# Evaluate the integral sinx/sin(x+a)

Solution:

$\\ I=\int sinx/sin(x+a)dx$

Let $\\x+a=y\Rightarrow dx=dy$

Substituting in the given integral, we get

$\\ I=\int sin(y-a)/siny dy$

$\\\Rightarrow sin(y-a)=siny\times cosa+cosy\times sina$

$\\ I=cosa\int dy-sina\int cot y dy\\ \\\Rightarrow I=(cosa)y-(sina)\log siny\\ \\\Rightarrow I=(cosa)(x+a)-(sina)\log [sin(x+a)+c]$

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