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受欢迎的微积分 >

integral of-2e^{-3cos(3x)}sin(3x)

解答

\int - 2 e^{- 3 c o s (3 x)} sin (3 x) d x

解答

- \frac{2}{9} e^{- 3 c o s (3 x)} + C

求解步骤

\int - 2 e^{- 3 c o s (3 x)} sin (3 x) d x

提出常数:

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

= - 2 \cdot \int e^{- 3 c o s (3 x)} sin (3 x) d x

使用换元积分法

= - 2 \cdot \int \frac{e ^{u}}{9} d u

提出常数:

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

= - 2 \cdot \frac{1}{9} \cdot \int e^{u} d u

使用积分常见定则:

\int e^{u} d u = e^{u}

= - 2 \cdot \frac{1}{9} e^{u}

u = - 3 cos (3 x)

代回

= - 2 \cdot \frac{1}{9} e^{- 3 c o s (3 x)}

化简

- 2 \cdot \frac{1}{9} e^{- 3 c o s (3 x)} : - \frac{2}{9} e^{- 3 c o s (3 x)}

= - \frac{2}{9} e^{- 3 c o s (3 x)}

解答补常数

= - \frac{2}{9} e^{- 3 c o s (3 x)} + C

作图

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