Solve ∫ 5y+9 wrt y

$$\int{ 5y+9 }d y$$

Evaluate

$$\frac{5y^{2}}{2}+9y+С$$

Solution Steps

Integrate the sum term by term.

$$\int 5y\mathrm{d}y+\int 9\mathrm{d}y$$

Factor out the constant in each of the terms.

$$5\int y\mathrm{d}y+\int 9\mathrm{d}y$$

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}. Multiply 5 times \frac{y^{2}}{2}.

$$\frac{5y^{2}}{2}+\int 9\mathrm{d}y$$

Find the integral of 9 using the table of common integrals rule \int a\mathrm{d}y=ay.

$$\frac{5y^{2}}{2}+9y$$

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.

$$\frac{5y^{2}}{2}+9y+С$$

Differentiate w.r.t. y

$$5y+9$$