Solve ∫ re^z wrt z

$$\int r e ^ { z } d z$$

Evaluate

$$re^{z}+С$$

Solution Steps

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

$$r\int e^{z}\mathrm{d}z$$

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

$$re^{z}$$

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

$$re^{z}+С$$

Differentiate w.r.t. r

$$e^{z}$$