Answer
$ \displaystyle \frac{x^{0.9}}{0.3}+40x^{-0.1}+C$
Work Step by Step
Written in exponent form,
applying Sum and Difference RuIes,
...$=\displaystyle \int 3x^{-0.1}dx-\displaystyle \int 4x^{-1.1}dx$
... Constant MultipIe Rule
$=3\displaystyle \int x^{-0.1}dx-4\int x^{-1.1}dx$
... Power Rule, both: $n\neq-1$
$=3\displaystyle \frac{x^{-0.1+1}}{-0.1+1}-4\cdot\frac{x^{-1.1+1}}{-1.1+1}+C$
$=3\displaystyle \cdot\frac{x^{0.9}}{0.9}+4\cdot\frac{x^{-0.1}}{-0.1}+C$
$=\displaystyle \frac{x^{0.9}}{0.3}+40x^{-0.1}+C$
