Optimal. Leaf size=59 \[ \frac{a^2 \left (a+b x^4\right )^{3/4}}{3 b^3}+\frac{\left (a+b x^4\right )^{11/4}}{11 b^3}-\frac{2 a \left (a+b x^4\right )^{7/4}}{7 b^3} \]
[Out]
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Rubi [A] time = 0.0859798, antiderivative size = 59, 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 \[ \frac{a^2 \left (a+b x^4\right )^{3/4}}{3 b^3}+\frac{\left (a+b x^4\right )^{11/4}}{11 b^3}-\frac{2 a \left (a+b x^4\right )^{7/4}}{7 b^3} \]
Antiderivative was successfully verified.
[In] Int[x^11/(a + b*x^4)^(1/4),x]
[Out]
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Rubi in Sympy [A] time = 10.5001, size = 51, normalized size = 0.86 \[ \frac{a^{2} \left (a + b x^{4}\right )^{\frac{3}{4}}}{3 b^{3}} - \frac{2 a \left (a + b x^{4}\right )^{\frac{7}{4}}}{7 b^{3}} + \frac{\left (a + b x^{4}\right )^{\frac{11}{4}}}{11 b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**11/(b*x**4+a)**(1/4),x)
[Out]
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Mathematica [A] time = 0.0299792, size = 39, normalized size = 0.66 \[ \frac{\left (a+b x^4\right )^{3/4} \left (32 a^2-24 a b x^4+21 b^2 x^8\right )}{231 b^3} \]
Antiderivative was successfully verified.
[In] Integrate[x^11/(a + b*x^4)^(1/4),x]
[Out]
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Maple [A] time = 0.009, size = 36, normalized size = 0.6 \[{\frac{21\,{b}^{2}{x}^{8}-24\,ab{x}^{4}+32\,{a}^{2}}{231\,{b}^{3}} \left ( b{x}^{4}+a \right ) ^{{\frac{3}{4}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^11/(b*x^4+a)^(1/4),x)
[Out]
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Maxima [A] time = 1.44959, size = 63, normalized size = 1.07 \[ \frac{{\left (b x^{4} + a\right )}^{\frac{11}{4}}}{11 \, b^{3}} - \frac{2 \,{\left (b x^{4} + a\right )}^{\frac{7}{4}} a}{7 \, b^{3}} + \frac{{\left (b x^{4} + a\right )}^{\frac{3}{4}} a^{2}}{3 \, b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/(b*x^4 + a)^(1/4),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.262473, size = 47, normalized size = 0.8 \[ \frac{{\left (21 \, b^{2} x^{8} - 24 \, a b x^{4} + 32 \, a^{2}\right )}{\left (b x^{4} + a\right )}^{\frac{3}{4}}}{231 \, b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/(b*x^4 + a)^(1/4),x, algorithm="fricas")
[Out]
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Sympy [A] time = 10.8317, size = 68, normalized size = 1.15 \[ \begin{cases} \frac{32 a^{2} \left (a + b x^{4}\right )^{\frac{3}{4}}}{231 b^{3}} - \frac{8 a x^{4} \left (a + b x^{4}\right )^{\frac{3}{4}}}{77 b^{2}} + \frac{x^{8} \left (a + b x^{4}\right )^{\frac{3}{4}}}{11 b} & \text{for}\: b \neq 0 \\\frac{x^{12}}{12 \sqrt [4]{a}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**11/(b*x**4+a)**(1/4),x)
[Out]
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GIAC/XCAS [A] time = 0.214156, size = 58, normalized size = 0.98 \[ \frac{21 \,{\left (b x^{4} + a\right )}^{\frac{11}{4}} - 66 \,{\left (b x^{4} + a\right )}^{\frac{7}{4}} a + 77 \,{\left (b x^{4} + a\right )}^{\frac{3}{4}} a^{2}}{231 \, b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/(b*x^4 + a)^(1/4),x, algorithm="giac")
[Out]