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If excos4xdx=Ae5xsin4x+54cos4x+C

then A is equal to 

 

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detailed solution

Correct option is A

Integrating by parts taking e4x as first function, we haveI=∫e5xcos⁡4xdx=14e5xsin⁡4x−54∫e5xsin⁡4xdx=14e5xsin⁡4x−54−e5xcos⁡4x4+54∫e5xcos⁡4xdx=14e5xsin⁡4x+516e5xcos⁡4x−2516I⇒1+2516I=416e5xsin⁡4x+54cos⁡4x⇒I=441e5xsin⁡4x+54cos⁡x+C


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