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受欢迎的微积分 >

integral of x^{12}e^{x^{13}}

解答

\int x^{12} e^{x^{13}} d x

解答

\frac{1}{13} e^{x^{13}} + C

求解步骤

\int x^{12} e^{x^{13}} d x

使用换元积分法

= \int \frac{e ^{u^{\frac{13}{12}}} u ^{\frac{1}{12}}}{12} d u

提出常数:

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

= \frac{1}{12} \cdot \int e^{u^{\frac{13}{12}}} u^{\frac{1}{12}} d u

使用换元积分法

= \frac{1}{12} \cdot \int \frac{12 e ^{v}}{13} d v

提出常数:

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

= \frac{1}{12} \cdot \frac{12}{13} \cdot \int e^{v} d v

使用积分常见定则:

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

= \frac{1}{12} \cdot \frac{12}{13} e^{v}

代回

= \frac{1}{12} \cdot \frac{12}{13} e^{(x^{12})^{\frac{13}{12}}}

化简

\frac{1}{12} \cdot \frac{12}{13} e^{(x^{12})^{\frac{13}{12}}} : \frac{1}{13} e^{x^{13}}

= \frac{1}{13} e^{x^{13}}

解答补常数

= \frac{1}{13} e^{x^{13}} + C

作图

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