Solve ∫ (x^2-3x^2) wrt x

$$\int ( x ^ { 2 } - 3 x ^ { 2 } ) d x$$

Evaluate

$$-\frac{2x^{3}}{3}+С$$

Solution Steps

Integrate the sum term by term.

$$\int x^{2}\mathrm{d}x+\int -3x^{2}\mathrm{d}x$$

Factor out the constant in each of the terms.

$$\int x^{2}\mathrm{d}x-3\int x^{2}\mathrm{d}x$$

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}.

$$\frac{x^{3}}{3}-3\int x^{2}\mathrm{d}x$$

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 -3 times \frac{x^{3}}{3}.

$$\frac{x^{3}}{3}-x^{3}$$

Simplify.

$$-\frac{2x^{3}}{3}$$

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.

$$-\frac{2x^{3}}{3}+С$$

Differentiate w.r.t. x

$$-2x^{2}$$