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Question
Find an antiderivative (or integral) of the following function by the method of inspection.
sin 2x – 4 e3x
Solution
we know that,
`d/dx` cos 2x = - 2 sin 2x
or sin 2x = `d/dx (- 1/2 "cos 2x")`
and `d/dx e^(3x) = 3e^(3x)`
or `e^(3x) = d/dx (1/3 e^(3x))`
Hence, sin 2x - 4e3x
`= d/dx (- 1/2 cos 2x) - 4 d/dx (1/3 e^(3x))`
`= d/dx (- 1/2 cos 2x - 4/3 e^(3x))`
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