5. sin 2x- 4 e3*

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Solution

The function is given as,

y=sin2x−4 e 3x

We have to calculate the integral or anti-derivative of y.

Calculate the derivative of cos2x.

d dx ( cos2x )=( sin2x )( −2 ) −1 2 [ ( d dx ( cos2x ) ) ]=( sin2x ) ( sin2x )= [ d dx ( −1 2 cos2x ) ]

Calculate the derivative of 4 e 3x .

d dx ( 4 e 3x )= ( e 3x )( 3 )( 4 ) 4 3 [ ( d dx ( e 3x ) ) ]=( 4 e 3x ) ( 4 e 3x )= [ 4 3 d dx ( e 3x ) ]

Thus, the anti-derivative of ( sin2x−4 e 3x )is [ ( −1 2 cos2x )+( −4 3 e 3x ) ].

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