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受欢迎的微积分 >

integral of (48x)/(8x^2+e)

解答

\int \frac{48 x}{8 x ^{2} + e} d x

解答

3 ln 8 x^{2} + e + C

求解步骤

\int \frac{48 x}{8 x ^{2} + e} d x

提出常数:

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

= 48 \cdot \int \frac{x}{8 x ^{2} + e} d x

使用换元积分法

= 48 \cdot \int \frac{1}{16 u} d u

提出常数:

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

= 48 \cdot \frac{1}{16} \cdot \int \frac{1}{u} d u

使用积分常见定则:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 48 \cdot \frac{1}{16} ln ∣ u ∣

u = 8 x^{2} + e

代回

= 48 \cdot \frac{1}{16} ln 8 x^{2} + e

化简

48 \cdot \frac{1}{16} ln 8 x^{2} + e : 3 ln 8 x^{2} + e

= 3 ln 8 x^{2} + e

解答补常数

= 3 ln 8 x^{2} + e + C

作图

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