integral of 3ln^2(x)

解答

\int 3 ln^{2} (x) d x

3 (x ln^{2} (x) - 2 (x ln (x) - x)) + C

求解步骤

\int 3 ln^{2} (x) d x

提出常数:

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

= 3 \cdot \int ln^{2} (x) d x

使用分布积分法

= 3 (x ln^{2} (x) - \int 2 ln (x) d x)

\int 2 ln (x) d x = 2 (x ln (x) - x)

= 3 (x ln^{2} (x) - 2 (x ln (x) - x))

解答补常数

= 3 (x ln^{2} (x) - 2 (x ln (x) - x)) + C

\frac{d y}{d t} (t) - 2 y = 3 e^{t}

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