ching the value of indefinite integral int (dx)/(0.5x-8)

To evaluate the indefinite integral $\int \frac{dx}{0.5x-8}$, we can use the substitution method.<br /><br />Let $u = 0.5x - 8$, then $du = 0.5dx$, and $dx = 2du$.<br /><br />Substituting these values into the integral, we get:<br /><br />$\int \frac{dx}{0.5x-8} = \int \frac{2du}{u} = 2\int \frac{du}{u} = 2\ln|u| + C$<br /><br />Now, substituting back $u = 0.5x - 8$, we have:<br /><br />$2\ln|0.5x - 8| + C$<br /><br />Therefore, the value of the indefinite integral $\int \frac{dx}{0.5x-8}$ is $2\ln|0.5x - 8| + C$, where $C$ is the constant of integration.