Answer
$\displaystyle \frac{3x^{1.1}}{1.1}-\frac{x^{5.3}}{5.3}-4.1x+C$
Work Step by Step
applying Sum and Difference RuIes,
...$=\displaystyle \int 3x^{0.1}dx-\displaystyle \int x^{4.3}dx-\int 4.1dx$
... 1st and 3rd integral: Constant MultipIe Rule
...$=3\displaystyle \int x^{0.1}dx-\displaystyle \int x^{4.3}dx-4.1\int 1\cdot dx$
... Power Rule, all: $n\neq-1$
... last integral: $1=x^{0}$
$=3\displaystyle \cdot\frac{x^{0.1+1}}{0.1+1}-\frac{x^{4.3+1}}{4.3+1}-4.1\cdot\frac{x^{0+1}}{0+1}+C$
$=\displaystyle \frac{3x^{1.1}}{1.1}-\frac{x^{5.3}}{5.3}-4.1x+C$
