

= - 2 cos (5 x) + C

作图

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