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