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受欢迎的微积分 >

integral of (12x^5)/(3+2x^6)

解答

\int \frac{12 x ^{5}}{3 + 2 x ^{6}} d x

解答

ln 3 + 2 x^{6} + C

求解步骤

\int \frac{12 x ^{5}}{3 + 2 x ^{6}} d x

提出常数:

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

= 12 \cdot \int \frac{x ^{5}}{3 + 2 x ^{6}} d x

使用换元积分法

= 12 \cdot \int \frac{1}{12 u} d u

提出常数:

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

= 12 \cdot \frac{1}{12} \cdot \int \frac{1}{u} d u

使用积分常见定则:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 12 \cdot \frac{1}{12} ln ∣ u ∣

u = 3 + 2 x^{6}

代回

= 12 \cdot \frac{1}{12} ln 3 + 2 x^{6}

化简

12 \cdot \frac{1}{12} ln 3 + 2 x^{6} : ln 3 + 2 x^{6}

= ln 3 + 2 x^{6}

解答补常数

= ln 3 + 2 x^{6} + C

作图

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