InterviewSolution
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InterviewSolution
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`int(tanx)/(sqrt(sin^(4)x+cos^(4)x))dx` is equal toA. `ln(tan^(2)x)+sqrt(1+tan^(2)x)+C`B. `secx+C`C. `sqrt(1-tan^(2)x)+C`D. None of the above |
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Answer» Correct Answer - D `I=int(tanx)/(sqrt(sin^(4)x+cos^(4)x))dx=int(tanx.sec^(2)x)/(sqrt(1+tan^(4)x))dx` `"Put "tanx=t` `rArr" "sec^(2)x dx=dt` `int(tanx)/(sqrt(sin^(4)x+cos^(4)x))dx=int(t)/(sqrt(1+t^(4)))dt` `"Let "t^(2)=t rArr 2t dt = dy` `therefore" "I=int(dy)/(2sqrt(1+y^(2)))=(1)/(2)ln|y+sqrt(y^(2)+1)|+C` `=(1)/(2)ln|tan^(2)x+sqrt(tan^(4)x+1)|+C` |
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