Solve ∫ y^3 wrt y

$$\int y ^ { 3 } d y$$

Evaluate

$$\frac{y^{4}}{4}+С$$

Solution Steps

Since \int y^{k}\mathrm{d}y=\frac{y^{k+1}}{k+1} for k\neq -1, replace \int y^{3}\mathrm{d}y with \frac{y^{4}}{4}.

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

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.

$$\frac{y^{4}}{4}+С$$

Differentiate w.r.t. y

$$y^{3}$$