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? [(x + sinx)/(1 + cosx)] dx is equal to A. x tan(x/2) B. x tan(x/2) + c C. log (1 + cosx) + c D. x log (cos x) + c

? [(x + sinx)/(1 + cosx)] dx is equal to
A. x tan(x/2)
B. x tan(x/2) + c
C. log (1 + cosx) + c
D. x log (cos x) + c

Grade:Upto college level

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
7 years ago
=\int (x+\sin x)/(1+\cos x)
=\int (x+\2sin (x/2) cos (x/2))/(2\cos^{2} (x/2))
=\int (x/2\\sec ^{2}(x/2)+\int (2sin (x/2) cos (x/2))/(2\cos^{2}(x/2))
=\int (x\\d(tan (x/2))+\int tan (x/2))+c
=(x\\tan (x/2))-\int tan (x/2)+\int tan (x/2)+c
=(x\\tan (x/2))+c
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

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