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The anti-derivative of sin 2x-4e^(3x) is...

The anti-derivative of `sin 2x-4e^(3x)` is

A

`(1)/(2)cos 2x-(4)/(3)e^(3x)+C`

B

`-(1)/(2)cos 2x+(4)/(3)e^(3x)+C`

C

`-(1)/(2)cos 2x-(4)/(3)e^(3x)+C`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
We have, `int(sin 2x-4e^(3x))dx`
`=intsin 2xdx-4inte^(3x)dx`
`=(-cos2x)/(2)-4e^(3x)dx`
`=(-cos2x)/(2)-4(e^(3x))/(3)+C`
`=-(1)/(2)cos2x-(4)/(3)e^(3x)+C`
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