$\int \frac{\sin 2x (1 - \frac{3}{2} \cos x)}{e^{\sin^2 x + \cos^3 x}} \, dx =$

  • A
    $e^{\sin^2 x + \cos^3 x} + c$,where $c$ is a constant of integration.
  • B
    $-e^{-(\sin^2 x + \cos^3 x)} + c$,where $c$ is a constant of integration.
  • C
    $e^{-(\sin^2 x + \cos^3 x)^2} + c$,where $c$ is a constant of integration.
  • D
    $e^{\sin^2 x + \cos x} + c$,where $c$ is a constant of integration.

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Assertion $(A):$ $\frac{1}{x^2 + a^2}$ can be integrated by a substitution $x = a \tan \theta$.
Reason $(R):$ Because all integrands are integrated by the method of substitution only.
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