InterviewSolution
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InterviewSolution
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`int(dx)/(sqrt(1+4x^2))`A. `(1)/(2)log|x+sqrt(2x^(2)+1)|+C`B. `(1)/(2)log|2x+sqrt(4x^(2)+1)|+C`C. `log|2x+sqrt(4x^(2)+1)|+C`D. None of these |
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Answer» Correct Answer - B `int(dx)/(sqrt(1-4x^(2)))=int(dx)/(sqrt(4{((1)/(2))^(2)+x^(2)}))` `=(1)/(2)int(dx)/(sqrt(x^(2)+((1)/(2))^(2)))=(1)/(2)log|x+sqrt(x^(2)+((1)/(2)))^(2)|+C_(1)` `=(1)/(2)log|x+(sqrt(4x^(2)+1))/(2)|+C_(1)` `=(1)/(2)log|2x+sqrt(4x^(2)+1)|-(1)/(2)log2+C_(1)` `=(1)/(2)log|2x+sqrt(4x^(2)+1)|+C" "[C=(1)/(2)log2+C_(1)]` |
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