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? [(x + sinx)/(1 + cosx)] dx is equal toA. x tan(x/2)B. x tan(x/2) + cC. log (1 + cosx) + cD. x log (cos x) + c

Manvendra Singh chahar , 10 Years ago
Grade Upto college level
anser 1 Answers
SHAIK AASIF AHAMED

Last Activity: 10 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
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