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Question

e3xsin4xdx=
  1. e3x(4cos4x3sin4x)25+c
  2. e3x(3cos4x+4sin4x)25+c
  3. e3x(4cos4x+3sin4x)25+c
  4. None of these


Solution

The correct option is C e3x(4cos4x+3sin4x)25+c
Using integration by parts 
I=e3xsin4xdx=e3xcos4x434e3xcos4xdx=e3xcos4x434(e3xsin4x4+3e3xsin4x4dx)25I16=e3xcos4x4316e3xsin4x+cI=e3x(4cos4x+3sin4x)25+c

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