Optimal. Leaf size=38 \[ \frac{3 \left (a+b x^2\right )^{10/3}}{20 b^2}-\frac{3 a \left (a+b x^2\right )^{7/3}}{14 b^2} \]
[Out]
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Rubi [A] time = 0.0702891, antiderivative size = 38, 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 \[ \frac{3 \left (a+b x^2\right )^{10/3}}{20 b^2}-\frac{3 a \left (a+b x^2\right )^{7/3}}{14 b^2} \]
Antiderivative was successfully verified.
[In] Int[x^3*(a + b*x^2)^(4/3),x]
[Out]
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Rubi in Sympy [A] time = 7.84642, size = 34, normalized size = 0.89 \[ - \frac{3 a \left (a + b x^{2}\right )^{\frac{7}{3}}}{14 b^{2}} + \frac{3 \left (a + b x^{2}\right )^{\frac{10}{3}}}{20 b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3*(b*x**2+a)**(4/3),x)
[Out]
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Mathematica [A] time = 0.0350308, size = 28, normalized size = 0.74 \[ \frac{3 \left (a+b x^2\right )^{7/3} \left (7 b x^2-3 a\right )}{140 b^2} \]
Antiderivative was successfully verified.
[In] Integrate[x^3*(a + b*x^2)^(4/3),x]
[Out]
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Maple [A] time = 0.008, size = 25, normalized size = 0.7 \[ -{\frac{-21\,b{x}^{2}+9\,a}{140\,{b}^{2}} \left ( b{x}^{2}+a \right ) ^{{\frac{7}{3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3*(b*x^2+a)^(4/3),x)
[Out]
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Maxima [A] time = 1.35679, size = 41, normalized size = 1.08 \[ \frac{3 \,{\left (b x^{2} + a\right )}^{\frac{10}{3}}}{20 \, b^{2}} - \frac{3 \,{\left (b x^{2} + a\right )}^{\frac{7}{3}} a}{14 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^(4/3)*x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.206714, size = 61, normalized size = 1.61 \[ \frac{3 \,{\left (7 \, b^{3} x^{6} + 11 \, a b^{2} x^{4} + a^{2} b x^{2} - 3 \, a^{3}\right )}{\left (b x^{2} + a\right )}^{\frac{1}{3}}}{140 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^(4/3)*x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 7.49349, size = 88, normalized size = 2.32 \[ \begin{cases} - \frac{9 a^{3} \sqrt [3]{a + b x^{2}}}{140 b^{2}} + \frac{3 a^{2} x^{2} \sqrt [3]{a + b x^{2}}}{140 b} + \frac{33 a x^{4} \sqrt [3]{a + b x^{2}}}{140} + \frac{3 b x^{6} \sqrt [3]{a + b x^{2}}}{20} & \text{for}\: b \neq 0 \\\frac{a^{\frac{4}{3}} x^{4}}{4} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3*(b*x**2+a)**(4/3),x)
[Out]
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GIAC/XCAS [A] time = 0.216017, size = 105, normalized size = 2.76 \[ \frac{3 \,{\left (\frac{5 \,{\left (4 \,{\left (b x^{2} + a\right )}^{\frac{7}{3}} - 7 \,{\left (b x^{2} + a\right )}^{\frac{4}{3}} a\right )} a}{b} + \frac{14 \,{\left (b x^{2} + a\right )}^{\frac{10}{3}} - 40 \,{\left (b x^{2} + a\right )}^{\frac{7}{3}} a + 35 \,{\left (b x^{2} + a\right )}^{\frac{4}{3}} a^{2}}{b}\right )}}{280 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^(4/3)*x^3,x, algorithm="giac")
[Out]