Solve ∫ (from -5 to -2) of 3/x^ wrt x

$$\int_{ -5 }^{ -2 } \frac{ 3 }{ { x }^{ } } d x$$

Evaluate

$$\ln(\frac{8}{125})\approx -2.748872196$$

Solution Steps

Evaluate the indefinite integral first.

$$\int \frac{3}{x}\mathrm{d}x$$

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

$$3\int \frac{1}{x}\mathrm{d}x$$

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

$$3\ln(|x|)$$

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.

$$3\ln(|-2|)-3\ln(|-5|)$$

Simplify.

$$\ln(\frac{8}{125})$$