Solve ∫ z wrt z/y

$$\int \frac { z d z } { y }$$

Evaluate

$$\frac{z^{2}}{2y}+С$$

Solution Steps

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

$$\frac{\int z\mathrm{d}z}{y}$$

Since \int z^{k}\mathrm{d}z=\frac{z^{k+1}}{k+1} for k\neq -1, replace \int z\mathrm{d}z with \frac{z^{2}}{2}.

$$\frac{z^{2}}{2y}$$

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.

$$\frac{z^{2}}{2y}+С$$

Differentiate w.r.t. z

$$\frac{z}{y}$$