Answer
$2.55t^{2}-1.2\cdot\ln|t|+15t^{-0.2}+C$
Work Step by Step
Written in exponent form,
applying Sum and Difference RuIes,
...$=\displaystyle \int 5.1tdt-\displaystyle \int 1.2t^{-1}dt+\int 3t^{-1.2}dt$
... Constant MultipIe Rule
$=5.1\displaystyle \int tdt-1.2\int t^{-1}dt+3\int t^{-1.2}dt$
... Power Rule, 1st and 3rd: $n\neq-1$
... 2nd integral: $n=-1$
$=5.1\displaystyle \cdot\frac{t^{1+1}}{1+1}-1.2\cdot\ln|t|+3\cdot\frac{t^{-1.2+1}}{-1.2+1}+C$
$=2.55t^{2}-1.2\displaystyle \cdot\ln|t|-\frac{3t^{0.2}}{-0.2}+C$
$=2.55t^{2}-1.2\cdot\ln|t|+15t^{-0.2}+C$
