Optimal. Leaf size=21 \[ -\frac{\left (a+b x^4\right )^{7/4}}{7 a x^7} \]
[Out]
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Rubi [A] time = 0.0197478, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ -\frac{\left (a+b x^4\right )^{7/4}}{7 a x^7} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^4)^(3/4)/x^8,x]
[Out]
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Rubi in Sympy [A] time = 2.67817, size = 17, normalized size = 0.81 \[ - \frac{\left (a + b x^{4}\right )^{\frac{7}{4}}}{7 a x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**4+a)**(3/4)/x**8,x)
[Out]
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Mathematica [A] time = 0.0177987, size = 21, normalized size = 1. \[ -\frac{\left (a+b x^4\right )^{7/4}}{7 a x^7} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^4)^(3/4)/x^8,x]
[Out]
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Maple [A] time = 0.006, size = 18, normalized size = 0.9 \[ -{\frac{1}{7\,a{x}^{7}} \left ( b{x}^{4}+a \right ) ^{{\frac{7}{4}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^4+a)^(3/4)/x^8,x)
[Out]
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Maxima [A] time = 1.44183, size = 23, normalized size = 1.1 \[ -\frac{{\left (b x^{4} + a\right )}^{\frac{7}{4}}}{7 \, a x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)^(3/4)/x^8,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.341981, size = 23, normalized size = 1.1 \[ -\frac{{\left (b x^{4} + a\right )}^{\frac{7}{4}}}{7 \, a x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)^(3/4)/x^8,x, algorithm="fricas")
[Out]
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Sympy [A] time = 6.71518, size = 68, normalized size = 3.24 \[ \frac{b^{\frac{3}{4}} \left (\frac{a}{b x^{4}} + 1\right )^{\frac{3}{4}} \Gamma \left (- \frac{7}{4}\right )}{4 x^{4} \Gamma \left (- \frac{3}{4}\right )} + \frac{b^{\frac{7}{4}} \left (\frac{a}{b x^{4}} + 1\right )^{\frac{3}{4}} \Gamma \left (- \frac{7}{4}\right )}{4 a \Gamma \left (- \frac{3}{4}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**4+a)**(3/4)/x**8,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (b x^{4} + a\right )}^{\frac{3}{4}}}{x^{8}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)^(3/4)/x^8,x, algorithm="giac")
[Out]