Question:
sin 2x
Solution:
The anti derivative of sin 2x is a function of x whose derivative is sin 2x.
It is known that,
$\frac{d}{d x}(\cos 2 x)=-2 \sin 2 x$
$\Rightarrow \sin 2 x=-\frac{1}{2} \frac{d}{d x}(\cos 2 x)$
$\therefore \sin 2 x=\frac{d}{d x}\left(-\frac{1}{2} \cos 2 x\right)$
Therefore, the anti derivative of $\sin 2 x$ is $-\frac{1}{2} \cos 2 x$
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