Optimal. Leaf size=19 \[ -\frac{\left (a-b x^4\right )^{5/4}}{5 b} \]
[Out]
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Rubi [A] time = 0.0108756, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062 \[ -\frac{\left (a-b x^4\right )^{5/4}}{5 b} \]
Antiderivative was successfully verified.
[In] Int[x^3*(a - b*x^4)^(1/4),x]
[Out]
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Rubi in Sympy [A] time = 2.38956, size = 14, normalized size = 0.74 \[ - \frac{\left (a - b x^{4}\right )^{\frac{5}{4}}}{5 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3*(-b*x**4+a)**(1/4),x)
[Out]
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Mathematica [A] time = 0.0093243, size = 19, normalized size = 1. \[ -\frac{\left (a-b x^4\right )^{5/4}}{5 b} \]
Antiderivative was successfully verified.
[In] Integrate[x^3*(a - b*x^4)^(1/4),x]
[Out]
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Maple [A] time = 0.005, size = 16, normalized size = 0.8 \[ -{\frac{1}{5\,b} \left ( -b{x}^{4}+a \right ) ^{{\frac{5}{4}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3*(-b*x^4+a)^(1/4),x)
[Out]
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Maxima [A] time = 1.41999, size = 20, normalized size = 1.05 \[ -\frac{{\left (-b x^{4} + a\right )}^{\frac{5}{4}}}{5 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-b*x^4 + a)^(1/4)*x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.234918, size = 32, normalized size = 1.68 \[ \frac{{\left (b x^{4} - a\right )}{\left (-b x^{4} + a\right )}^{\frac{1}{4}}}{5 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-b*x^4 + a)^(1/4)*x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.39672, size = 39, normalized size = 2.05 \[ \begin{cases} - \frac{a \sqrt [4]{a - b x^{4}}}{5 b} + \frac{x^{4} \sqrt [4]{a - b x^{4}}}{5} & \text{for}\: b \neq 0 \\\frac{\sqrt [4]{a} x^{4}}{4} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3*(-b*x**4+a)**(1/4),x)
[Out]
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GIAC/XCAS [A] time = 0.253951, size = 20, normalized size = 1.05 \[ -\frac{{\left (-b x^{4} + a\right )}^{\frac{5}{4}}}{5 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-b*x^4 + a)^(1/4)*x^3,x, algorithm="giac")
[Out]