Solve ∫ (from 25 * 10 to -3) of ^ 100*10^-32*373.15*8.314/x wrt x

$$\int_{ 25 \times { 10 }^{ -3 } }^{ 100 \times { 10 }^{ -3 } } \frac{ 2 \cdot 373.15 \cdot 8.314 }{ x } d x$$

Evaluate

$$\frac{31023691\ln(2)}{2500}\approx 8601.593578885$$

Solution Steps

Multiply 2 and 373.15 to get 746.3.

$$\int _{25\times 10^{-3}}^{100\times 10^{-3}}\frac{746.3\times 8.314}{x}\mathrm{d}x$$

Multiply 746.3 and 8.314 to get 6204.7382.

$$\int _{25\times 10^{-3}}^{100\times 10^{-3}}\frac{6204.7382}{x}\mathrm{d}x$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$\int _{25\times \frac{1}{1000}}^{100\times 10^{-3}}\frac{6204.7382}{x}\mathrm{d}x$$

Multiply 25 and \frac{1}{1000} to get \frac{1}{40}.

$$\int _{\frac{1}{40}}^{100\times 10^{-3}}\frac{6204.7382}{x}\mathrm{d}x$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$\int _{\frac{1}{40}}^{100\times \frac{1}{1000}}\frac{6204.7382}{x}\mathrm{d}x$$

Multiply 100 and \frac{1}{1000} to get \frac{1}{10}.

$$\int _{\frac{1}{40}}^{\frac{1}{10}}\frac{6204.7382}{x}\mathrm{d}x$$

Evaluate the indefinite integral first.

$$\int \frac{31023691}{5000x}\mathrm{d}x$$

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

$$\frac{31023691\int \frac{1}{x}\mathrm{d}x}{5000}$$

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

$$\frac{31023691\ln(|x|)}{5000}$$

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.

$$6204.7382\ln(|\frac{1}{10}|)-6204.7382\ln(|\frac{1}{40}|)$$

Simplify.

$$\frac{31023691\ln(2)}{2500}$$