Solve ∫ (from 0.012 to 0.123) of 5*300*8.315/x wrt x

$$\int _ { 0.012 } ^ { 0.123 } \frac { 5 \times 300 \times 8.315 } { x } d x$$

Evaluate

$$\frac{24945\ln(41)}{2}-24945\ln(2)\approx 29026.971182902$$

Solution Steps

Evaluate the indefinite integral first.

$$\int \frac{5\times 8.315\times 300}{x}\mathrm{d}x$$

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

$$5\times 8.315\times 300\int \frac{1}{x}\mathrm{d}x$$

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

$$5\times 8.315\times 300\ln(|x|)$$

Simplify.

$$\frac{24945\ln(|x|)}{2}$$

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.

$$12472.5\ln(|0.123|)-12472.5\ln(|0.012|)$$

Simplify.

$$\frac{24945\ln(41)}{2}-24945\ln(2)$$