Optimal. Leaf size=7 \[ -2 \log \left (\cos \left (x^2\right )\right ) \]
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Rubi [A] time = 0.0072001, antiderivative size = 7, 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, 3747, 3475} \[ -2 \log \left (\cos \left (x^2\right )\right ) \]
Antiderivative was successfully verified.
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Rule 12
Rule 3747
Rule 3475
Rubi steps
\begin{align*} \int 4 x \tan \left (x^2\right ) \, dx &=4 \int x \tan \left (x^2\right ) \, dx\\ &=2 \operatorname{Subst}\left (\int \tan (x) \, dx,x,x^2\right )\\ &=-2 \log \left (\cos \left (x^2\right )\right )\\ \end{align*}
Mathematica [A] time = 0.0058107, size = 7, normalized size = 1. \[ -2 \log \left (\cos \left (x^2\right )\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 8, normalized size = 1.1 \begin{align*} -2\,\ln \left ( \cos \left ({x}^{2} \right ) \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.961662, size = 9, normalized size = 1.29 \begin{align*} 2 \, \log \left (\sec \left (x^{2}\right )\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.27923, size = 35, normalized size = 5. \begin{align*} -\log \left (\frac{1}{\tan \left (x^{2}\right )^{2} + 1}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.127445, size = 8, normalized size = 1.14 \begin{align*} \log{\left (\tan ^{2}{\left (x^{2} \right )} + 1 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06695, size = 12, normalized size = 1.71 \begin{align*} \log \left (\tan \left (x^{2}\right )^{2} + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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