What is the integral from 0.5 to 4 of 2/x-1/8 x ?

The integral from 0.5 to 4 of 2/x-1/8 x is 3.17450…

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integral from 0.5 to 4 of 2/x-1/8 x

\int_{0.5}^{4} \frac{2}{x} - \frac{1}{8} x d x

3.17450 \dots

Solution steps

\int_{0.5}^{4} \frac{2}{x} - \frac{1}{8} 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_{0.5}^{4} \frac{2}{x} d x - \int_{0.5}^{4} \frac{1}{8} x d x

\int_{0.5}^{4} \frac{2}{x} d x = 4.15888 \dots

\int_{0.5}^{4} \frac{1}{8} x d x = 0.984375

= 4.15888 \dots - 0.984375

Simplify

= 3.17450 \dots

\int \frac{x}{x ^{2} + 1} d x

\frac{\partial}{\partial x} (\frac{( x + y )}{2})

(x^{2} + 4) y = 8

\frac{\partial}{\partial y} (y - \frac{3}{x} + 1)

\int \frac{1}{x ( x ^{2} - 1 ) ^{\frac{3}{2}}} d x

What is the integral from 0.5 to 4 of 2/x-1/8 x ?
The integral from 0.5 to 4 of 2/x-1/8 x is 3.17450…