Provide an Appropriate Response $\frac { 3 x - 1 } { x ^ { 2 } - 3 x - 10 }$

question 270

Essay

Provide an appropriate response.
-(a) Express $\frac { 3 x - 1 } { x ^ { 2 } - 3 x - 10 }$ as a sum of partial fractions.
(b) Evaluate $\int \frac { 3 x - 1 } { x ^ { 2 } - 3 x - 10 } d x$ .
(c) Evaluate $\int \frac { 2 x ^ { 2 } - 3 x - 21 } { x ^ { 2 } - 3 x - 10 } d x$ .
(d) Find a solution to the initial value problem: $\frac { d y } { d x } = \frac { 3 x y - y } { x ^ { 2 } - 3 x - 10 } , \quad y ( 4 ) = 12 .$

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