Question

Write a value of

\[\int e^{\text{ log  sin x  }}\text{ cos x}. \text{ dx}\]

Answer 1

Let I= e^log sin x . cos x dx 

\[\int\] sin x × cos x dx            \[\left( \because e^{log \text{ a} }= a \right)\]

Let sin x = t
⇒​ cos x dx = dt

\[\therefore I\]\[\int\] t . dt

\[= \frac{t^2}{2} + C\]
\[ = \frac{\sin^2 x}{2} + C \left( \because t = \sin x \right)\]