What is the integral from 1 to 1.6 of (2x)/(x-4) ?

The integral from 1 to 1.6 of (2x)/(x-4) is -0.58514…

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integral from 1 to 1.6 of (2x)/(x-4)

\int_{1}^{1.6} \frac{2 x}{x - 4} d x

- 0.58514 \dots

Solution steps

\int_{1}^{1.6} \frac{2 x}{x - 4} d x

Take the constant out:

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

= 2 \cdot \int_{1}^{1.6} \frac{x}{x - 4} d x

Apply u-substitution

: \int_{- 3}^{- 2.4} \frac{u + 4}{u} d u

= 2 \cdot \int_{- 3}^{- 2.4} \frac{u + 4}{u} d u

Expand

\frac{u + 4}{u} : 1 + \frac{4}{u}

= 2 \cdot \int_{- 3}^{- 2.4} 1 + \frac{4}{u} d u

Apply the Sum Rule:

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

= 2 (\int_{- 3}^{- 2.4} 1 d u + \int_{- 3}^{- 2.4} \frac{4}{u} d u)

\int_{- 3}^{- 2.4} 1 d u = 0.6

\int_{- 3}^{- 2.4} \frac{4}{u} d u = - 0.89257 \dots

= 2 (0.6 - 0.89257 \dots)

Simplify

= - 0.58514 \dots

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What is the integral from 1 to 1.6 of (2x)/(x-4) ?
The integral from 1 to 1.6 of (2x)/(x-4) is -0.58514…