Solve ∫ 5/2y wrt y

$$\int{ \frac{ 5 }{ 2 } y }d y$$

Evaluate

$$\frac{5y^{2}}{4}+С$$

Solution Steps

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

$$\frac{5\int y\mathrm{d}y}{2}$$

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

$$\frac{5y^{2}}{4}$$

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

$$\frac{5y^{2}}{4}+С$$

Differentiate w.r.t. y

$$\frac{5y}{2}$$