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受欢迎的微积分 >

integral of 3cos(3x)

解答

\int 3 cos (3 x) d x

解答

sin (3 x) + C

求解步骤

\int 3 cos (3 x) d x

提出常数:

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

= 3 \cdot \int cos (3 x) d x

使用换元积分法

= 3 \cdot \int cos (u) \frac{1}{3} d u

提出常数:

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

= 3 \cdot \frac{1}{3} \cdot \int cos (u) d u

使用积分常见定则:

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

= 3 \cdot \frac{1}{3} sin (u)

u = 3 x

代回

= 3 \cdot \frac{1}{3} sin (3 x)

化简

3 \cdot \frac{1}{3} sin (3 x) : sin (3 x)

= sin (3 x)

解答补常数

= sin (3 x) + C

作图

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