Optimal. Leaf size=19 \[ \frac{a x^5}{5}+\frac{3}{16} b x^{16/3} \]
[Out]
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Rubi [A] time = 0.0167725, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{a x^5}{5}+\frac{3}{16} b x^{16/3} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^(1/3))*x^4,x]
[Out]
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Rubi in Sympy [A] time = 2.91699, size = 15, normalized size = 0.79 \[ \frac{a x^{5}}{5} + \frac{3 b x^{\frac{16}{3}}}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**(1/3))*x**4,x)
[Out]
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Mathematica [A] time = 0.00628031, size = 19, normalized size = 1. \[ \frac{a x^5}{5}+\frac{3}{16} b x^{16/3} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^(1/3))*x^4,x]
[Out]
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Maple [A] time = 0.002, size = 14, normalized size = 0.7 \[{\frac{a{x}^{5}}{5}}+{\frac{3\,b}{16}{x}^{{\frac{16}{3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^(1/3))*x^4,x)
[Out]
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Maxima [A] time = 1.44817, size = 339, normalized size = 17.84 \[ \frac{3 \,{\left (b x^{\frac{1}{3}} + a\right )}^{16}}{16 \, b^{15}} - \frac{14 \,{\left (b x^{\frac{1}{3}} + a\right )}^{15} a}{5 \, b^{15}} + \frac{39 \,{\left (b x^{\frac{1}{3}} + a\right )}^{14} a^{2}}{2 \, b^{15}} - \frac{84 \,{\left (b x^{\frac{1}{3}} + a\right )}^{13} a^{3}}{b^{15}} + \frac{1001 \,{\left (b x^{\frac{1}{3}} + a\right )}^{12} a^{4}}{4 \, b^{15}} - \frac{546 \,{\left (b x^{\frac{1}{3}} + a\right )}^{11} a^{5}}{b^{15}} + \frac{9009 \,{\left (b x^{\frac{1}{3}} + a\right )}^{10} a^{6}}{10 \, b^{15}} - \frac{1144 \,{\left (b x^{\frac{1}{3}} + a\right )}^{9} a^{7}}{b^{15}} + \frac{9009 \,{\left (b x^{\frac{1}{3}} + a\right )}^{8} a^{8}}{8 \, b^{15}} - \frac{858 \,{\left (b x^{\frac{1}{3}} + a\right )}^{7} a^{9}}{b^{15}} + \frac{1001 \,{\left (b x^{\frac{1}{3}} + a\right )}^{6} a^{10}}{2 \, b^{15}} - \frac{1092 \,{\left (b x^{\frac{1}{3}} + a\right )}^{5} a^{11}}{5 \, b^{15}} + \frac{273 \,{\left (b x^{\frac{1}{3}} + a\right )}^{4} a^{12}}{4 \, b^{15}} - \frac{14 \,{\left (b x^{\frac{1}{3}} + a\right )}^{3} a^{13}}{b^{15}} + \frac{3 \,{\left (b x^{\frac{1}{3}} + a\right )}^{2} a^{14}}{2 \, b^{15}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)*x^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.222381, size = 18, normalized size = 0.95 \[ \frac{3}{16} \, b x^{\frac{16}{3}} + \frac{1}{5} \, a x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)*x^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 5.63077, size = 15, normalized size = 0.79 \[ \frac{a x^{5}}{5} + \frac{3 b x^{\frac{16}{3}}}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*x**(1/3))*x**4,x)
[Out]
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GIAC/XCAS [A] time = 0.260224, size = 18, normalized size = 0.95 \[ \frac{3}{16} \, b x^{\frac{16}{3}} + \frac{1}{5} \, a x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)*x^4,x, algorithm="giac")
[Out]