Optimal. Leaf size=71 \[ -\frac{32 b^2 \left (a-b x^4\right )^{5/4}}{585 a^3 x^5}-\frac{8 b \left (a-b x^4\right )^{5/4}}{117 a^2 x^9}-\frac{\left (a-b x^4\right )^{5/4}}{13 a x^{13}} \]
[Out]
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Rubi [A] time = 0.0672735, antiderivative size = 71, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ -\frac{32 b^2 \left (a-b x^4\right )^{5/4}}{585 a^3 x^5}-\frac{8 b \left (a-b x^4\right )^{5/4}}{117 a^2 x^9}-\frac{\left (a-b x^4\right )^{5/4}}{13 a x^{13}} \]
Antiderivative was successfully verified.
[In] Int[(a - b*x^4)^(1/4)/x^14,x]
[Out]
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Rubi in Sympy [A] time = 7.34424, size = 63, normalized size = 0.89 \[ - \frac{\left (a - b x^{4}\right )^{\frac{5}{4}}}{13 a x^{13}} - \frac{8 b \left (a - b x^{4}\right )^{\frac{5}{4}}}{117 a^{2} x^{9}} - \frac{32 b^{2} \left (a - b x^{4}\right )^{\frac{5}{4}}}{585 a^{3} x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((-b*x**4+a)**(1/4)/x**14,x)
[Out]
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Mathematica [A] time = 0.0348209, size = 54, normalized size = 0.76 \[ \frac{\sqrt [4]{a-b x^4} \left (-45 a^3+5 a^2 b x^4+8 a b^2 x^8+32 b^3 x^{12}\right )}{585 a^3 x^{13}} \]
Antiderivative was successfully verified.
[In] Integrate[(a - b*x^4)^(1/4)/x^14,x]
[Out]
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Maple [A] time = 0.008, size = 40, normalized size = 0.6 \[ -{\frac{32\,{b}^{2}{x}^{8}+40\,ab{x}^{4}+45\,{a}^{2}}{585\,{x}^{13}{a}^{3}} \left ( -b{x}^{4}+a \right ) ^{{\frac{5}{4}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((-b*x^4+a)^(1/4)/x^14,x)
[Out]
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Maxima [A] time = 1.41353, size = 74, normalized size = 1.04 \[ -\frac{\frac{117 \,{\left (-b x^{4} + a\right )}^{\frac{5}{4}} b^{2}}{x^{5}} + \frac{130 \,{\left (-b x^{4} + a\right )}^{\frac{9}{4}} b}{x^{9}} + \frac{45 \,{\left (-b x^{4} + a\right )}^{\frac{13}{4}}}{x^{13}}}{585 \, a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-b*x^4 + a)^(1/4)/x^14,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.236575, size = 68, normalized size = 0.96 \[ \frac{{\left (32 \, b^{3} x^{12} + 8 \, a b^{2} x^{8} + 5 \, a^{2} b x^{4} - 45 \, a^{3}\right )}{\left (-b x^{4} + a\right )}^{\frac{1}{4}}}{585 \, a^{3} x^{13}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-b*x^4 + a)^(1/4)/x^14,x, algorithm="fricas")
[Out]
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Sympy [A] time = 16.5758, size = 1100, normalized size = 15.49 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-b*x**4+a)**(1/4)/x**14,x)
[Out]
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GIAC/XCAS [A] time = 0.258182, size = 151, normalized size = 2.13 \[ \frac{\frac{117 \,{\left (-b x^{4} + a\right )}^{\frac{1}{4}}{\left (b - \frac{a}{x^{4}}\right )} b^{2}}{x} - \frac{130 \,{\left (b^{2} x^{8} - 2 \, a b x^{4} + a^{2}\right )}{\left (-b x^{4} + a\right )}^{\frac{1}{4}} b}{x^{9}} + \frac{45 \,{\left (b^{3} x^{12} - 3 \, a b^{2} x^{8} + 3 \, a^{2} b x^{4} - a^{3}\right )}{\left (-b x^{4} + a\right )}^{\frac{1}{4}}}{x^{13}}}{585 \, a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-b*x^4 + a)^(1/4)/x^14,x, algorithm="giac")
[Out]