Solve ∫ 2x^2-7s-15

$$\int 2 x ^ { 2 } - 7 s - 15$$

Evaluate

$$\frac{2x^{3}}{3}-7sx-15x+С$$

Solution Steps

Integrate the sum term by term.

$$\int 2x^{2}\mathrm{d}x+\int -7s\mathrm{d}x+\int -15\mathrm{d}x$$

Factor out the constant in each of the terms.

$$2\int x^{2}\mathrm{d}x-7\int s\mathrm{d}x+\int -15\mathrm{d}x$$

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{2}\mathrm{d}x with \frac{x^{3}}{3}. Multiply 2 times \frac{x^{3}}{3}.

$$\frac{2x^{3}}{3}-7\int s\mathrm{d}x+\int -15\mathrm{d}x$$

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

$$\frac{2x^{3}}{3}-7sx+\int -15\mathrm{d}x$$

Find the integral of -15 using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\frac{2x^{3}}{3}-7sx-15x$$

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.

$$\frac{2x^{3}}{3}-7sx-15x+С$$

Differentiate w.r.t. x

$$2x^{2}-7s-15$$