$\text { Use integration tables to find } \int ( 2 x + 5 ) ^ { 2 } \sqrt { ( 2 x + 5 ) ^ { 2 } - 9 } d x \text {. }$

question 27

Multiple Choice

$\text { Use integration tables to find } \int ( 2 x + 5 ) ^ { 2 } \sqrt { ( 2 x + 5 ) ^ { 2 } - 9 } d x \text {. }$

• A) \(\frac { 1 } { 32 } \left[ ( 2 x + 5 ) \left( 2 ( 2 x + 5 ) ^ { 2 } + 9 \right) \sqrt { ( 2 x + 5 ) ^ { 2 } - 9 } - 81 \ln \left| ( 2 x + 5 ) + \sqrt { ( 2 x + 5 ) ^ { 2 } + 9 } \right| \right] + C\)
• B) \(\frac { 1 } { 16 } \left[ ( 2 x + 5 ) \left( 2 ( 2 x + 5 ) ^ { 2 } - 9 \right) \sqrt { ( 2 x + 5 ) ^ { 2 } - 9 } - 81 \ln \left| ( 2 x + 5 ) + \sqrt { ( 2 x + 5 ) ^ { 2 } - 9 } \right| \right] + C\)
• C) \(\frac { 1 } { 16 } \left[ ( 2 x + 5 ) \left( 2 ( 2 x + 5 ) ^ { 2 } \pm 9 \right) \sqrt { ( 2 x + 5 ) ^ { 2 } \pm 9 } - 81 \ln \left| ( 2 x + 5 ) + \sqrt { ( 2 x + 5 ) ^ { 2 } \pm 9 } \right| \right] + C\)
• D)
• \(\frac { 1 } { 8 } \left[ ( 2 x + 5 ) \left( 2 ( 2 x + 5 ) ^ { 2 } - 9 \right) \sqrt { ( 2 x + 5 ) ^ { 2 } - 9 } - 81 \ln \left| ( 2 x + 5 ) + \sqrt { ( 2 x + 5 ) ^ { 2 } - 9 } \right| \right] + C\)
• E)
• \(\frac { 1 } { 16 } \left[ ( 2 x + 5 ) \left( 2 ( 2 x + 5 ) ^ { 2 } + 9 \right) \sqrt { ( 2 x + 5 ) ^ { 2 } + 9 } - 81 \ln \left| ( 2 x + 5 ) + \sqrt { ( 2 x + 5 ) ^ { 2 } + 9 } \right| \right] + C\)

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