Solve ∫ (from - 4 to - 1) of -4/x wrt x

$$\int _ { - 4 } ^ { - 1 } - \frac { 4 } { x } d x$$

Evaluate

$$8\ln(2)\approx 5.545177444$$

Solution Steps

Evaluate the indefinite integral first.

$$\int -\frac{4}{x}\mathrm{d}x$$

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

$$-4\int \frac{1}{x}\mathrm{d}x$$

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

$$-4\ln(|x|)$$

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.

$$-4\ln(|-1|)+4\ln(|-4|)$$

Simplify.

$$8\ln(2)$$