Solve ∫ (1-3x^2)

$$\int ( 1 - 3 x ^ { 2 } )$$

Evaluate

$$С+x-x^{3}$$

Solution Steps

Integrate the sum term by term.

$$\int 1\mathrm{d}x+\int -3x^{2}\mathrm{d}x$$

Factor out the constant in each of the terms.

$$\int 1\mathrm{d}x-3\int x^{2}\mathrm{d}x$$

Find the integral of 1 using the table of common integrals rule \int a\mathrm{d}x=ax.

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

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

$$x-x^{3}$$

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.

$$x-x^{3}+С$$

Differentiate w.r.t. x

$$1-3x^{2}$$