Question

Write a value of $\int e^{\log \sin x}\cos xdx$.

Answer 1

Let I=$\int$ e^{log sin x} . cos x dx
= $\int$ sin x × cos x dx $\left(\because e^{\log a}=a\right)$
Let sin x = t
⇒​ cos x dx = dt
$\therefore I$=$\int$ t . dt
$$\begin{gathered} =\frac{t^2}{2}+C \\ =\frac{{\sin }^{2}x}{2}+C\mathit{}\left(\because t=\sin x\right) \end{gathered}$$