Evaluate the integrals in Exercises 53–76.
61. ∫(from 0 to 2)dt/√(8+2t²)

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Identify the integral to evaluate: \(\int_0^2 \frac{dt}{\sqrt{8 + 2t^2}}\).

Factor out the constant inside the square root to simplify the integrand: rewrite \(\sqrt{8 + 2t^2}\) as \(\sqrt{2(4 + t^2)} = \sqrt{2} \sqrt{4 + t^2}\).

Rewrite the integral using this simplification: \(\int_0^2 \frac{dt}{\sqrt{2} \sqrt{4 + t^2}} = \frac{1}{\sqrt{2}} \int_0^2 \frac{dt}{\sqrt{4 + t^2}}\).

Recognize that the integral \(\int \frac{dt}{\sqrt{a^2 + t^2}}\) has a standard antiderivative: \(\ln|t + \sqrt{t^2 + a^2}| + C\), where \(a\) is a constant.

Apply the antiderivative formula with \(a = 2\), evaluate the resulting expression at the limits \(t=2\) and \(t=0\), and subtract to find the definite integral value.

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