What is the integral from-4 to-1 of-4/x+4x ?

The integral from-4 to-1 of-4/x+4x is 8ln(2)-30

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integral from-4 to-1 of-4/x+4x

\int_{- 4}^{- 1} - \frac{4}{x} + 4 x d x

8 ln (2) - 30

Decimal

- 24.45482 \dots

Solution steps

\int_{- 4}^{- 1} - \frac{4}{x} + 4 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_{- 4}^{- 1} \frac{4}{x} d x + \int_{- 4}^{- 1} 4 x d x

\int_{- 4}^{- 1} \frac{4}{x} d x = - 8 ln (2)

\int_{- 4}^{- 1} 4 x d x = - 30

= - (- 8 ln (2)) - 30

Simplify

= 8 ln (2) - 30

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What is the integral from-4 to-1 of-4/x+4x ?
The integral from-4 to-1 of-4/x+4x is 8ln(2)-30