Calculus Examples

$c' (x) = - \frac{1000}{x}$

Step 1

The function $c (x)$ can be found by evaluating the indefinite integral of the derivative $c' (x)$ .

$c (x) = \int c' (x) d x$

Step 2

Since $- 1$ is constant with respect to $x$ , move $- 1$ out of the integral.

$- \int \frac{1000}{x} d x$

Step 3

Since $1000$ is constant with respect to $x$ , move $1000$ out of the integral.

$- (1000 \int \frac{1}{x} d x)$

Step 4

Multiply $1000$ by $- 1$ .

$- 1000 \int \frac{1}{x} d x$

Step 5

The integral of $\frac{1}{x}$ with respect to $x$ is $\ln (| x |)$ .

$- 1000 (\ln (| x |) + C)$

Step 6

Simplify.

$- 1000 \ln (| x |) + C$

Step 7

The function $c$ if derived from the integral of the derivative of the function. This is valid by the fundamental theorem of calculus.

$c (x) = - 1000 \ln (| x |) + C$