Convergence of $\int_{1}^{\infty} e^{\sin(x)}\cdot\frac{\sin(x)}{x^2} $

Determine if the following integral converge or diverge. Please show your steps.

$\int_{1}^{\infty} e^{\sin(x)}\cdot\frac{\sin(x)}{x^2} $

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  • According to your reasoning, the answer should not be e? and therefore converges?

  • I'm not calculating the value of the integral. I'm showing that it is bounded by a constant, so it must converge.

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