integral of 2pix^3

解答

\int 2 π x^{3} d x

\frac{π x ^{4}}{2} + C

求解步骤

\int 2 π x^{3} d x

提出常数:

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

= 2 π \cdot \int x^{3} d x

使用幂法则

= 2 π \frac{x ^{4}}{4}

化简

2 π \frac{x ^{4}}{4} : \frac{π x ^{4}}{2}

= \frac{π x ^{4}}{2}

解答补常数

= \frac{π x ^{4}}{2} + C

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\int - e