Solve ∫ 2^x/log2

$$\int \frac { 2 ^ { x } } { \log 2 }$$

Evaluate

$$\frac{\ln(10)\times 2^{x}}{\ln(2)^{2}}+С$$

Solution Steps

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

$$\frac{1}{\ln(2)\times \frac{1}{\ln(10)}}\int 2^{x}\mathrm{d}x$$

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

$$\frac{1}{\ln(2)\times \frac{1}{\ln(10)}}\times \frac{2^{x}}{\ln(2)}$$

Simplify.

$$\frac{\ln(10)\times 2^{x}}{\ln(2)^{2}}$$

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.

$$\frac{\ln(10)\times 2^{x}}{\ln(2)^{2}}+С$$

Differentiate w.r.t. x

$$\log_{2}\left(10\right)\times 2^{x}$$