Optimal. Leaf size=7 \[ -2 \log \left (\cos \left (x^2\right )\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 7, 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, 3747, 3475} \[ -2 \log \left (\cos \left (x^2\right )\right ) \]
Antiderivative was successfully verified.
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Rule 12
Rule 3475
Rule 3747
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*}
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Mathematica [A] time = 0.01, size = 7, normalized size = 1.00 \[ -2 \log \left (\cos \left (x^2\right )\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.61, size = 13, normalized size = 1.86 \[ -\log \left (\frac {1}{\tan \left (x^{2}\right )^{2} + 1}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 9, normalized size = 1.29 \[ \log \left (\tan \left (x^{2}\right )^{2} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 8, normalized size = 1.14 \[ -2 \ln \left (\cos \left (x^{2}\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.33, size = 7, normalized size = 1.00 \[ 2 \, \log \left (\sec \left (x^{2}\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 9, normalized size = 1.29 \[ \ln \left ({\mathrm {tan}\left (x^2\right )}^2+1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 8, normalized size = 1.14 \[ \log {\left (\tan ^{2}{\left (x^{2} \right )} + 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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