Optimal. Leaf size=1 \[ x \]
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Rubi [A] time = 0.0103859, antiderivative size = 1, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222, Rules used = {2635, 8} \[ x \]
Antiderivative was successfully verified.
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Rule 2635
Rule 8
Rubi steps
\begin{align*} \int \left (\cos ^2(x)+\sin ^2(x)\right ) \, dx &=\int \cos ^2(x) \, dx+\int \sin ^2(x) \, dx\\ &=2 \frac{\int 1 \, dx}{2}\\ &=x\\ \end{align*}
Mathematica [A] time = 0.000303, size = 1, normalized size = 1. \[ x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 2, normalized size = 2. \begin{align*} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.963386, size = 1, normalized size = 1. \begin{align*} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.82605, size = 4, normalized size = 4. \begin{align*} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.059741, size = 0, normalized size = 0. \begin{align*} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.068, size = 1, normalized size = 1. \begin{align*} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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