Optimal. Leaf size=70 \[ \frac{3 a^3}{b^4 \sqrt [3]{a+b x}}+\frac{9 a^2 (a+b x)^{2/3}}{2 b^4}-\frac{9 a (a+b x)^{5/3}}{5 b^4}+\frac{3 (a+b x)^{8/3}}{8 b^4} \]
[Out]
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Rubi [A] time = 0.0516654, antiderivative size = 70, 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 \[ \frac{3 a^3}{b^4 \sqrt [3]{a+b x}}+\frac{9 a^2 (a+b x)^{2/3}}{2 b^4}-\frac{9 a (a+b x)^{5/3}}{5 b^4}+\frac{3 (a+b x)^{8/3}}{8 b^4} \]
Antiderivative was successfully verified.
[In] Int[x^3/(a + b*x)^(4/3),x]
[Out]
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Rubi in Sympy [A] time = 10.9331, size = 66, normalized size = 0.94 \[ \frac{3 a^{3}}{b^{4} \sqrt [3]{a + b x}} + \frac{9 a^{2} \left (a + b x\right )^{\frac{2}{3}}}{2 b^{4}} - \frac{9 a \left (a + b x\right )^{\frac{5}{3}}}{5 b^{4}} + \frac{3 \left (a + b x\right )^{\frac{8}{3}}}{8 b^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3/(b*x+a)**(4/3),x)
[Out]
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Mathematica [A] time = 0.0264444, size = 46, normalized size = 0.66 \[ \frac{3 \left (81 a^3+27 a^2 b x-9 a b^2 x^2+5 b^3 x^3\right )}{40 b^4 \sqrt [3]{a+b x}} \]
Antiderivative was successfully verified.
[In] Integrate[x^3/(a + b*x)^(4/3),x]
[Out]
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Maple [A] time = 0.007, size = 43, normalized size = 0.6 \[{\frac{15\,{b}^{3}{x}^{3}-27\,a{b}^{2}{x}^{2}+81\,{a}^{2}bx+243\,{a}^{3}}{40\,{b}^{4}}{\frac{1}{\sqrt [3]{bx+a}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3/(b*x+a)^(4/3),x)
[Out]
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Maxima [A] time = 1.32441, size = 76, normalized size = 1.09 \[ \frac{3 \,{\left (b x + a\right )}^{\frac{8}{3}}}{8 \, b^{4}} - \frac{9 \,{\left (b x + a\right )}^{\frac{5}{3}} a}{5 \, b^{4}} + \frac{9 \,{\left (b x + a\right )}^{\frac{2}{3}} a^{2}}{2 \, b^{4}} + \frac{3 \, a^{3}}{{\left (b x + a\right )}^{\frac{1}{3}} b^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(b*x + a)^(4/3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.207542, size = 57, normalized size = 0.81 \[ \frac{3 \,{\left (5 \, b^{3} x^{3} - 9 \, a b^{2} x^{2} + 27 \, a^{2} b x + 81 \, a^{3}\right )}}{40 \,{\left (b x + a\right )}^{\frac{1}{3}} b^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(b*x + a)^(4/3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 8.7926, size = 1538, normalized size = 21.97 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3/(b*x+a)**(4/3),x)
[Out]
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GIAC/XCAS [A] time = 0.2417, size = 84, normalized size = 1.2 \[ \frac{3 \, a^{3}}{{\left (b x + a\right )}^{\frac{1}{3}} b^{4}} + \frac{3 \,{\left (5 \,{\left (b x + a\right )}^{\frac{8}{3}} b^{28} - 24 \,{\left (b x + a\right )}^{\frac{5}{3}} a b^{28} + 60 \,{\left (b x + a\right )}^{\frac{2}{3}} a^{2} b^{28}\right )}}{40 \, b^{32}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(b*x + a)^(4/3),x, algorithm="giac")
[Out]