Optimal. Leaf size=19 \[ -\frac{\sqrt [4]{a+b x^4}}{a x} \]
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Rubi [A] time = 0.0203061, antiderivative size = 19, 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 \[ -\frac{\sqrt [4]{a+b x^4}}{a x} \]
Antiderivative was successfully verified.
[In] Int[1/(x^2*(a + b*x^4)^(3/4)),x]
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Rubi in Sympy [A] time = 2.66739, size = 14, normalized size = 0.74 \[ - \frac{\sqrt [4]{a + b x^{4}}}{a x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**2/(b*x**4+a)**(3/4),x)
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Mathematica [A] time = 0.0156404, size = 19, normalized size = 1. \[ -\frac{\sqrt [4]{a+b x^4}}{a x} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^2*(a + b*x^4)^(3/4)),x]
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Maple [A] time = 0.006, size = 18, normalized size = 1. \[ -{\frac{1}{ax}\sqrt [4]{b{x}^{4}+a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^2/(b*x^4+a)^(3/4),x)
[Out]
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Maxima [A] time = 1.43666, size = 23, normalized size = 1.21 \[ -\frac{{\left (b x^{4} + a\right )}^{\frac{1}{4}}}{a x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^4 + a)^(3/4)*x^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.239482, size = 23, normalized size = 1.21 \[ -\frac{{\left (b x^{4} + a\right )}^{\frac{1}{4}}}{a x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^4 + a)^(3/4)*x^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.41035, size = 31, normalized size = 1.63 \[ \frac{\sqrt [4]{b} \sqrt [4]{\frac{a}{b x^{4}} + 1} \Gamma \left (- \frac{1}{4}\right )}{4 a \Gamma \left (\frac{3}{4}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**2/(b*x**4+a)**(3/4),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (b x^{4} + a\right )}^{\frac{3}{4}} x^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^4 + a)^(3/4)*x^2),x, algorithm="giac")
[Out]