Solve ∫ e^x+y

$$\int e ^ { x } + y$$

Evaluate

$$xy+e^{x}+С$$

Solution Steps

Integrate the sum term by term.

$$\int e^{x}\mathrm{d}x+\int y\mathrm{d}x$$

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

$$e^{x}+\int y\mathrm{d}x$$

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

$$e^{x}+yx$$

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.

$$e^{x}+yx+С$$

Differentiate w.r.t. x

$$y+e^{x}$$