Solve ∫ 1/x*x*x wrt x

$$\int{ \frac{ 1 }{ x \times x \times x } }d x$$

Evaluate

$$-\frac{1}{2x^{2}}+С$$

Solution Steps

Multiply x and x to get x^{2}.

$$\int \frac{1}{x^{2}x}\mathrm{d}x$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\int \frac{1}{x^{3}}\mathrm{d}x$$

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

$$-\frac{1}{2x^{2}}$$

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.

$$-\frac{1}{2x^{2}}+С$$

Differentiate w.r.t. x

$$\frac{1}{x^{3}}$$