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受欢迎的微积分 >

integral of (6e^{7x})

解答

\int (6 e^{7 x}) d x

解答

\frac{6}{7} e^{7 x} + C

求解步骤

\int 6 e^{7 x} d x

提出常数:

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

= 6 \cdot \int e^{7 x} d x

使用换元积分法

= 6 \cdot \int e^{u} \frac{1}{7} d u

提出常数:

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

= 6 \cdot \frac{1}{7} \cdot \int e^{u} d u

使用积分常见定则:

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

= 6 \cdot \frac{1}{7} e^{u}

u = 7 x

代回

= 6 \cdot \frac{1}{7} e^{7 x}

化简

6 \cdot \frac{1}{7} e^{7 x} : \frac{6}{7} e^{7 x}

= \frac{6}{7} e^{7 x}

解答补常数

= \frac{6}{7} e^{7 x} + C

作图

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