Solve ∫ (from -3 to -1) of 2/x wrt x

$$\int_{ -3 }^{ -1 } \frac{ 2 }{ x } d x$$

Evaluate

$$-2\ln(3)\approx -2.197224577$$

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.

$$2\ln(|-1|)-2\ln(|-3|)$$

Simplify.

$$-2\ln(3)$$