Optimal. Leaf size=46 \[ -\frac{4 b \left (a-b x^4\right )^{5/4}}{45 a^2 x^5}-\frac{\left (a-b x^4\right )^{5/4}}{9 a x^9} \]
[Out]
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Rubi [A] time = 0.0431228, antiderivative size = 46, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ -\frac{4 b \left (a-b x^4\right )^{5/4}}{45 a^2 x^5}-\frac{\left (a-b x^4\right )^{5/4}}{9 a x^9} \]
Antiderivative was successfully verified.
[In] Int[(a - b*x^4)^(1/4)/x^10,x]
[Out]
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Rubi in Sympy [A] time = 4.71999, size = 39, normalized size = 0.85 \[ - \frac{\left (a - b x^{4}\right )^{\frac{5}{4}}}{9 a x^{9}} - \frac{4 b \left (a - b x^{4}\right )^{\frac{5}{4}}}{45 a^{2} x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((-b*x**4+a)**(1/4)/x**10,x)
[Out]
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Mathematica [A] time = 0.0263842, size = 42, normalized size = 0.91 \[ \frac{\sqrt [4]{a-b x^4} \left (-5 a^2+a b x^4+4 b^2 x^8\right )}{45 a^2 x^9} \]
Antiderivative was successfully verified.
[In] Integrate[(a - b*x^4)^(1/4)/x^10,x]
[Out]
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Maple [A] time = 0.007, size = 29, normalized size = 0.6 \[ -{\frac{4\,b{x}^{4}+5\,a}{45\,{a}^{2}{x}^{9}} \left ( -b{x}^{4}+a \right ) ^{{\frac{5}{4}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((-b*x^4+a)^(1/4)/x^10,x)
[Out]
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Maxima [A] time = 1.43261, size = 50, normalized size = 1.09 \[ -\frac{\frac{9 \,{\left (-b x^{4} + a\right )}^{\frac{5}{4}} b}{x^{5}} + \frac{5 \,{\left (-b x^{4} + a\right )}^{\frac{9}{4}}}{x^{9}}}{45 \, a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-b*x^4 + a)^(1/4)/x^10,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.249515, size = 51, normalized size = 1.11 \[ \frac{{\left (4 \, b^{2} x^{8} + a b x^{4} - 5 \, a^{2}\right )}{\left (-b x^{4} + a\right )}^{\frac{1}{4}}}{45 \, a^{2} x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-b*x^4 + a)^(1/4)/x^10,x, algorithm="fricas")
[Out]
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Sympy [A] time = 7.63955, size = 413, normalized size = 8.98 \[ \begin{cases} - \frac{5 \sqrt [4]{b} \sqrt [4]{\frac{a}{b x^{4}} - 1} \Gamma \left (- \frac{9}{4}\right )}{16 x^{8} \Gamma \left (- \frac{1}{4}\right )} + \frac{b^{\frac{5}{4}} \sqrt [4]{\frac{a}{b x^{4}} - 1} \Gamma \left (- \frac{9}{4}\right )}{16 a x^{4} \Gamma \left (- \frac{1}{4}\right )} + \frac{b^{\frac{9}{4}} \sqrt [4]{\frac{a}{b x^{4}} - 1} \Gamma \left (- \frac{9}{4}\right )}{4 a^{2} \Gamma \left (- \frac{1}{4}\right )} & \text{for}\: \left |{\frac{a}{b x^{4}}}\right | > 1 \\\frac{5 a^{3} b^{\frac{5}{4}} \sqrt [4]{- \frac{a}{b x^{4}} + 1} e^{\frac{17 i \pi }{4}} \Gamma \left (- \frac{9}{4}\right )}{x^{4} \left (- 16 a^{3} b x^{4} \Gamma \left (- \frac{1}{4}\right ) + 16 a^{2} b^{2} x^{8} \Gamma \left (- \frac{1}{4}\right )\right )} - \frac{6 a^{2} b^{\frac{9}{4}} \sqrt [4]{- \frac{a}{b x^{4}} + 1} e^{\frac{17 i \pi }{4}} \Gamma \left (- \frac{9}{4}\right )}{- 16 a^{3} b x^{4} \Gamma \left (- \frac{1}{4}\right ) + 16 a^{2} b^{2} x^{8} \Gamma \left (- \frac{1}{4}\right )} - \frac{3 a b^{\frac{13}{4}} x^{4} \sqrt [4]{- \frac{a}{b x^{4}} + 1} e^{\frac{17 i \pi }{4}} \Gamma \left (- \frac{9}{4}\right )}{- 16 a^{3} b x^{4} \Gamma \left (- \frac{1}{4}\right ) + 16 a^{2} b^{2} x^{8} \Gamma \left (- \frac{1}{4}\right )} + \frac{4 b^{\frac{17}{4}} x^{8} \sqrt [4]{- \frac{a}{b x^{4}} + 1} e^{\frac{17 i \pi }{4}} \Gamma \left (- \frac{9}{4}\right )}{- 16 a^{3} b x^{4} \Gamma \left (- \frac{1}{4}\right ) + 16 a^{2} b^{2} x^{8} \Gamma \left (- \frac{1}{4}\right )} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-b*x**4+a)**(1/4)/x**10,x)
[Out]
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GIAC/XCAS [A] time = 0.247327, size = 85, normalized size = 1.85 \[ \frac{\frac{9 \,{\left (-b x^{4} + a\right )}^{\frac{1}{4}}{\left (b - \frac{a}{x^{4}}\right )} b}{x} - \frac{5 \,{\left (b^{2} x^{8} - 2 \, a b x^{4} + a^{2}\right )}{\left (-b x^{4} + a\right )}^{\frac{1}{4}}}{x^{9}}}{45 \, a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-b*x^4 + a)^(1/4)/x^10,x, algorithm="giac")
[Out]