Solve ∫ 1/sqrt[5]{x^2 wrt x

$$\int{ \frac{ 1 }{ \sqrt[ 5 ]{ { x }^{ 2 } } } }d x$$

Evaluate

$$\frac{5x^{\frac{3}{5}}}{3}+С$$

Solution Steps

Rewrite \frac{1}{x^{\frac{2}{5}}} as x^{-\frac{2}{5}}. Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{-\frac{2}{5}}\mathrm{d}x with \frac{x^{\frac{3}{5}}}{\frac{3}{5}}. Simplify.

$$\frac{5x^{\frac{3}{5}}}{3}$$

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.

$$\frac{5x^{\frac{3}{5}}}{3}+С$$

Differentiate w.r.t. x

$$\frac{1}{x^{\frac{2}{5}}}$$