Answer
$$ \frac{1}{0.8}x^{0.8}-\frac{1}{1.2}x^{1.2}+C$$
Work Step by Step
$\int (x^{-0.2-x^{0.2}})dx$
$=\frac{1}{-0.2+1}x^{-0.2+1}-\frac{1}{0.2+1}x^{0.2+1}+C$
$= \frac{1}{0.8}x^{0.8}-\frac{1}{1.2}x^{1.2}+C$
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