Solve ∫ 6y^3 wrt y

$$\int{ 6 { y }^{ 3 } }d y$$

Evaluate

$$\frac{3y^{4}}{2}+С$$

Solution Steps

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

$$6\int y^{3}\mathrm{d}y$$

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}. Multiply 6 times \frac{y^{4}}{4}.

$$\frac{3y^{4}}{2}$$

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.

$$\frac{3y^{4}}{2}+С$$

Differentiate w.r.t. y

$$6y^{3}$$