$\text { Complete the square and find } \int \frac { x } { \sqrt { x ^ { 2 } + 10 x + 30 } } d x \text {. }$

question 13

Multiple Choice

$\text { Complete the square and find } \int \frac { x } { \sqrt { x ^ { 2 } + 10 x + 30 } } d x \text {. }$

• A) \(\int \frac { x } { \sqrt { x ^ { 2 } + 10 x + 30 } } d x = \sqrt { x ^ { 2 } + 10 x + 30 } - 5 \ln \left| \sqrt { x ^ { 2 } + 10 x + 30 } + ( x + 5 ) \right| + C\)
• B) \(\int \frac { x } { \sqrt { x ^ { 2 } + 10 x + 30 } } d x = \sqrt { x ^ { 2 } + 10 x + 30 } + \ln \left| \sqrt { x ^ { 2 } + 10 x + 30 } + ( x + 5 ) \right| + C\)
• C) \(\int \frac { x } { \sqrt { x ^ { 2 } + 10 x + 30 } } d x = \ln \left| \sqrt { x ^ { 2 } + 10 x + 30 } \right| + C\)
• D) \(\int \frac { x } { \sqrt { x ^ { 2 } + 10 x + 30 } } d x = 5 \ln \left| \sqrt { x ^ { 2 } + 10 x + 30 } + ( x + 5 ) \right| + C\)
• E) \(\int \frac { x } { \sqrt { x ^ { 2 } + 10 x + 30 } } d x = \sqrt { x ^ { 2 } + 10 x + 30 } - 5 \ln \left| \sqrt { x ^ { 2 } + 10 x + 30 } \right| + C\)

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