Optimal. Leaf size=10 \[ \frac{1}{6} \tan ^3\left (x^2\right ) \]
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Rubi [A] time = 0.0369431, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.071, Rules used = {6686} \[ \frac{1}{6} \tan ^3\left (x^2\right ) \]
Antiderivative was successfully verified.
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Rule 6686
Rubi steps
\begin{align*} \int x \sec ^2\left (x^2\right ) \tan ^2\left (x^2\right ) \, dx &=\frac{1}{6} \tan ^3\left (x^2\right )\\ \end{align*}
Mathematica [A] time = 0.00331, size = 10, normalized size = 1. \[ \frac{1}{6} \tan ^3\left (x^2\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.022, size = 15, normalized size = 1.5 \begin{align*}{\frac{ \left ( \sin \left ({x}^{2} \right ) \right ) ^{3}}{6\, \left ( \cos \left ({x}^{2} \right ) \right ) ^{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.935444, size = 11, normalized size = 1.1 \begin{align*} \frac{1}{6} \, \tan \left (x^{2}\right )^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 2.05899, size = 58, normalized size = 5.8 \begin{align*} -\frac{{\left (\cos \left (x^{2}\right )^{2} - 1\right )} \sin \left (x^{2}\right )}{6 \, \cos \left (x^{2}\right )^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.73092, size = 7, normalized size = 0.7 \begin{align*} \frac{\tan ^{3}{\left (x^{2} \right )}}{6} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06285, size = 11, normalized size = 1.1 \begin{align*} \frac{1}{6} \, \tan \left (x^{2}\right )^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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