Question

`int(cosx)/(sqrt(1+sinx))dx` is equal to
A. `sin.(x)/(2)-cos.(x)/(2)+C`
B. `sin.(x)/(2)+cos.(x)/(2)+C`
C. `2[sin.(x)/(2)-cos.(x)/(2)]+C`
D. `2[sin.(x)/(2)+cos.(x)/(2)]+C`

Answer 1

Correct Answer - D
`int(cosx)/(sqrt(1+sinx))dx`
`=int(cos^(2).(x)/(2)-sin^(2).(x)/(2))/(sqrt(sin^(2).(x)/(2)+cos^(2).(x)/(2)+2sin.(x)/(2)cos.(x)/(2)))dx`
`=int(cos^(2).(x)/(2)-sin^(2).(x)/(2))/(sin.(x)/(2)+cos.(x)/(2))dx=int(cos.(x)/(2)-sin.(x)/(2))dx`
`=2[sin.(x)/(2)+cos.(x)/(2)]+C`