Optimal. Leaf size=17 \[ \frac{\sec ^8(x)}{8}-\frac{\sec ^6(x)}{6} \]
[Out]
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Rubi [A] time = 0.0368012, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222 \[ \frac{\sec ^8(x)}{8}-\frac{\sec ^6(x)}{6} \]
Antiderivative was successfully verified.
[In] Int[Sec[x]^6*Tan[x]^3,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\tan ^{3}{\left (x \right )}}{\cos ^{6}{\left (x \right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(sec(x)**6*tan(x)**3,x)
[Out]
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Mathematica [A] time = 0.0104471, size = 17, normalized size = 1. \[ \frac{\sec ^8(x)}{8}-\frac{\sec ^6(x)}{6} \]
Antiderivative was successfully verified.
[In] Integrate[Sec[x]^6*Tan[x]^3,x]
[Out]
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Maple [B] time = 0.02, size = 32, normalized size = 1.9 \[{\frac{ \left ( \sin \left ( x \right ) \right ) ^{4}}{8\, \left ( \cos \left ( x \right ) \right ) ^{8}}}+{\frac{ \left ( \sin \left ( x \right ) \right ) ^{4}}{12\, \left ( \cos \left ( x \right ) \right ) ^{6}}}+{\frac{ \left ( \sin \left ( x \right ) \right ) ^{4}}{24\, \left ( \cos \left ( x \right ) \right ) ^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(sec(x)^6*tan(x)^3,x)
[Out]
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Maxima [A] time = 1.37368, size = 49, normalized size = 2.88 \[ \frac{4 \, \sin \left (x\right )^{2} - 1}{24 \,{\left (\sin \left (x\right )^{8} - 4 \, \sin \left (x\right )^{6} + 6 \, \sin \left (x\right )^{4} - 4 \, \sin \left (x\right )^{2} + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sec(x)^6*tan(x)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.25274, size = 19, normalized size = 1.12 \[ -\frac{4 \, \cos \left (x\right )^{2} - 3}{24 \, \cos \left (x\right )^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sec(x)^6*tan(x)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.132363, size = 15, normalized size = 0.88 \[ - \frac{4 \cos ^{2}{\left (x \right )} - 3}{24 \cos ^{8}{\left (x \right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sec(x)**6*tan(x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.204358, size = 19, normalized size = 1.12 \[ -\frac{4 \, \cos \left (x\right )^{2} - 3}{24 \, \cos \left (x\right )^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sec(x)^6*tan(x)^3,x, algorithm="giac")
[Out]