Optimal. Leaf size=18 \[ \frac{\left (a+b x^4\right )^{9/4}}{9 b} \]
[Out]
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Rubi [A] time = 0.0108455, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ \frac{\left (a+b x^4\right )^{9/4}}{9 b} \]
Antiderivative was successfully verified.
[In] Int[x^3*(a + b*x^4)^(5/4),x]
[Out]
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Rubi in Sympy [A] time = 2.12816, size = 12, normalized size = 0.67 \[ \frac{\left (a + b x^{4}\right )^{\frac{9}{4}}}{9 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3*(b*x**4+a)**(5/4),x)
[Out]
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Mathematica [A] time = 0.00843763, size = 18, normalized size = 1. \[ \frac{\left (a+b x^4\right )^{9/4}}{9 b} \]
Antiderivative was successfully verified.
[In] Integrate[x^3*(a + b*x^4)^(5/4),x]
[Out]
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Maple [A] time = 0.007, size = 15, normalized size = 0.8 \[{\frac{1}{9\,b} \left ( b{x}^{4}+a \right ) ^{{\frac{9}{4}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3*(b*x^4+a)^(5/4),x)
[Out]
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Maxima [A] time = 1.43556, size = 19, normalized size = 1.06 \[ \frac{{\left (b x^{4} + a\right )}^{\frac{9}{4}}}{9 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)^(5/4)*x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.282678, size = 43, normalized size = 2.39 \[ \frac{{\left (b^{2} x^{8} + 2 \, a b x^{4} + a^{2}\right )}{\left (b x^{4} + a\right )}^{\frac{1}{4}}}{9 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)^(5/4)*x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 14.3177, size = 61, normalized size = 3.39 \[ \begin{cases} \frac{a^{2} \sqrt [4]{a + b x^{4}}}{9 b} + \frac{2 a x^{4} \sqrt [4]{a + b x^{4}}}{9} + \frac{b x^{8} \sqrt [4]{a + b x^{4}}}{9} & \text{for}\: b \neq 0 \\\frac{a^{\frac{5}{4}} x^{4}}{4} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3*(b*x**4+a)**(5/4),x)
[Out]
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GIAC/XCAS [A] time = 0.215666, size = 19, normalized size = 1.06 \[ \frac{{\left (b x^{4} + a\right )}^{\frac{9}{4}}}{9 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)^(5/4)*x^3,x, algorithm="giac")
[Out]