Question

can someone check my work. Integration with long division

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

7r -21
------------
r+3 | 7r^2
(7r^2+21r)
----------
-21r
(-21r -63)
--------
63


seems fine to me