Solve ∫ 2^x/(frac{1{2^2})}

$$\int \frac { 2 ^ { x } } { ( \frac { 1 } { 2 ^ { 2 } } ) }$$

Evaluate

$$\frac{4\times 2^{x}}{\ln(2)}+С$$

Solution Steps

Factor out the constant using \int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x.

$$2^{2}\int 2^{x}\mathrm{d}x$$

Use \int p^{q}\mathrm{d}q=\frac{p^{q}}{\ln(p)} from the table of common integrals to obtain the result.

$$2^{2}\times \frac{2^{x}}{\ln(2)}$$

Simplify.

$$\frac{4\times 2^{x}}{\ln(2)}$$

If F\left(x\right) is an antiderivative of f\left(x\right), then the set of all antiderivatives of f\left(x\right) is given by F\left(x\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.

$$\frac{4\times 2^{x}}{\ln(2)}+С$$

Differentiate w.r.t. x

$$4\times 2^{x}$$