Q100 / 180 · COMEDK 2017 · Mathematics

The value of $\int e^{2 x}(2 \sin 3 x+3 \cos 3 x) d x$ is

  • Correct answer
    A
    $e^{2 x} \sin 3 x+C$
  • B
    $e^{x} \operatorname{cosec} x+C$
  • C
    $e^{2 x}+C$
  • D
    $e^{2 x}(\sin 3 x)+C$

Solution

$\int e^{2 x}(2 \sin 3 x+3 \cos 3 x) d x$ $=2 \int e^{2 x} \sin 3 x d x+3 \int e^{2 x} \cos 3 x d x$ $=e^{2 x} \sin 3 x-3 \int e^{2 x} \cos 3 x d x$ $+3 \int e^{2 x} \cos 3 x d x+C$ $=e^{2 x} \sin 3 x+C$

Hence, the correct answer is option: 'A'.

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