What is the integral from-6 to-1 of (x^{-1}+5x) ?

The integral from-6 to-1 of (x^{-1}+5x) is -ln(6)-175/2

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

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

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

Decimal

- 89.29175 \dots

Solution steps

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

Apply the Sum Rule:

\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

\int_{- 1}^{1} (3 x - 5) d x

\int_{- 1}^{1} (9 x^{2} + 5 z + 4 x y) d z

\int_{1}^{5} (\frac{x ^{2} + 4}{x}) d x

\int_{0}^{1} 3 x + 1 d x

What is the integral from-6 to-1 of (x^{-1}+5x) ?
The integral from-6 to-1 of (x^{-1}+5x) is -ln(6)-175/2