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受欢迎的微积分 >

integral of-5sin(3x)

解答

\int - 5 sin (3 x) d x

解答

\frac{5}{3} cos (3 x) + C

求解步骤

\int - 5 sin (3 x) d x

提出常数:

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

= - 5 \cdot \int sin (3 x) d x

使用换元积分法

= - 5 \cdot \int sin (u) \frac{1}{3} d u

提出常数:

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

= - 5 \cdot \frac{1}{3} \cdot \int sin (u) d u

使用积分常见定则:

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

= - 5 \cdot \frac{1}{3} (- cos (u))

u = 3 x

代回

= - 5 \cdot \frac{1}{3} (- cos (3 x))

化简

- 5 \cdot \frac{1}{3} (- cos (3 x)) : \frac{5}{3} cos (3 x)

= \frac{5}{3} cos (3 x)

解答补常数

= \frac{5}{3} cos (3 x) + C

作图

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