Optimal. Leaf size=49 \[ -\frac{3 a^2}{b^3 \sqrt [3]{a+b x}}-\frac{3 a (a+b x)^{2/3}}{b^3}+\frac{3 (a+b x)^{5/3}}{5 b^3} \]
[Out]
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Rubi [A] time = 0.0388706, antiderivative size = 49, 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 \[ -\frac{3 a^2}{b^3 \sqrt [3]{a+b x}}-\frac{3 a (a+b x)^{2/3}}{b^3}+\frac{3 (a+b x)^{5/3}}{5 b^3} \]
Antiderivative was successfully verified.
[In] Int[x^2/(a + b*x)^(4/3),x]
[Out]
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Rubi in Sympy [A] time = 7.86509, size = 46, normalized size = 0.94 \[ - \frac{3 a^{2}}{b^{3} \sqrt [3]{a + b x}} - \frac{3 a \left (a + b x\right )^{\frac{2}{3}}}{b^{3}} + \frac{3 \left (a + b x\right )^{\frac{5}{3}}}{5 b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2/(b*x+a)**(4/3),x)
[Out]
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Mathematica [A] time = 0.0215493, size = 34, normalized size = 0.69 \[ \frac{3 \left (-9 a^2-3 a b x+b^2 x^2\right )}{5 b^3 \sqrt [3]{a+b x}} \]
Antiderivative was successfully verified.
[In] Integrate[x^2/(a + b*x)^(4/3),x]
[Out]
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Maple [A] time = 0.007, size = 32, normalized size = 0.7 \[ -{\frac{-3\,{b}^{2}{x}^{2}+9\,abx+27\,{a}^{2}}{5\,{b}^{3}}{\frac{1}{\sqrt [3]{bx+a}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2/(b*x+a)^(4/3),x)
[Out]
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Maxima [A] time = 1.35337, size = 55, normalized size = 1.12 \[ \frac{3 \,{\left (b x + a\right )}^{\frac{5}{3}}}{5 \, b^{3}} - \frac{3 \,{\left (b x + a\right )}^{\frac{2}{3}} a}{b^{3}} - \frac{3 \, a^{2}}{{\left (b x + a\right )}^{\frac{1}{3}} b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(b*x + a)^(4/3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.203969, size = 41, normalized size = 0.84 \[ \frac{3 \,{\left (b^{2} x^{2} - 3 \, a b x - 9 \, a^{2}\right )}}{5 \,{\left (b x + a\right )}^{\frac{1}{3}} b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(b*x + a)^(4/3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 5.76842, size = 534, normalized size = 10.9 \[ - \frac{27 a^{\frac{29}{3}} \left (1 + \frac{b x}{a}\right )^{\frac{2}{3}}}{5 a^{8} b^{3} + 15 a^{7} b^{4} x + 15 a^{6} b^{5} x^{2} + 5 a^{5} b^{6} x^{3}} + \frac{27 a^{\frac{29}{3}}}{5 a^{8} b^{3} + 15 a^{7} b^{4} x + 15 a^{6} b^{5} x^{2} + 5 a^{5} b^{6} x^{3}} - \frac{63 a^{\frac{26}{3}} b x \left (1 + \frac{b x}{a}\right )^{\frac{2}{3}}}{5 a^{8} b^{3} + 15 a^{7} b^{4} x + 15 a^{6} b^{5} x^{2} + 5 a^{5} b^{6} x^{3}} + \frac{81 a^{\frac{26}{3}} b x}{5 a^{8} b^{3} + 15 a^{7} b^{4} x + 15 a^{6} b^{5} x^{2} + 5 a^{5} b^{6} x^{3}} - \frac{42 a^{\frac{23}{3}} b^{2} x^{2} \left (1 + \frac{b x}{a}\right )^{\frac{2}{3}}}{5 a^{8} b^{3} + 15 a^{7} b^{4} x + 15 a^{6} b^{5} x^{2} + 5 a^{5} b^{6} x^{3}} + \frac{81 a^{\frac{23}{3}} b^{2} x^{2}}{5 a^{8} b^{3} + 15 a^{7} b^{4} x + 15 a^{6} b^{5} x^{2} + 5 a^{5} b^{6} x^{3}} - \frac{3 a^{\frac{20}{3}} b^{3} x^{3} \left (1 + \frac{b x}{a}\right )^{\frac{2}{3}}}{5 a^{8} b^{3} + 15 a^{7} b^{4} x + 15 a^{6} b^{5} x^{2} + 5 a^{5} b^{6} x^{3}} + \frac{27 a^{\frac{20}{3}} b^{3} x^{3}}{5 a^{8} b^{3} + 15 a^{7} b^{4} x + 15 a^{6} b^{5} x^{2} + 5 a^{5} b^{6} x^{3}} + \frac{3 a^{\frac{17}{3}} b^{4} x^{4} \left (1 + \frac{b x}{a}\right )^{\frac{2}{3}}}{5 a^{8} b^{3} + 15 a^{7} b^{4} x + 15 a^{6} b^{5} x^{2} + 5 a^{5} b^{6} x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2/(b*x+a)**(4/3),x)
[Out]
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GIAC/XCAS [A] time = 0.215462, size = 62, normalized size = 1.27 \[ -\frac{3 \, a^{2}}{{\left (b x + a\right )}^{\frac{1}{3}} b^{3}} + \frac{3 \,{\left ({\left (b x + a\right )}^{\frac{5}{3}} b^{12} - 5 \,{\left (b x + a\right )}^{\frac{2}{3}} a b^{12}\right )}}{5 \, b^{15}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(b*x + a)^(4/3),x, algorithm="giac")
[Out]