InterviewSolution
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InterviewSolution
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`int(dx)/(cos^(3)xsqrt(2sin 2x))` is equal toA. `sqrt(tanx)+(tan^(5//2)x)/(5)+C`B. `sqrt(tanx)+(2)/(5)tan^(5//2)x+C`C. `2sqrt(tanx)+(2)/(5)tan^(5//2)x+C`D. None of the above |
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Answer» Correct Answer - A Let `l=int(dx)/(cos^(3)x sqrt(2sin 2x))=int(dx)/(cos^(3)x sqrt(4sin x cos x))` `=(1)/(2)int(dx)/(cos^(7//2)x sin^(1//2)x)` `=(1)/(4)int(sec^(4)x)/(sqrt(tanx))dx` `=(1)/(2)int((1+tan)^(2)sec^(2)x)/(sqrt(tanx))` Put `tan x = t rArr sec^(2)x dx =dt` `therefore" "l=(1)/(2)int(1+t^(2))/(sqrtt)dt` `=(1)/(2)int t^(-1//2)dt+(1)/(2)intt^(3//2)dt=intt+(t^(5//2))/(5)+C` `=sqrt(tanx)+(1)/(5)tan^(5//2)x+C` |
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