Evaluate the following functions : (x+a) (x-b) d x - Vidyadip

Question

Evaluate the following functions : $\int \frac{\sin (x+a)}{\cos (x-b)} \cdot d x$

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Answer

$
\begin{aligned}
& =\int \frac{\sin [(x-b)+(a+b)]}{\cos (x-b)} \cdot d x \\
& =\int \frac{\sin (x-b) \cdot \cos (a+b)+\cos (x-b) \cdot \sin (a+b)}{\cos (x-b)} \cdot d x \\
& =\int\left[\frac{\sin (x-b) \cdot \cos (a+b)}{\cos (x-b)}+\frac{\cos (x-b) \cdot \sin (a+b)}{\cos (x-b)}\right] \\
& =\int[\cos (a+b) \cdot \tan (x-b)+\sin (a+b)] \cdot d x \\
& =\cos (a+b) \cdot \log (\sec (x-b))+x \cdot \sin (a+b)+c
\end{aligned}
$

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