Optimal. Leaf size=8 \[ \frac{\sec ^3(x)}{3} \]
[Out]
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Rubi [A] time = 0.0200002, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.286 \[ \frac{\sec ^3(x)}{3} \]
Antiderivative was successfully verified.
[In] Int[Sec[x]^3*Tan[x],x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\tan{\left (x \right )}}{\cos ^{3}{\left (x \right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(sec(x)**3*tan(x),x)
[Out]
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Mathematica [A] time = 0.00297648, size = 8, normalized size = 1. \[ \frac{\sec ^3(x)}{3} \]
Antiderivative was successfully verified.
[In] Integrate[Sec[x]^3*Tan[x],x]
[Out]
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Maple [A] time = 0.001, size = 7, normalized size = 0.9 \[{\frac{ \left ( \sec \left ( x \right ) \right ) ^{3}}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(sec(x)^3*tan(x),x)
[Out]
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Maxima [A] time = 1.44046, size = 8, normalized size = 1. \[ \frac{1}{3 \, \cos \left (x\right )^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sec(x)^3*tan(x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.249965, size = 8, normalized size = 1. \[ \frac{1}{3 \, \cos \left (x\right )^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sec(x)^3*tan(x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.050763, size = 7, normalized size = 0.88 \[ \frac{1}{3 \cos ^{3}{\left (x \right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sec(x)**3*tan(x),x)
[Out]
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GIAC/XCAS [A] time = 0.199054, size = 8, normalized size = 1. \[ \frac{1}{3 \, \cos \left (x\right )^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sec(x)^3*tan(x),x, algorithm="giac")
[Out]