Optimal. Leaf size=71 \[ -\frac{32 b^2 \sqrt [4]{a-b x^4}}{45 a^3 x}-\frac{8 b \sqrt [4]{a-b x^4}}{45 a^2 x^5}-\frac{\sqrt [4]{a-b x^4}}{9 a x^9} \]
[Out]
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Rubi [A] time = 0.0696853, antiderivative size = 71, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ -\frac{32 b^2 \sqrt [4]{a-b x^4}}{45 a^3 x}-\frac{8 b \sqrt [4]{a-b x^4}}{45 a^2 x^5}-\frac{\sqrt [4]{a-b x^4}}{9 a x^9} \]
Antiderivative was successfully verified.
[In] Int[1/(x^10*(a - b*x^4)^(3/4)),x]
[Out]
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Rubi in Sympy [A] time = 7.69216, size = 61, normalized size = 0.86 \[ - \frac{\sqrt [4]{a - b x^{4}}}{9 a x^{9}} - \frac{8 b \sqrt [4]{a - b x^{4}}}{45 a^{2} x^{5}} - \frac{32 b^{2} \sqrt [4]{a - b x^{4}}}{45 a^{3} x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**10/(-b*x**4+a)**(3/4),x)
[Out]
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Mathematica [A] time = 0.0325752, size = 43, normalized size = 0.61 \[ -\frac{\sqrt [4]{a-b x^4} \left (5 a^2+8 a b x^4+32 b^2 x^8\right )}{45 a^3 x^9} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^10*(a - b*x^4)^(3/4)),x]
[Out]
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Maple [A] time = 0.006, size = 40, normalized size = 0.6 \[ -{\frac{32\,{b}^{2}{x}^{8}+8\,ab{x}^{4}+5\,{a}^{2}}{45\,{a}^{3}{x}^{9}}\sqrt [4]{-b{x}^{4}+a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^10/(-b*x^4+a)^(3/4),x)
[Out]
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Maxima [A] time = 1.44039, size = 74, normalized size = 1.04 \[ -\frac{\frac{45 \,{\left (-b x^{4} + a\right )}^{\frac{1}{4}} b^{2}}{x} + \frac{18 \,{\left (-b x^{4} + a\right )}^{\frac{5}{4}} b}{x^{5}} + \frac{5 \,{\left (-b x^{4} + a\right )}^{\frac{9}{4}}}{x^{9}}}{45 \, a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((-b*x^4 + a)^(3/4)*x^10),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.226916, size = 53, normalized size = 0.75 \[ -\frac{{\left (32 \, b^{2} x^{8} + 8 \, a b x^{4} + 5 \, a^{2}\right )}{\left (-b x^{4} + a\right )}^{\frac{1}{4}}}{45 \, a^{3} x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((-b*x^4 + a)^(3/4)*x^10),x, algorithm="fricas")
[Out]
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Sympy [A] time = 11.2171, size = 864, normalized size = 12.17 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**10/(-b*x**4+a)**(3/4),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (-b x^{4} + a\right )}^{\frac{3}{4}} x^{10}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((-b*x^4 + a)^(3/4)*x^10),x, algorithm="giac")
[Out]