Calculus Examples

$(20 \ln (4 x + 1)) - (\frac{x}{4})$

Step 1

Simplify $20 \ln (4 x + 1)$ by moving $20$ inside the logarithm.

$\ln ({(4 x + 1)}^{20}) - \frac{x}{4}$

Step 2

To write $\ln ({(4 x + 1)}^{20})$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\ln ({(4 x + 1)}^{20}) \cdot \frac{4}{4} - \frac{x}{4}$

Step 3

Simplify terms.

Tap for more steps...

Step 3.1

Combine $\ln ({(4 x + 1)}^{20})$ and $\frac{4}{4}$ .

$\frac{\ln ({(4 x + 1)}^{20}) \cdot 4}{4} - \frac{x}{4}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{\ln ({(4 x + 1)}^{20}) \cdot 4 - x}{4}$

Step 4

Simplify the numerator.

Tap for more steps...

Step 4.1

Multiply $\ln ({(4 x + 1)}^{20}) \cdot 4$ .

Tap for more steps...

Step 4.1.1

Reorder $\ln ({(4 x + 1)}^{20})$ and $4$ .

$\frac{4 \cdot \ln ({(4 x + 1)}^{20}) - x}{4}$

Step 4.1.2

Simplify $4 \cdot \ln ({(4 x + 1)}^{20})$ by moving $4$ inside the logarithm.

$\frac{\ln ({({(4 x + 1)}^{20})}^{4}) - x}{4}$

Step 4.2

Multiply the exponents in ${({(4 x + 1)}^{20})}^{4}$ .

Tap for more steps...

Step 4.2.1

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

$\frac{\ln ({(4 x + 1)}^{20 \cdot 4}) - x}{4}$

Step 4.2.2

Multiply $20$ by $4$ .

$\frac{\ln ({(4 x + 1)}^{80}) - x}{4}$