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11-83.

Use integration by parts.
Let f = x2 and dg = ex.

Use substitution.
Let u = x2.

You should recognize the integrand as the derivative of an inverse trigonometric function.

This is an improper integral, so a limit will need to be used to evaluate it.
The symmetry of the graph can also be used to evaluate the integral.

Review the first Fundamental Theorem of Calculus.