$\text { Use partial fractions to find } \int \frac { 6 x ^ { 2 } + 14 x - 3 } { x ^ { 3 } + 3 x ^ { 2 } } d x$

question 8

Multiple Choice

$\text { Use partial fractions to find } \int \frac { 6 x ^ { 2 } + 14 x - 3 } { x ^ { 3 } + 3 x ^ { 2 } } d x$

• A)\(\int \frac { 6 x ^ { 2 } + 14 x - 3 } { x ^ { 2 } ( x + 3 ) } d x = \ln \left| x ^ { 6 } + 3 x ^ { 5 } \right| + C\)
• B)\(\int \frac { 6 x ^ { 2 } + 14 x - 3 } { x ^ { 2 } ( x + 3 ) } d x = \frac { 1 } { x } + \left( x ^ { 6 } + 3 x ^ { 5 } \right) + C\)
• C)\(\int \frac { 6 x ^ { 2 } + 14 x - 3 } { x ^ { 2 } ( x + 3 ) } d x = \frac { 1 } { x } + \ln \left| x ^ { 7 } + x ^ { 5 } \right| + C\)
• D)\(\int \frac { 6 x ^ { 2 } + 14 x - 3 } { x ^ { 2 } ( x + 3 ) } d x = \ln \left| x ^ { 6 } + 5 x ^ { 4 } \right| + C\)
• E)\(\int \frac { 6 x ^ { 2 } + 14 x - 3 } { x ^ { 2 } ( x + 3 ) } d x = \frac { 1 } { x } + \ln \left| x ^ { 6 } + 3 x ^ { 5 } \right| + C\)

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