Optimal. Leaf size=14 \[ x+\frac{\tan ^3(x)}{3}-\tan (x) \]
[Out]
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Rubi [A] time = 0.0159044, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 4, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.5 \[ x+\frac{\tan ^3(x)}{3}-\tan (x) \]
Antiderivative was successfully verified.
[In] Int[Tan[x]^4,x]
[Out]
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Rubi in Sympy [A] time = 0.473357, size = 10, normalized size = 0.71 \[ x + \frac{\tan ^{3}{\left (x \right )}}{3} - \tan{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(tan(x)**4,x)
[Out]
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Mathematica [A] time = 0.0051962, size = 18, normalized size = 1.29 \[ x-\frac{4 \tan (x)}{3}+\frac{1}{3} \tan (x) \sec ^2(x) \]
Antiderivative was successfully verified.
[In] Integrate[Tan[x]^4,x]
[Out]
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Maple [A] time = 0.004, size = 13, normalized size = 0.9 \[ x-\tan \left ( x \right ) +{\frac{ \left ( \tan \left ( x \right ) \right ) ^{3}}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(tan(x)^4,x)
[Out]
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Maxima [A] time = 1.49914, size = 16, normalized size = 1.14 \[ \frac{1}{3} \, \tan \left (x\right )^{3} + x - \tan \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(tan(x)^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.242919, size = 16, normalized size = 1.14 \[ \frac{1}{3} \, \tan \left (x\right )^{3} + x - \tan \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(tan(x)^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.049686, size = 19, normalized size = 1.36 \[ x + \frac{\sin ^{3}{\left (x \right )}}{3 \cos ^{3}{\left (x \right )}} - \frac{\sin{\left (x \right )}}{\cos{\left (x \right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(tan(x)**4,x)
[Out]
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GIAC/XCAS [A] time = 0.232812, size = 16, normalized size = 1.14 \[ \frac{1}{3} \, \tan \left (x\right )^{3} + x - \tan \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(tan(x)^4,x, algorithm="giac")
[Out]