Calculus Examples

$\int_{1}^{2} 4^{x} d x$

Step 1

The integral of $4^{x}$ with respect to $x$ is $\frac{4^{x}}{\ln (4)}$ .

$\frac{4^{x}}{\ln (4)}]_{1}^{2}$

Step 2

Substitute and simplify.

Tap for more steps...

Step 2.1

Evaluate $\frac{4^{x}}{\ln (4)}$ at $2$ and at $1$ .

$(\frac{4^{2}}{\ln (4)}) - \frac{4^{1}}{\ln (4)}$

Step 2.2

Simplify.

Tap for more steps...

Step 2.2.1

Raise $4$ to the power of $2$ .

$\frac{16}{\ln (4)} - \frac{4^{1}}{\ln (4)}$

Step 2.2.2

Evaluate the exponent.

$\frac{16}{\ln (4)} - \frac{4}{\ln (4)}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{16 - 4}{\ln (4)}$

Step 2.2.4

Subtract $4$ from $16$ .

$\frac{12}{\ln (4)}$

Step 3

Simplify.

Tap for more steps...

Step 3.1

Rewrite $\ln (4)$ as $\ln (2^{2})$ .

$\frac{12}{\ln (2^{2})}$

Step 3.2

Expand $\ln (2^{2})$ by moving $2$ outside the logarithm.

$\frac{12}{2 \ln (2)}$

Step 3.3

Cancel the common factor of $12$ and $2$ .

Tap for more steps...

Step 3.3.1

Factor $2$ out of $12$ .

$\frac{2 \cdot 6}{2 \ln (2)}$

Step 3.3.2

Cancel the common factors.

Tap for more steps...

Step 3.3.2.1

Factor $2$ out of $2 \ln (2)$ .

$\frac{2 \cdot 6}{2 (\ln (2))}$

Step 3.3.2.2

Cancel the common factor.

$\frac{2 \cdot 6}{2 \ln (2)}$

Step 3.3.2.3

Rewrite the expression.

$\frac{6}{\ln (2)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{6}{\ln (2)}$

Decimal Form:

$8.65617024 \dots$

Step 5