Optimal. Leaf size=44 \[ \frac{4 b \sqrt [4]{a+b x^4}}{5 a^2 x}-\frac{\sqrt [4]{a+b x^4}}{5 a x^5} \]
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Rubi [A] time = 0.041665, antiderivative size = 44, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{4 b \sqrt [4]{a+b x^4}}{5 a^2 x}-\frac{\sqrt [4]{a+b x^4}}{5 a x^5} \]
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 = 4.24671, size = 36, normalized size = 0.82 \[ - \frac{\sqrt [4]{a + b x^{4}}}{5 a x^{5}} + \frac{4 b \sqrt [4]{a + b x^{4}}}{5 a^{2} x} \]
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 = 0.0225761, size = 29, normalized size = 0.66 \[ -\frac{\left (a-4 b x^4\right ) \sqrt [4]{a+b x^4}}{5 a^2 x^5} \]
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 = 26, 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 = 1.4426, size = 47, 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 = 0.237305, size = 36, normalized size = 0.82 \[ \frac{{\left (4 \, b x^{4} - a\right )}{\left (b x^{4} + a\right )}^{\frac{1}{4}}}{5 \, a^{2} x^{5}} \]
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 = 4.64174, size = 68, normalized size = 1.55 \[ - \frac{\sqrt [4]{b} \sqrt [4]{\frac{a}{b x^{4}} + 1} \Gamma \left (- \frac{5}{4}\right )}{16 a x^{4} \Gamma \left (\frac{3}{4}\right )} + \frac{b^{\frac{5}{4}} \sqrt [4]{\frac{a}{b x^{4}} + 1} \Gamma \left (- \frac{5}{4}\right )}{4 a^{2} \Gamma \left (\frac{3}{4}\right )} \]
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]