Optimal. Leaf size=46 \[ -\frac{4 b \sqrt [4]{a-b x^4}}{5 a^2 x}-\frac{\sqrt [4]{a-b x^4}}{5 a x^5} \]
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Rubi [A] time = 0.0439068, 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 \[ -\frac{4 b \sqrt [4]{a-b x^4}}{5 a^2 x}-\frac{\sqrt [4]{a-b x^4}}{5 a x^5} \]
Antiderivative was successfully verified.
[In] Int[1/(x^6*(a - b*x^4)^(3/4)),x]
[Out]
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Rubi in Sympy [A] time = 4.94272, size = 37, normalized size = 0.8 \[ - \frac{\sqrt [4]{a - b x^{4}}}{5 a x^{5}} - \frac{4 b \sqrt [4]{a - b x^{4}}}{5 a^{2} x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**6/(-b*x**4+a)**(3/4),x)
[Out]
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Mathematica [A] time = 0.0245878, size = 30, normalized size = 0.65 \[ -\frac{\sqrt [4]{a-b x^4} \left (a+4 b x^4\right )}{5 a^2 x^5} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^6*(a - b*x^4)^(3/4)),x]
[Out]
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Maple [A] time = 0.007, size = 27, normalized size = 0.6 \[ -{\frac{4\,b{x}^{4}+a}{5\,{x}^{5}{a}^{2}}\sqrt [4]{-b{x}^{4}+a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^6/(-b*x^4+a)^(3/4),x)
[Out]
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Maxima [A] time = 1.44282, size = 49, normalized size = 1.07 \[ -\frac{\frac{5 \,{\left (-b x^{4} + a\right )}^{\frac{1}{4}} b}{x} + \frac{{\left (-b x^{4} + a\right )}^{\frac{5}{4}}}{x^{5}}}{5 \, a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((-b*x^4 + a)^(3/4)*x^6),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.225262, size = 35, normalized size = 0.76 \[ -\frac{{\left (4 \, b x^{4} + a\right )}{\left (-b x^{4} + a\right )}^{\frac{1}{4}}}{5 \, a^{2} x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((-b*x^4 + a)^(3/4)*x^6),x, algorithm="fricas")
[Out]
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Sympy [A] time = 5.14577, size = 286, normalized size = 6.22 \[ \begin{cases} - \frac{\sqrt [4]{b} \sqrt [4]{\frac{a}{b x^{4}} - 1} \Gamma \left (- \frac{5}{4}\right )}{16 a x^{4} \Gamma \left (\frac{3}{4}\right )} - \frac{b^{\frac{5}{4}} \sqrt [4]{\frac{a}{b x^{4}} - 1} \Gamma \left (- \frac{5}{4}\right )}{4 a^{2} \Gamma \left (\frac{3}{4}\right )} & \text{for}\: \left |{\frac{a}{b x^{4}}}\right | > 1 \\- \frac{a^{2} b^{\frac{5}{4}} \sqrt [4]{- \frac{a}{b x^{4}} + 1} e^{\frac{5 i \pi }{4}} \Gamma \left (- \frac{5}{4}\right )}{- 16 a^{3} b x^{4} \Gamma \left (\frac{3}{4}\right ) + 16 a^{2} b^{2} x^{8} \Gamma \left (\frac{3}{4}\right )} - \frac{3 a b^{\frac{9}{4}} x^{4} \sqrt [4]{- \frac{a}{b x^{4}} + 1} e^{\frac{5 i \pi }{4}} \Gamma \left (- \frac{5}{4}\right )}{- 16 a^{3} b x^{4} \Gamma \left (\frac{3}{4}\right ) + 16 a^{2} b^{2} x^{8} \Gamma \left (\frac{3}{4}\right )} + \frac{4 b^{\frac{13}{4}} x^{8} \sqrt [4]{- \frac{a}{b x^{4}} + 1} e^{\frac{5 i \pi }{4}} \Gamma \left (- \frac{5}{4}\right )}{- 16 a^{3} b x^{4} \Gamma \left (\frac{3}{4}\right ) + 16 a^{2} b^{2} x^{8} \Gamma \left (\frac{3}{4}\right )} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**6/(-b*x**4+a)**(3/4),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (-b x^{4} + a\right )}^{\frac{3}{4}} x^{6}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((-b*x^4 + a)^(3/4)*x^6),x, algorithm="giac")
[Out]