can someone check my work. Integration with long division

Question

anonymous · Answer

this will take me a couple mins to type it all in

anonymous · Answer

$$\int\limits \frac{ 7r^2 }{ (r+3) }$$ =$$\frac{ 7r^2 +0r+0  }{ (r+3)}= \int\limits (7r-21+\frac{ 63 }{ (r+3) })dr$$=$$\frac{ 7r^2 }{ 2 }-21r+63 \ln \left| r+3 \right|+c$$

freckles · Answer

your partial fractions is right 
and your answer looks great to me

amistre64 · Answer

7r -21
       ------------
r+3 | 7r^2
        (7r^2+21r)
        ----------
                -21r
               (-21r -63)
                 --------
                           63


seems fine to me