Calculus Examples

$\ln (x) (x + 2) (x + 1)$

Step 1

Apply the distributive property.

$(\ln (x) x + \ln (x) \cdot 2) (x + 1)$

Step 2

Multiply $\ln (x) \cdot 2$ .

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Step 2.1

Reorder $\ln (x)$ and $2$ .

$(\ln (x) x + 2 \cdot \ln (x)) (x + 1)$

Step 2.2

Simplify $2 \cdot \ln (x)$ by moving $2$ inside the logarithm.

$(\ln (x) x + \ln (x^{2})) (x + 1)$

Step 3

Expand $(\ln (x) x + \ln (x^{2})) (x + 1)$ using the FOIL Method.

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Step 3.1

Apply the distributive property.

$\ln (x) x (x + 1) + \ln (x^{2}) (x + 1)$

Step 3.2

Apply the distributive property.

$\ln (x) x \cdot x + \ln (x) x \cdot 1 + \ln (x^{2}) (x + 1)$

Step 3.3

Apply the distributive property.

$\ln (x) x \cdot x + \ln (x) x \cdot 1 + \ln (x^{2}) x + \ln (x^{2}) \cdot 1$

Step 4

Simplify terms.

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Step 4.1

Simplify each term.

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Step 4.1.1

Multiply $x$ by $x$ by adding the exponents.

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Step 4.1.1.1

Move $x$ .

$\ln (x) (x \cdot x) + \ln (x) x \cdot 1 + \ln (x^{2}) x + \ln (x^{2}) \cdot 1$

Step 4.1.1.2

Multiply $x$ by $x$ .

$\ln (x) x^{2} + \ln (x) x \cdot 1 + \ln (x^{2}) x + \ln (x^{2}) \cdot 1$

Step 4.1.2

Multiply $\ln (x)$ by $1$ .

$\ln (x) x^{2} + x \cdot \ln (x) + \ln (x^{2}) x + \ln (x^{2}) \cdot 1$

Step 4.1.3

Multiply $\ln (x^{2})$ by $1$ .

$\ln (x) x^{2} + x \ln (x) + \ln (x^{2}) x + \ln (x^{2})$

Step 4.2

Reorder factors in $\ln (x) x^{2} + x \ln (x) + \ln (x^{2}) x + \ln (x^{2})$ .

$x^{2} \ln (x) + x \ln (x) + x \ln (x^{2}) + \ln (x^{2})$