Optimal. Leaf size=8 \[ \frac{\sec \left (x^2\right )}{2} \]
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Rubi [A] time = 0.063054, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.3, Rules used = {6715, 2606, 8} \[ \frac{\sec \left (x^2\right )}{2} \]
Antiderivative was successfully verified.
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Rule 6715
Rule 2606
Rule 8
Rubi steps
\begin{align*} \int x \sec \left (x^2\right ) \tan \left (x^2\right ) \, dx &=\frac{1}{2} \operatorname{Subst}\left (\int \sec (x) \tan (x) \, dx,x,x^2\right )\\ &=\frac{1}{2} \operatorname{Subst}\left (\int 1 \, dx,x,\sec \left (x^2\right )\right )\\ &=\frac{\sec \left (x^2\right )}{2}\\ \end{align*}
Mathematica [A] time = 0.0056369, size = 8, normalized size = 1. \[ \frac{\sec \left (x^2\right )}{2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 7, normalized size = 0.9 \begin{align*}{\frac{\sec \left ({x}^{2} \right ) }{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 0.972905, size = 76, normalized size = 9.5 \begin{align*} \frac{\cos \left (2 \, x^{2}\right ) \cos \left (x^{2}\right ) + \sin \left (2 \, x^{2}\right ) \sin \left (x^{2}\right ) + \cos \left (x^{2}\right )}{\cos \left (2 \, x^{2}\right )^{2} + \sin \left (2 \, x^{2}\right )^{2} + 2 \, \cos \left (2 \, x^{2}\right ) + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.95153, size = 19, normalized size = 2.38 \begin{align*} \frac{1}{2 \, \cos \left (x^{2}\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.331556, size = 5, normalized size = 0.62 \begin{align*} \frac{\sec{\left (x^{2} \right )}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.08242, size = 11, normalized size = 1.38 \begin{align*} \frac{1}{2 \, \cos \left (x^{2}\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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