integral of 3^{2x^6}3x^5

解答

\int 3^{2 x^{6}} 3 x^{5} d x

\frac{729}{2} x^{6} + C

求解步骤

\int 3^{2 x^{6}} \cdot 3 x^{5} d x

提出常数:

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

= 3 \cdot \int 3^{2 x^{6}} x^{5} d x

3^{2 x^{6}} = 9^{x^{6}}

= 3 \cdot \int 9^{x^{6}} x^{5} d x

使用换元积分法

= 3 \cdot \int \frac{243}{2} d u

常数积分:

\int a d x = a x

= 3 \cdot \frac{243}{2} u

u = x^{6}

代回

= 3 \cdot \frac{243}{2} x^{6}

化简

3 \cdot \frac{243}{2} x^{6} : \frac{729}{2} x^{6}

= \frac{729}{2} x^{6}

解答补常数

= \frac{729}{2} x^{6} + C

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