integral of (3x+4)/(2sqrt(x))

解答

\int \frac{3 x + 4}{2 x} d x

x (x + 4) + C

求解步骤

\int \frac{3 x + 4}{2 x} d x

提出常数:

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

= \frac{1}{2} \cdot \int \frac{3 x + 4}{x} d x

使用分布积分法

= \frac{1}{2} (2 x (3 x + 4) - \int 6 x d x)

\int 6 x d x = 4 x^{\frac{3}{2}}

= \frac{1}{2} (2 x (3 x + 4) - 4 x^{\frac{3}{2}})

化简

\frac{1}{2} (2 x (3 x + 4) - 4 x^{\frac{3}{2}}) : x (x + 4)

= x (x + 4)

解答补常数

= x (x + 4) + C

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