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B
(x+1)√(x2+2x+5)+2log|x+1+√(x2+2x+5)|+C
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C
(x+1)√(x2+2x+5)−2log|x+1+√(x2+2x+5)|+C
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D
(x+1)√(x2+2x+5)+12log|x+1+√(x2+2x+5)|+C
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Solution
The correct option is A12(x+1)√(x2+2x+5)+2log|x+1+√(x2+2x+5)|+C ∫√x2+a2dx=x(√x2+a2)2+a22log|x+√x2+a2| ∫√(x2+2x+5)dx=∫√(x+1)2+22dx ∴∫√(x2+2x+5)dx=12(x+1)√(x2+2x+5)+2log|x+1+√(x2+2x+5)|+C