InterviewSolution
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InterviewSolution
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`int(x+sinx)/(1+cosx) dx` is equal toA. `log|1+cosx|+C`B. `log|x+sinx|+C`C. `x-tanx//2 +C`D. `x tan((x)/(2))+C` |
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Answer» Correct Answer - D Let `l=int(x+sinx)/(1+cosx)dx` `int(x)/(2cos^(2)x//2)dx+int(2sin x//2cos x//2)/(2cos^(2)x//2)dx` `=(1)/(2)intx sec^(2).(x)/(2)dx+int tan.(x)/(2)dx` On integrating by parts in first integral, we get `=(1)/(2)[x int sec^(2).(x)/(2)dx-int[(d)/(dx)(x)intsec^(2).(x)/(2)dx]dx]+inttan.(x)/(2)dx` `=(1)/(2)[x tan.(x)/(2).2-2 int tan.(x)/(2)dx]+int tan.(x)/(2)dx` `=x tan .(x)/(2)-int tan.(x)/(2)dx+int tan.(x)/(2)dx` `=x tan.(x)/(2)+C` |
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