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受欢迎的微积分 >

integral of e^{(4x)/9}(4/9)

解答

\int e^{\frac{4 x}{9}} (\frac{4}{9}) d x

解答

e^{\frac{4 x}{9}} + C

求解步骤

\int e^{\frac{4 x}{9}} \frac{4}{9} d x

提出常数:

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

= \frac{4}{9} \cdot \int e^{\frac{4 x}{9}} d x

使用换元积分法

= \frac{4}{9} \cdot \int e^{u} \frac{9}{4} d u

提出常数:

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

= \frac{4}{9} \cdot \frac{9}{4} \cdot \int e^{u} d u

使用积分常见定则:

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

= \frac{4}{9} \cdot \frac{9}{4} e^{u}

u = \frac{4 x}{9}

代回

= \frac{4}{9} \cdot \frac{9}{4} e^{\frac{4 x}{9}}

化简

\frac{4}{9} \cdot \frac{9}{4} e^{\frac{4 x}{9}} : e^{\frac{4 x}{9}}

= e^{\frac{4 x}{9}}

解答补常数

= e^{\frac{4 x}{9}} + C

作图

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