Geometric Interpretation of Def.Int as Limit of Sum
Evaluate the ...
Question
Evaluate the integral ∫2x+3√x2+4x+1dx
A
2√x2+4x+1−log∣∣x+2+√x2+4x+1∣∣+C
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B
√x2+4x−1−log∣∣x+2+√x2+4x−1∣∣+C
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C
2√x2+4x+1−log∣∣x−2+√x2−4x+1∣∣+C
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D
√x2+4x−1−log∣∣x−2+√x2+4x−1∣∣+C
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Solution
The correct option is A2√x2+4x+1−log∣∣x+2+√x2+4x+1∣∣+C I=∫2x+3√x2+4x+1dx=∫(2x+4)−1√x2+4x+1dx =∫2x+4√x2+4x+1dx−∫1√x2+4x+1dx =∫dt√t−∫1√(x+2)2−(√3)2dx, where t=x2+4x+1⇒dt=(2x+4)dx =2√t−log∣∣(x+2)+√x2+4x+1∣∣+C =2√x2+4x+1−log∣∣x+2+√x2+4x+1∣∣+C