Question

What is \[\int\frac{\sin x}{\sin(x+a)}\,dx\]?

Options

• \[x\sin a-\cos a\log|\sin(x+a)|+C\]

• \[x\cos a-\sin a\log|\cos(x+a)|+C\]

• \[x\cos a-\sin a\log|\sin(x+a)|+C\]

• \[x\cos a+\sin a\log|\sin(x+a)|+C\]

Answer 1

After integration, substitute \[t=x+a\]. The terms \[a\cos a\] and \[-C_1\sin a\] are combined into another arbitrary constant \[C\].