Solve ∫ 2e^x+5

$$\int 2 e ^ { x } + 5$$

Evaluate

$$5x+2e^{x}+С$$

Solution Steps

Integrate the sum term by term.

$$\int 2e^{x}\mathrm{d}x+\int 5\mathrm{d}x$$

Factor out the constant in each of the terms.

$$2\int e^{x}\mathrm{d}x+\int 5\mathrm{d}x$$

Use \int e^{x}\mathrm{d}x=e^{x} from the table of common integrals to obtain the result.

$$2e^{x}+\int 5\mathrm{d}x$$

Find the integral of 5 using the table of common integrals rule \int a\mathrm{d}x=ax.

$$2e^{x}+5x$$

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.

$$2e^{x}+5x+С$$

Differentiate w.r.t. x

$$2e^{x}+5$$