Optimal. Leaf size=10 \[ -\frac {1}{4} \cos \left (2 x^2\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {3379, 2638} \[ -\frac {1}{4} \cos \left (2 x^2\right ) \]
Antiderivative was successfully verified.
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Rule 2638
Rule 3379
Rubi steps
\begin {align*} \int x \sin \left (2 x^2\right ) \, dx &=\frac {1}{2} \operatorname {Subst}\left (\int \sin (2 x) \, dx,x,x^2\right )\\ &=-\frac {1}{4} \cos \left (2 x^2\right )\\ \end {align*}
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Mathematica [A] time = 0.01, size = 10, normalized size = 1.00 \[ -\frac {1}{4} \cos \left (2 x^2\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.70, size = 8, normalized size = 0.80 \[ -\frac {1}{4} \, \cos \left (2 \, x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 8, normalized size = 0.80 \[ -\frac {1}{4} \, \cos \left (2 \, x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 9, normalized size = 0.90 \[ -\frac {\cos \left (2 x^{2}\right )}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.32, size = 8, normalized size = 0.80 \[ -\frac {1}{4} \, \cos \left (2 \, x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 8, normalized size = 0.80 \[ \frac {{\sin \left (x^2\right )}^2}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 8, normalized size = 0.80 \[ - \frac {\cos {\left (2 x^{2} \right )}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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