integral of 3x^3e^2x

解答

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

\frac{3 e ^{2} x ^{5}}{5} + C

求解步骤

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

提出常数:

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

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

化简

x^{3} x : x^{4}

= 3 e^{2} \cdot \int x^{4} d x

使用幂法则

= 3 e^{2} \frac{x ^{5}}{5}

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 e ^{2} x ^{5}}{5}

解答补常数

= \frac{3 e ^{2} x ^{5}}{5} + C

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