integral from-6 to-1 of (x^{-1}+5x)

解答

\int_{- 6}^{- 1} (x^{- 1} + 5 x) d x

- ln (6) - \frac{175}{2}

十进制

- 89.29175 \dots

求解步骤

\int_{- 6}^{- 1} x^{- 1} + 5 x d x

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{- 6}^{- 1} x^{- 1} d x + \int_{- 6}^{- 1} 5 x d x

\int_{- 6}^{- 1} x^{- 1} d x = - ln (6)

\int_{- 6}^{- 1} 5 x d x = - \frac{175}{2}

= - ln (6) - \frac{175}{2}

\int_{- 2}^{0} \frac{15}{64} + \frac{x}{64} d x

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