Solve ∫ 2*3^x wrt x

$$\int{ 2 \times { 3 }^{ x } }d x$$

Evaluate

$$\frac{2\times 3^{x}}{\ln(3)}+С$$

Solution Steps

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

$$2\int 3^{x}\mathrm{d}x$$

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

$$2\times \frac{3^{x}}{\ln(3)}$$

Simplify.

$$\frac{2\times 3^{x}}{\ln(3)}$$

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.

$$\frac{2\times 3^{x}}{\ln(3)}+С$$

Differentiate w.r.t. x

$$2\times 3^{x}$$