Optimal. Leaf size=59 \[ \frac{3 a^2 \left (a+b x^2\right )^{4/3}}{8 b^3}+\frac{3 \left (a+b x^2\right )^{10/3}}{20 b^3}-\frac{3 a \left (a+b x^2\right )^{7/3}}{7 b^3} \]
[Out]
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Rubi [A] time = 0.0959325, antiderivative size = 59, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{3 a^2 \left (a+b x^2\right )^{4/3}}{8 b^3}+\frac{3 \left (a+b x^2\right )^{10/3}}{20 b^3}-\frac{3 a \left (a+b x^2\right )^{7/3}}{7 b^3} \]
Antiderivative was successfully verified.
[In] Int[x^5*(a + b*x^2)^(1/3),x]
[Out]
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Rubi in Sympy [A] time = 11.5431, size = 54, normalized size = 0.92 \[ \frac{3 a^{2} \left (a + b x^{2}\right )^{\frac{4}{3}}}{8 b^{3}} - \frac{3 a \left (a + b x^{2}\right )^{\frac{7}{3}}}{7 b^{3}} + \frac{3 \left (a + b x^{2}\right )^{\frac{10}{3}}}{20 b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**5*(b*x**2+a)**(1/3),x)
[Out]
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Mathematica [A] time = 0.0236736, size = 50, normalized size = 0.85 \[ \frac{3 \sqrt [3]{a+b x^2} \left (9 a^3-3 a^2 b x^2+2 a b^2 x^4+14 b^3 x^6\right )}{280 b^3} \]
Antiderivative was successfully verified.
[In] Integrate[x^5*(a + b*x^2)^(1/3),x]
[Out]
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Maple [A] time = 0.008, size = 36, normalized size = 0.6 \[{\frac{42\,{b}^{2}{x}^{4}-36\,ab{x}^{2}+27\,{a}^{2}}{280\,{b}^{3}} \left ( b{x}^{2}+a \right ) ^{{\frac{4}{3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^5*(b*x^2+a)^(1/3),x)
[Out]
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Maxima [A] time = 1.35652, size = 63, normalized size = 1.07 \[ \frac{3 \,{\left (b x^{2} + a\right )}^{\frac{10}{3}}}{20 \, b^{3}} - \frac{3 \,{\left (b x^{2} + a\right )}^{\frac{7}{3}} a}{7 \, b^{3}} + \frac{3 \,{\left (b x^{2} + a\right )}^{\frac{4}{3}} a^{2}}{8 \, b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^(1/3)*x^5,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.203324, size = 62, normalized size = 1.05 \[ \frac{3 \,{\left (14 \, b^{3} x^{6} + 2 \, a b^{2} x^{4} - 3 \, a^{2} b x^{2} + 9 \, a^{3}\right )}{\left (b x^{2} + a\right )}^{\frac{1}{3}}}{280 \, b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^(1/3)*x^5,x, algorithm="fricas")
[Out]
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Sympy [A] time = 6.42102, size = 700, normalized size = 11.86 \[ \frac{27 a^{\frac{34}{3}} \sqrt [3]{1 + \frac{b x^{2}}{a}}}{280 a^{8} b^{3} + 840 a^{7} b^{4} x^{2} + 840 a^{6} b^{5} x^{4} + 280 a^{5} b^{6} x^{6}} - \frac{27 a^{\frac{34}{3}}}{280 a^{8} b^{3} + 840 a^{7} b^{4} x^{2} + 840 a^{6} b^{5} x^{4} + 280 a^{5} b^{6} x^{6}} + \frac{72 a^{\frac{31}{3}} b x^{2} \sqrt [3]{1 + \frac{b x^{2}}{a}}}{280 a^{8} b^{3} + 840 a^{7} b^{4} x^{2} + 840 a^{6} b^{5} x^{4} + 280 a^{5} b^{6} x^{6}} - \frac{81 a^{\frac{31}{3}} b x^{2}}{280 a^{8} b^{3} + 840 a^{7} b^{4} x^{2} + 840 a^{6} b^{5} x^{4} + 280 a^{5} b^{6} x^{6}} + \frac{60 a^{\frac{28}{3}} b^{2} x^{4} \sqrt [3]{1 + \frac{b x^{2}}{a}}}{280 a^{8} b^{3} + 840 a^{7} b^{4} x^{2} + 840 a^{6} b^{5} x^{4} + 280 a^{5} b^{6} x^{6}} - \frac{81 a^{\frac{28}{3}} b^{2} x^{4}}{280 a^{8} b^{3} + 840 a^{7} b^{4} x^{2} + 840 a^{6} b^{5} x^{4} + 280 a^{5} b^{6} x^{6}} + \frac{60 a^{\frac{25}{3}} b^{3} x^{6} \sqrt [3]{1 + \frac{b x^{2}}{a}}}{280 a^{8} b^{3} + 840 a^{7} b^{4} x^{2} + 840 a^{6} b^{5} x^{4} + 280 a^{5} b^{6} x^{6}} - \frac{27 a^{\frac{25}{3}} b^{3} x^{6}}{280 a^{8} b^{3} + 840 a^{7} b^{4} x^{2} + 840 a^{6} b^{5} x^{4} + 280 a^{5} b^{6} x^{6}} + \frac{135 a^{\frac{22}{3}} b^{4} x^{8} \sqrt [3]{1 + \frac{b x^{2}}{a}}}{280 a^{8} b^{3} + 840 a^{7} b^{4} x^{2} + 840 a^{6} b^{5} x^{4} + 280 a^{5} b^{6} x^{6}} + \frac{132 a^{\frac{19}{3}} b^{5} x^{10} \sqrt [3]{1 + \frac{b x^{2}}{a}}}{280 a^{8} b^{3} + 840 a^{7} b^{4} x^{2} + 840 a^{6} b^{5} x^{4} + 280 a^{5} b^{6} x^{6}} + \frac{42 a^{\frac{16}{3}} b^{6} x^{12} \sqrt [3]{1 + \frac{b x^{2}}{a}}}{280 a^{8} b^{3} + 840 a^{7} b^{4} x^{2} + 840 a^{6} b^{5} x^{4} + 280 a^{5} b^{6} x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**5*(b*x**2+a)**(1/3),x)
[Out]
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GIAC/XCAS [A] time = 0.21708, size = 58, normalized size = 0.98 \[ \frac{3 \,{\left (14 \,{\left (b x^{2} + a\right )}^{\frac{10}{3}} - 40 \,{\left (b x^{2} + a\right )}^{\frac{7}{3}} a + 35 \,{\left (b x^{2} + a\right )}^{\frac{4}{3}} a^{2}\right )}}{280 \, b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^(1/3)*x^5,x, algorithm="giac")
[Out]