integral of ((sqrt(a)-sqrt(b))^4)/(sqrt(ax))

解答

\int \frac{( a - b ) ^{4}}{a x} d x

\frac{2 x ( a - b ) ^{4}}{a} + C

求解步骤

\int \frac{( a - b ) ^{4}}{a x} d x

提出常数:

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

= (a - b)^{4} \cdot \int \frac{1}{a x} d x

\frac{1}{a x} = \frac{1}{a} \frac{1}{x}

= (a - b)^{4} \cdot \int \frac{1}{a} \cdot \frac{1}{x} d x

提出常数:

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

= (a - b)^{4} \frac{1}{a} \cdot \int \frac{1}{x} d x

使用幂法则

= (a - b)^{4} \frac{1}{a} \cdot 2 x^{\frac{1}{2}}

化简

(a - b)^{4} \frac{1}{a} \cdot 2 x^{\frac{1}{2}} : \frac{2 x ( a - b ) ^{4}}{a}

= \frac{2 x ( a - b ) ^{4}}{a}

解答补常数

= \frac{2 x ( a - b ) ^{4}}{a} + C

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