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受欢迎的微积分 >

integral of 1/4 e^{x/4}

解答

\int \frac{1}{4} e^{\frac{x}{4}} d x

解答

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

求解步骤

\int \frac{1}{4} e^{\frac{x}{4}} d x

提出常数:

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

= \frac{1}{4} \cdot \int e^{\frac{x}{4}} d x

使用换元积分法

= \frac{1}{4} \cdot \int e^{u} \cdot 4 d u

提出常数:

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

= \frac{1}{4} \cdot 4 \cdot \int e^{u} d u

使用积分常见定则:

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

= \frac{1}{4} \cdot 4 e^{u}

u = \frac{x}{4}

代回

= \frac{1}{4} \cdot 4 e^{\frac{x}{4}}

化简

\frac{1}{4} \cdot 4 e^{\frac{x}{4}} : e^{\frac{x}{4}}

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

解答补常数

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

作图

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