Optimal. Leaf size=44 \[ \frac{4 b \left (a+b x^4\right )^{7/4}}{77 a^2 x^7}-\frac{\left (a+b x^4\right )^{7/4}}{11 a x^{11}} \]
[Out]
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Rubi [A] time = 0.0415044, 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 \[ \frac{4 b \left (a+b x^4\right )^{7/4}}{77 a^2 x^7}-\frac{\left (a+b x^4\right )^{7/4}}{11 a x^{11}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^4)^(3/4)/x^12,x]
[Out]
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Rubi in Sympy [A] time = 4.24587, size = 37, normalized size = 0.84 \[ - \frac{\left (a + b x^{4}\right )^{\frac{7}{4}}}{11 a x^{11}} + \frac{4 b \left (a + b x^{4}\right )^{\frac{7}{4}}}{77 a^{2} x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**4+a)**(3/4)/x**12,x)
[Out]
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Mathematica [A] time = 0.0258143, size = 44, normalized size = 1. \[ \left (\frac{4 b^2}{77 a^2 x^3}-\frac{3 b}{77 a x^7}-\frac{1}{11 x^{11}}\right ) \left (a+b x^4\right )^{3/4} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^4)^(3/4)/x^12,x]
[Out]
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Maple [A] time = 0.007, size = 28, normalized size = 0.6 \[ -{\frac{-4\,b{x}^{4}+7\,a}{77\,{x}^{11}{a}^{2}} \left ( b{x}^{4}+a \right ) ^{{\frac{7}{4}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^4+a)^(3/4)/x^12,x)
[Out]
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Maxima [A] time = 1.43879, size = 47, normalized size = 1.07 \[ \frac{\frac{11 \,{\left (b x^{4} + a\right )}^{\frac{7}{4}} b}{x^{7}} - \frac{7 \,{\left (b x^{4} + a\right )}^{\frac{11}{4}}}{x^{11}}}{77 \, a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)^(3/4)/x^12,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.284959, size = 51, normalized size = 1.16 \[ \frac{{\left (4 \, b^{2} x^{8} - 3 \, a b x^{4} - 7 \, a^{2}\right )}{\left (b x^{4} + a\right )}^{\frac{3}{4}}}{77 \, a^{2} x^{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)^(3/4)/x^12,x, algorithm="fricas")
[Out]
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Sympy [A] time = 14.8968, size = 110, normalized size = 2.5 \[ - \frac{7 b^{\frac{3}{4}} \left (\frac{a}{b x^{4}} + 1\right )^{\frac{3}{4}} \Gamma \left (- \frac{11}{4}\right )}{16 x^{8} \Gamma \left (- \frac{3}{4}\right )} - \frac{3 b^{\frac{7}{4}} \left (\frac{a}{b x^{4}} + 1\right )^{\frac{3}{4}} \Gamma \left (- \frac{11}{4}\right )}{16 a x^{4} \Gamma \left (- \frac{3}{4}\right )} + \frac{b^{\frac{11}{4}} \left (\frac{a}{b x^{4}} + 1\right )^{\frac{3}{4}} \Gamma \left (- \frac{11}{4}\right )}{4 a^{2} \Gamma \left (- \frac{3}{4}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**4+a)**(3/4)/x**12,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (b x^{4} + a\right )}^{\frac{3}{4}}}{x^{12}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)^(3/4)/x^12,x, algorithm="giac")
[Out]