Optimal. Leaf size=4 \[ \sin \left (x^2\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 4, normalized size of antiderivative = 1.00, 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 2637
Rule 3380
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*}
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Mathematica [A] time = 0.00, size = 4, normalized size = 1.00 \[ \sin \left (x^2\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.79, size = 4, normalized size = 1.00 \[ \sin \left (x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 4, normalized size = 1.00 \[ \sin \left (x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 5, normalized size = 1.25 \[ \sin \left (x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.33, size = 4, normalized size = 1.00 \[ \sin \left (x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.92, size = 4, normalized size = 1.00 \[ \sin \left (x^2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 3, normalized size = 0.75 \[ \sin {\left (x^{2} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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