integral of arctan(a)x

解答

\int arctan (a) x d x

\frac{1}{2} x^{2} arctan (a) + C

求解步骤

\int arctan (a) x d x

提出常数:

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

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

使用幂法则

= arctan (a) \frac{x ^{2}}{2}

化简

arctan (a) \frac{x ^{2}}{2} : \frac{1}{2} x^{2} arctan (a)

= \frac{1}{2} x^{2} arctan (a)

解答补常数

= \frac{1}{2} x^{2} arctan (a) + C

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