Optimal. Leaf size=68 \[ -\frac{32 b^2 \left (a+b x^4\right )^{3/4}}{231 a^3 x^3}+\frac{8 b \left (a+b x^4\right )^{3/4}}{77 a^2 x^7}-\frac{\left (a+b x^4\right )^{3/4}}{11 a x^{11}} \]
[Out]
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Rubi [A] time = 0.0637947, antiderivative size = 68, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ -\frac{32 b^2 \left (a+b x^4\right )^{3/4}}{231 a^3 x^3}+\frac{8 b \left (a+b x^4\right )^{3/4}}{77 a^2 x^7}-\frac{\left (a+b x^4\right )^{3/4}}{11 a x^{11}} \]
Antiderivative was successfully verified.
[In] Int[1/(x^12*(a + b*x^4)^(1/4)),x]
[Out]
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Rubi in Sympy [A] time = 6.69093, size = 61, normalized size = 0.9 \[ - \frac{\left (a + b x^{4}\right )^{\frac{3}{4}}}{11 a x^{11}} + \frac{8 b \left (a + b x^{4}\right )^{\frac{3}{4}}}{77 a^{2} x^{7}} - \frac{32 b^{2} \left (a + b x^{4}\right )^{\frac{3}{4}}}{231 a^{3} x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**12/(b*x**4+a)**(1/4),x)
[Out]
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Mathematica [A] time = 0.0339857, size = 42, normalized size = 0.62 \[ -\frac{\left (a+b x^4\right )^{3/4} \left (21 a^2-24 a b x^4+32 b^2 x^8\right )}{231 a^3 x^{11}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^12*(a + b*x^4)^(1/4)),x]
[Out]
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Maple [A] time = 0.007, size = 39, normalized size = 0.6 \[ -{\frac{32\,{b}^{2}{x}^{8}-24\,ab{x}^{4}+21\,{a}^{2}}{231\,{x}^{11}{a}^{3}} \left ( b{x}^{4}+a \right ) ^{{\frac{3}{4}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^12/(b*x^4+a)^(1/4),x)
[Out]
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Maxima [A] time = 1.41631, size = 70, normalized size = 1.03 \[ -\frac{\frac{77 \,{\left (b x^{4} + a\right )}^{\frac{3}{4}} b^{2}}{x^{3}} - \frac{66 \,{\left (b x^{4} + a\right )}^{\frac{7}{4}} b}{x^{7}} + \frac{21 \,{\left (b x^{4} + a\right )}^{\frac{11}{4}}}{x^{11}}}{231 \, a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^4 + a)^(1/4)*x^12),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.244139, size = 51, normalized size = 0.75 \[ -\frac{{\left (32 \, b^{2} x^{8} - 24 \, a b x^{4} + 21 \, a^{2}\right )}{\left (b x^{4} + a\right )}^{\frac{3}{4}}}{231 \, a^{3} x^{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^4 + a)^(1/4)*x^12),x, algorithm="fricas")
[Out]
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Sympy [A] time = 11.5983, size = 406, normalized size = 5.97 \[ \frac{21 a^{4} b^{\frac{19}{4}} \left (\frac{a}{b x^{4}} + 1\right )^{\frac{3}{4}} \Gamma \left (- \frac{11}{4}\right )}{64 a^{5} b^{4} x^{8} \Gamma \left (\frac{1}{4}\right ) + 128 a^{4} b^{5} x^{12} \Gamma \left (\frac{1}{4}\right ) + 64 a^{3} b^{6} x^{16} \Gamma \left (\frac{1}{4}\right )} + \frac{18 a^{3} b^{\frac{23}{4}} x^{4} \left (\frac{a}{b x^{4}} + 1\right )^{\frac{3}{4}} \Gamma \left (- \frac{11}{4}\right )}{64 a^{5} b^{4} x^{8} \Gamma \left (\frac{1}{4}\right ) + 128 a^{4} b^{5} x^{12} \Gamma \left (\frac{1}{4}\right ) + 64 a^{3} b^{6} x^{16} \Gamma \left (\frac{1}{4}\right )} + \frac{5 a^{2} b^{\frac{27}{4}} x^{8} \left (\frac{a}{b x^{4}} + 1\right )^{\frac{3}{4}} \Gamma \left (- \frac{11}{4}\right )}{64 a^{5} b^{4} x^{8} \Gamma \left (\frac{1}{4}\right ) + 128 a^{4} b^{5} x^{12} \Gamma \left (\frac{1}{4}\right ) + 64 a^{3} b^{6} x^{16} \Gamma \left (\frac{1}{4}\right )} + \frac{40 a b^{\frac{31}{4}} x^{12} \left (\frac{a}{b x^{4}} + 1\right )^{\frac{3}{4}} \Gamma \left (- \frac{11}{4}\right )}{64 a^{5} b^{4} x^{8} \Gamma \left (\frac{1}{4}\right ) + 128 a^{4} b^{5} x^{12} \Gamma \left (\frac{1}{4}\right ) + 64 a^{3} b^{6} x^{16} \Gamma \left (\frac{1}{4}\right )} + \frac{32 b^{\frac{35}{4}} x^{16} \left (\frac{a}{b x^{4}} + 1\right )^{\frac{3}{4}} \Gamma \left (- \frac{11}{4}\right )}{64 a^{5} b^{4} x^{8} \Gamma \left (\frac{1}{4}\right ) + 128 a^{4} b^{5} x^{12} \Gamma \left (\frac{1}{4}\right ) + 64 a^{3} b^{6} x^{16} \Gamma \left (\frac{1}{4}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**12/(b*x**4+a)**(1/4),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (b x^{4} + a\right )}^{\frac{1}{4}} x^{12}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^4 + a)^(1/4)*x^12),x, algorithm="giac")
[Out]