Optimal. Leaf size=22 \[ -x+\frac{\tan ^5(x)}{5}-\frac{\tan ^3(x)}{3}+\tan (x) \]
[Out]
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Rubi [A] time = 0.0230807, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 2, integrand size = 4, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.5 \[ -x+\frac{\tan ^5(x)}{5}-\frac{\tan ^3(x)}{3}+\tan (x) \]
Antiderivative was successfully verified.
[In] Int[Tan[x]^6,x]
[Out]
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Rubi in Sympy [A] time = 0.53301, size = 17, normalized size = 0.77 \[ - x + \frac{\tan ^{5}{\left (x \right )}}{5} - \frac{\tan ^{3}{\left (x \right )}}{3} + \tan{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(tan(x)**6,x)
[Out]
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Mathematica [A] time = 0.00637214, size = 30, normalized size = 1.36 \[ -x+\frac{23 \tan (x)}{15}+\frac{1}{5} \tan (x) \sec ^4(x)-\frac{11}{15} \tan (x) \sec ^2(x) \]
Antiderivative was successfully verified.
[In] Integrate[Tan[x]^6,x]
[Out]
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Maple [A] time = 0.004, size = 19, normalized size = 0.9 \[ -x+\tan \left ( x \right ) -{\frac{ \left ( \tan \left ( x \right ) \right ) ^{3}}{3}}+{\frac{ \left ( \tan \left ( x \right ) \right ) ^{5}}{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(tan(x)^6,x)
[Out]
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Maxima [A] time = 1.61045, size = 24, normalized size = 1.09 \[ \frac{1}{5} \, \tan \left (x\right )^{5} - \frac{1}{3} \, \tan \left (x\right )^{3} - x + \tan \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(tan(x)^6,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.218354, size = 24, normalized size = 1.09 \[ \frac{1}{5} \, \tan \left (x\right )^{5} - \frac{1}{3} \, \tan \left (x\right )^{3} - x + \tan \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(tan(x)^6,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.060743, size = 31, normalized size = 1.41 \[ - x + \frac{\sin ^{5}{\left (x \right )}}{5 \cos ^{5}{\left (x \right )}} - \frac{\sin ^{3}{\left (x \right )}}{3 \cos ^{3}{\left (x \right )}} + \frac{\sin{\left (x \right )}}{\cos{\left (x \right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(tan(x)**6,x)
[Out]
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GIAC/XCAS [A] time = 0.20299, size = 24, normalized size = 1.09 \[ \frac{1}{5} \, \tan \left (x\right )^{5} - \frac{1}{3} \, \tan \left (x\right )^{3} - x + \tan \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(tan(x)^6,x, algorithm="giac")
[Out]