Question
Write an anti derivative of function cos 2x using the method of inspection.
✓
Answer
A function whose derivative is cos 2x.
$\frac{d}{d x} \sin 2 x=2 \cos 2 x$
or $\cos 2 x=\frac{1}{2} \frac{d}{d x}(\sin 2 x)=\frac{d}{d x}\left(\frac{1}{2} \sin 2 x\right)$
Therefore, an anti derivative of cos 2x is $\frac{1}{2} \sin 2 x$
$\frac{d}{d x} \sin 2 x=2 \cos 2 x$
or $\cos 2 x=\frac{1}{2} \frac{d}{d x}(\sin 2 x)=\frac{d}{d x}\left(\frac{1}{2} \sin 2 x\right)$
Therefore, an anti derivative of cos 2x is $\frac{1}{2} \sin 2 x$
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