Solve ∫ 4/x^8 wrt x

$$\int \frac { 4 } { x ^ { 8 } } d x$$

Evaluate

$$-\frac{4}{7x^{7}}+С$$

Solution Steps

Factor out the constant using \int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x.

$$4\int \frac{1}{x^{8}}\mathrm{d}x$$

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int \frac{1}{x^{8}}\mathrm{d}x with -\frac{1}{7x^{7}}.

$$-\frac{\frac{4}{x^{7}}}{7}$$

Simplify.

$$-\frac{4}{7x^{7}}$$

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.

$$-\frac{4}{7x^{7}}+С$$

Differentiate w.r.t. x

$$\frac{4}{x^{8}}$$