Evaluate the Integral by First Performing Long Division on the Integrand

question 430

Multiple Choice

Evaluate the integral by first performing long division on the integrand and then writing the proper fraction as a sum of partial fractions.
- $$\int \frac { 9 x ^ { 3 } + 18 x ^ { 2 } + 12 x + 5 } { 9 x ^ { 2 } + 18 x + 9 } d x$$

• A) \(\frac { 1 } { 2 } x ^ { 2 } + \ln | 3 x + 3 | - \frac { 2 } { 3 x + 3 } + C\)
• B) \(\frac { 1 } { 2 } x ^ { 2 } - \frac { 3 x + 5 } { 3 x + 3 } + C\)
• C) \(\frac { 1 } { 2 } x ^ { 2 } + \frac { 1 } { 3 } \ln | 3 x + 3 | - \frac { 2 } { 3 } \frac { 1 } { 3 x + 3 } + C\)
• D) \(\frac { 1 } { 2 } x ^ { 2 } + \ln | 3 x + 3 | - \frac { 2 } { 3 } \frac { 1 } { 3 x + 3 } + C\)

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A threshold in hypothesis testing that determines the probability of rejecting the null hypothesis when it is true.