Calculus Examples

$\int (\frac{3 x^{2} - 2 x^{3}}{6 x}) d x$

Step 1

Reorder terms.

$\frac{- 2 x^{3} + 3 x^{2}}{6 x}$

Step 2

Factor $x^{2}$ out of $- 2 x^{3} + 3 x^{2}$ .

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Step 2.1

Factor $x^{2}$ out of $- 2 x^{3}$ .

$\frac{x^{2} (- 2 x) + 3 x^{2}}{6 x}$

Step 2.2

Factor $x^{2}$ out of $3 x^{2}$ .

$\frac{x^{2} (- 2 x) + x^{2} \cdot 3}{6 x}$

Step 2.3

Factor $x^{2}$ out of $x^{2} (- 2 x) + x^{2} \cdot 3$ .

$\frac{x^{2} (- 2 x + 3)}{6 x}$

$\frac{x^{2} (- 2 x + 3)}{6 x}$

Step 3

Cancel the common factor of $x^{2}$ and $x$ .

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Step 3.1

Factor $x$ out of $x^{2} (- 2 x + 3)$ .

$\frac{x (x (- 2 x + 3))}{6 x}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $x$ out of $6 x$ .

$\frac{x (x (- 2 x + 3))}{x \cdot 6}$

Step 3.2.2

Cancel the common factor.

$\frac{x (x (- 2 x + 3))}{x \cdot 6}$

Step 3.2.3

Rewrite the expression.

$\frac{x (- 2 x + 3)}{6}$

$\frac{x (- 2 x + 3)}{6}$

$\frac{x (- 2 x + 3)}{6}$

Step 4

Factor $- 1$ out of $- 2 x$ .

$\frac{x (- (2 x) + 3)}{6}$

Step 5

Rewrite $3$ as $- 1 (- 3)$ .

$\frac{x (- (2 x) - 1 (- 3))}{6}$

Step 6

Factor $- 1$ out of $- (2 x) - 1 (- 3)$ .

$\frac{x (- (2 x - 3))}{6}$

Step 7

Rewrite $- (2 x - 3)$ as $- 1 (2 x - 3)$ .

$\frac{x (- 1 (2 x - 3))}{6}$

Step 8

Move the negative in front of the fraction.

$- \frac{x (2 x - 3)}{6}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$