Optimal. Leaf size=4 \[ \sin \left (x^2\right ) \]
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Rubi [A] time = 0.0065855, antiderivative size = 4, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.429, Rules used = {12, 3380, 2637} \[ \sin \left (x^2\right ) \]
Antiderivative was successfully verified.
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Rule 12
Rule 3380
Rule 2637
Rubi steps
\begin{align*} \int 2 x \cos \left (x^2\right ) \, dx &=2 \int x \cos \left (x^2\right ) \, dx\\ &=\operatorname{Subst}\left (\int \cos (x) \, dx,x,x^2\right )\\ &=\sin \left (x^2\right )\\ \end{align*}
Mathematica [A] time = 0.0014906, size = 4, normalized size = 1. \[ \sin \left (x^2\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 5, normalized size = 1.3 \begin{align*} \sin \left ({x}^{2} \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.960729, size = 5, normalized size = 1.25 \begin{align*} \sin \left (x^{2}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.01673, size = 14, normalized size = 3.5 \begin{align*} \sin \left (x^{2}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.163815, size = 3, normalized size = 0.75 \begin{align*} \sin{\left (x^{2} \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.09887, size = 5, normalized size = 1.25 \begin{align*} \sin \left (x^{2}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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