∫1+sinx4dx=
8sinx8+cosx8+c
8sinx8-cosx8+c
8sinx8+sinx8+c
18sinx8-cosx8+c
Explanation for the correct option:
Integrating the given function:
Consider the given equation as,
I=∫1+sinx4dxI=∫1+sin2x8dx
We know that,
sin2x=2sinxcosx
Then,
I=∫1+2sinx8cosx8dx
We know that, sin2x+cos2x=1
I=∫sin2x8+cos2x8+2sinx8cosx8dx=∫sinx8+cosx82dx=∫sinx8+cosx8dx=-cosx818+sinx818+c∵∫sinxdx=-cosxand∫cosxdx=sinx=-8cosx8+8sinx8+cI=8sinx8-cosx8+c
Hence, the correct answer is Option (B).