Calculus Examples

$\int - \frac{2000}{x^{2}} d x$

Step 1

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

$- \int \frac{2000}{x^{2}} d x$

Step 2

Since $2000$ is constant with respect to $x$ , move $2000$ out of the integral.

$- (2000 \int \frac{1}{x^{2}} d x)$

Step 3

Simplify the expression.

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Step 3.1

Multiply $2000$ by $- 1$ .

$- 2000 \int \frac{1}{x^{2}} d x$

Step 3.2

Move $x^{2}$ out of the denominator by raising it to the $- 1$ power.

$- 2000 \int {(x^{2})}^{- 1} d x$

Step 3.3

Multiply the exponents in ${(x^{2})}^{- 1}$ .

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Step 3.3.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- 2000 \int x^{2 \cdot - 1} d x$

Step 3.3.2

Multiply $2$ by $- 1$ .

$- 2000 \int x^{- 2} d x$

Step 4

By the Power Rule, the integral of $x^{- 2}$ with respect to $x$ is $- x^{- 1}$ .

$- 2000 (- x^{- 1} + C)$

Step 5

Simplify the answer.

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Step 5.1

Rewrite $- 2000 (- x^{- 1} + C)$ as $- 2000 (- \frac{1}{x}) + C$ .

$- 2000 (- \frac{1}{x}) + C$

Step 5.2

Simplify.

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Step 5.2.1

Multiply $- 1$ by $- 2000$ .

$2000 \frac{1}{x} + C$

Step 5.2.2

Combine $2000$ and $\frac{1}{x}$ .

$\frac{2000}{x} + C$