Solved

 Use integration tables to find (2x+5)2(2x+5)29dx\text { Use integration tables to find } \int ( 2 x + 5 ) ^ { 2 } \sqrt { ( 2 x + 5 ) ^ { 2 } - 9 } d x \text {. }

Question 27

Multiple Choice

 Use integration tables to find (2x+5) 2(2x+5) 29dx\text { Use integration tables to find } \int ( 2 x + 5 ) ^ { 2 } \sqrt { ( 2 x + 5 ) ^ { 2 } - 9 } d x \text {. }


A) 132[(2x+5) (2(2x+5) 2+9) (2x+5) 2981ln(2x+5) +(2x+5) 2+9]+C\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) 116[(2x+5) (2(2x+5) 29) (2x+5) 2981ln(2x+5) +(2x+5) 29]+C\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) 116[(2x+5) (2(2x+5) 2±9) (2x+5) 2±981ln(2x+5) +(2x+5) 2±9]+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)
18[(2x+5) (2(2x+5) 29) (2x+5) 2981ln(2x+5) +(2x+5) 29]+C\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)
116[(2x+5) (2(2x+5) 2+9) (2x+5) 2+981ln(2x+5) +(2x+5) 2+9]+C\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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