Solve ∫ 12x-8-12

$$\int 12 x - 8 - 12$$

Evaluate

$$6x^{2}-20x+С$$

Solution Steps

Integrate the sum term by term.

$$\int 12x\mathrm{d}x+\int -8\mathrm{d}x+\int -12\mathrm{d}x$$

Factor out the constant in each of the terms.

$$12\int x\mathrm{d}x+\int -8\mathrm{d}x+\int -12\mathrm{d}x$$

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 12 times \frac{x^{2}}{2}.

$$6x^{2}+\int -8\mathrm{d}x+\int -12\mathrm{d}x$$

Find the integral of -8 using the table of common integrals rule \int a\mathrm{d}x=ax.

$$6x^{2}-8x+\int -12\mathrm{d}x$$

Find the integral of -12 using the table of common integrals rule \int a\mathrm{d}x=ax.

$$6x^{2}-8x-12x$$

Simplify.

$$6x^{2}-20x$$

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.

$$6x^{2}-20x+С$$

Differentiate w.r.t. x

$$12x-20$$