integral of (x^5)/(x^6+9)

解答

\int \frac{x ^{5}}{x ^{6} + 9} d x

\frac{1}{6} ln x^{6} + 9 + C

求解步骤

\int \frac{x ^{5}}{x ^{6} + 9} d x

使用换元积分法

= \int \frac{1}{6 u} d u

提出常数:

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

= \frac{1}{6} \cdot \int \frac{1}{u} d u

使用积分常见定则:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{6} ln ∣ u ∣

u = x^{6} + 9

代回

= \frac{1}{6} ln x^{6} + 9

解答补常数

= \frac{1}{6} ln x^{6} + 9 + C

\int x^{4} 13 + x^{5} d x

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