integral of (7x^3)/(4sqrt(x^6))

解答

\int \frac{7 x ^{3}}{4 x ^{6}} d x

\frac{7}{4} x + C

求解步骤

\int \frac{7 x ^{3}}{4 x ^{6}} d x

提出常数:

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

= \frac{7}{4} \cdot \int \frac{x ^{3}}{x ^{6}} d x

x^{6} = x^{3},

假定

x \geq 0

= \frac{7}{4} \cdot \int \frac{x ^{3}}{x ^{3}} d x

化简

= \frac{7}{4} \cdot \int 1 d x

常数积分:

\int a d x = a x

= \frac{7}{4} \cdot 1 \cdot x

化简

= \frac{7}{4} x

解答补常数

= \frac{7}{4} x + C

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