Optimal. Leaf size=8 \[ \frac{\sec ^6(x)}{6} \]
[Out]
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Rubi [A] time = 0.0189001, 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 \[ \frac{\sec ^6(x)}{6} \]
Antiderivative was successfully verified.
[In] Int[Sec[x]^6*Tan[x],x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\tan{\left (x \right )}}{\cos ^{6}{\left (x \right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(sec(x)**6*tan(x),x)
[Out]
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Mathematica [A] time = 0.0030136, size = 8, normalized size = 1. \[ \frac{\sec ^6(x)}{6} \]
Antiderivative was successfully verified.
[In] Integrate[Sec[x]^6*Tan[x],x]
[Out]
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Maple [A] time = 0.01, size = 7, normalized size = 0.9 \[{\frac{ \left ( \sec \left ( x \right ) \right ) ^{6}}{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(sec(x)^6*tan(x),x)
[Out]
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Maxima [A] time = 1.36296, size = 14, normalized size = 1.75 \[ -\frac{1}{6 \,{\left (\sin \left (x\right )^{2} - 1\right )}^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sec(x)^6*tan(x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.216379, size = 8, normalized size = 1. \[ \frac{1}{6 \, \cos \left (x\right )^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sec(x)^6*tan(x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.050575, size = 7, normalized size = 0.88 \[ \frac{1}{6 \cos ^{6}{\left (x \right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sec(x)**6*tan(x),x)
[Out]
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GIAC/XCAS [A] time = 0.198959, size = 8, normalized size = 1. \[ \frac{1}{6 \, \cos \left (x\right )^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sec(x)^6*tan(x),x, algorithm="giac")
[Out]