Solve ∫ (-24x^5-10x) wrt x

$$\int ( - 24 x ^ { 5 } - 10 x ) d x$$

Evaluate

$$С-5x^{2}-4x^{6}$$

Solution Steps

Integrate the sum term by term.

$$\int -24x^{5}\mathrm{d}x+\int -10x\mathrm{d}x$$

Factor out the constant in each of the terms.

$$-24\int x^{5}\mathrm{d}x-10\int x\mathrm{d}x$$

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{5}\mathrm{d}x with \frac{x^{6}}{6}. Multiply -24 times \frac{x^{6}}{6}.

$$-4x^{6}-10\int x\mathrm{d}x$$

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 -10 times \frac{x^{2}}{2}.

$$-4x^{6}-5x^{2}$$

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.

$$-4x^{6}-5x^{2}+С$$

Differentiate w.r.t. x

$$-24x^{5}-10x$$