Calculus Examples

$\frac{x^{2}}{x}$

Step 1

Write $\frac{x^{2}}{x}$ as a function.

$f (x) = \frac{x^{2}}{x}$

Step 2

The function $F (x)$ can be found by finding the indefinite integral of the derivative $f (x)$ .

$F (x) = \int f (x) d x$

Step 3

Set up the integral to solve.

$F (x) = \int \frac{x^{2}}{x} d x$

Step 4

Split the fraction into multiple fractions.

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Step 4.1

Factor $x$ out of $x^{2}$ .

$\int \frac{x \cdot x}{x} d x$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Raise $x$ to the power of $1$ .

$\int \frac{x \cdot x}{x^{1}} d x$

Step 4.2.2

Factor $x$ out of $x^{1}$ .

$\int \frac{x \cdot x}{x \cdot 1} d x$

Step 4.2.3

Cancel the common factor.

$\int \frac{x \cdot x}{x \cdot 1} d x$

Step 4.2.4

Rewrite the expression.

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

Step 4.2.5

Divide $x$ by $1$ .

$\int x d x$

Step 5

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

$\frac{1}{2} x^{2} + C$

Step 6

The answer is the antiderivative of the function $f (x) = \frac{x^{2}}{x}$ .

$F (x) =$ $\frac{1}{2} x^{2} + C$