Solve ∫ (from 1 to 8) of 2 wrt x/x

$$\int _ { 1 } ^ { 8 } \frac { 2 d x } { x }$$

Evaluate

$$6\ln(2)\approx 4.158883083$$

Solution Steps

Evaluate the indefinite integral first.

$$\int \frac{2}{x}\mathrm{d}x$$

Factor out the constant using \int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x.

$$2\int \frac{1}{x}\mathrm{d}x$$

Use \int \frac{1}{x}\mathrm{d}x=\ln(|x|) from the table of common integrals to obtain the result.

$$2\ln(|x|)$$

The definite integral is the antiderivative of the expression evaluated at the upper limit of integration minus the antiderivative evaluated at the lower limit of integration.

$$2\ln(|8|)-2\ln(|1|)$$

Simplify.

$$6\ln(2)$$