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受欢迎的微积分 >

integral of 7e^{cos(x)}sin(x)

解答

\int 7 e^{c o s (x)} sin (x) d x

解答

- 7 e^{c o s (x)} + C

求解步骤

\int 7 e^{c o s (x)} sin (x) d x

提出常数:

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

= 7 \cdot \int e^{c o s (x)} sin (x) d x

使用换元积分法

= 7 \cdot \int - e^{u} d u

提出常数:

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

= 7 (- \int e^{u} d u)

使用积分常见定则:

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

= 7 (- e^{u})

u = cos (x)

代回

= 7 (- e^{c o s (x)})

化简

= - 7 e^{c o s (x)}

解答补常数

= - 7 e^{c o s (x)} + C

作图

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