Question

$\int \frac{\sin x}{\sin (x+a)}dx$

Answer 1

$\int \frac{\sin x}{\sin \left(x+a\right)}dx$

$x+a=t$

$dx=dt$

$=\int \frac{\sin \left(t-a\right)}{\sin t}dt$

$=\int \frac{\sin t\cos a-\cos t\sin a}{\sin t}dt$

$=\cos a\int dt-\sin a\int \cot tdt$

$=\cos a\left(t\right)-\sin a\times \log /\sin /tc$

$=\left(x+a\right)\cos a-\sin a\log \left|\sin \left(x+a\right)\right|+c$