Calculus Examples

$e^{3 \ln (x - 1)}$

Step 1

Simplify $3 \ln (x - 1)$ by moving $3$ inside the logarithm.

$e^{\ln ({(x - 1)}^{3})}$

Step 2

Exponentiation and log are inverse functions.

${(x - 1)}^{3}$

Step 3

Use the Binomial Theorem.

$x^{3} + 3 x^{2} \cdot - 1 + 3 x {(- 1)}^{2} + {(- 1)}^{3}$

Step 4

Simplify each term.

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Step 4.1

Multiply $- 1$ by $3$ .

$x^{3} - 3 x^{2} + 3 x {(- 1)}^{2} + {(- 1)}^{3}$

Step 4.2

Raise $- 1$ to the power of $2$ .

$x^{3} - 3 x^{2} + 3 x \cdot 1 + {(- 1)}^{3}$

Step 4.3

Multiply $3$ by $1$ .

$x^{3} - 3 x^{2} + 3 x + {(- 1)}^{3}$

Step 4.4

Raise $- 1$ to the power of $3$ .

$x^{3} - 3 x^{2} + 3 x - 1$