Solve ∫ 14(x+2)

$$\int 14 ( x + 2 )$$

Evaluate

$$7x^{2}+28x+С$$

Solution Steps

Use the distributive property to multiply 14 by x+2.

$$\int 14x+28\mathrm{d}x$$

Integrate the sum term by term.

$$\int 14x\mathrm{d}x+\int 28\mathrm{d}x$$

Factor out the constant in each of the terms.

$$14\int x\mathrm{d}x+\int 28\mathrm{d}x$$

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x\mathrm{d}x with \frac{x^{2}}{2}. Multiply 14 times \frac{x^{2}}{2}.

$$7x^{2}+\int 28\mathrm{d}x$$

Find the integral of 28 using the table of common integrals rule \int a\mathrm{d}x=ax.

$$7x^{2}+28x$$

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

$$7x^{2}+28x+С$$

Differentiate w.r.t. x

$$14\left(x+2\right)$$