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受欢迎的微积分 >

integral of 3r^2e^{r^3}

解答

\int 3 r^{2} e^{r^{3}} d r

解答

e^{r^{3}} + C

求解步骤

\int 3 r^{2} e^{r^{3}} d r

提出常数:

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

= 3 \cdot \int r^{2} e^{r^{3}} d r

使用换元积分法

= 3 \cdot \int \frac{e ^{u}}{3} d u

提出常数:

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

= 3 \cdot \frac{1}{3} \cdot \int e^{u} d u

使用积分常见定则:

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

= 3 \cdot \frac{1}{3} e^{u}

u = r^{3}

代回

= 3 \cdot \frac{1}{3} e^{r^{3}}

化简

3 \cdot \frac{1}{3} e^{r^{3}} : e^{r^{3}}

= e^{r^{3}}

解答补常数

= e^{r^{3}} + C

作图

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