Optimal. Leaf size=90 \[ -\frac{128 b^3 x}{77 a^4 \sqrt [4]{a+b x^4}}-\frac{32 b^2}{77 a^3 x^3 \sqrt [4]{a+b x^4}}+\frac{12 b}{77 a^2 x^7 \sqrt [4]{a+b x^4}}-\frac{1}{11 a x^{11} \sqrt [4]{a+b x^4}} \]
[Out]
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Rubi [A] time = 0.0822382, antiderivative size = 90, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ -\frac{128 b^3 x}{77 a^4 \sqrt [4]{a+b x^4}}-\frac{32 b^2}{77 a^3 x^3 \sqrt [4]{a+b x^4}}+\frac{12 b}{77 a^2 x^7 \sqrt [4]{a+b x^4}}-\frac{1}{11 a x^{11} \sqrt [4]{a+b x^4}} \]
Antiderivative was successfully verified.
[In] Int[1/(x^12*(a + b*x^4)^(5/4)),x]
[Out]
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Rubi in Sympy [A] time = 8.99094, size = 85, normalized size = 0.94 \[ - \frac{1}{11 a x^{11} \sqrt [4]{a + b x^{4}}} + \frac{12 b}{77 a^{2} x^{7} \sqrt [4]{a + b x^{4}}} - \frac{32 b^{2}}{77 a^{3} x^{3} \sqrt [4]{a + b x^{4}}} - \frac{128 b^{3} x}{77 a^{4} \sqrt [4]{a + b x^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**12/(b*x**4+a)**(5/4),x)
[Out]
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Mathematica [A] time = 0.0487353, size = 53, normalized size = 0.59 \[ -\frac{7 a^3-12 a^2 b x^4+32 a b^2 x^8+128 b^3 x^{12}}{77 a^4 x^{11} \sqrt [4]{a+b x^4}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^12*(a + b*x^4)^(5/4)),x]
[Out]
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Maple [A] time = 0.009, size = 50, normalized size = 0.6 \[ -{\frac{128\,{b}^{3}{x}^{12}+32\,a{b}^{2}{x}^{8}-12\,{a}^{2}b{x}^{4}+7\,{a}^{3}}{77\,{x}^{11}{a}^{4}}{\frac{1}{\sqrt [4]{b{x}^{4}+a}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^12/(b*x^4+a)^(5/4),x)
[Out]
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Maxima [A] time = 1.44094, size = 96, normalized size = 1.07 \[ -\frac{b^{3} x}{{\left (b x^{4} + a\right )}^{\frac{1}{4}} a^{4}} - \frac{\frac{77 \,{\left (b x^{4} + a\right )}^{\frac{3}{4}} b^{2}}{x^{3}} - \frac{33 \,{\left (b x^{4} + a\right )}^{\frac{7}{4}} b}{x^{7}} + \frac{7 \,{\left (b x^{4} + a\right )}^{\frac{11}{4}}}{x^{11}}}{77 \, a^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^4 + a)^(5/4)*x^12),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.250339, size = 82, normalized size = 0.91 \[ -\frac{{\left (128 \, b^{3} x^{12} + 32 \, a b^{2} x^{8} - 12 \, a^{2} b x^{4} + 7 \, a^{3}\right )}{\left (b x^{4} + a\right )}^{\frac{3}{4}}}{77 \,{\left (a^{4} b x^{15} + a^{5} x^{11}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^4 + a)^(5/4)*x^12),x, algorithm="fricas")
[Out]
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Sympy [A] time = 23.1003, size = 592, normalized size = 6.58 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**12/(b*x**4+a)**(5/4),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (b x^{4} + a\right )}^{\frac{5}{4}} x^{12}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^4 + a)^(5/4)*x^12),x, algorithm="giac")
[Out]