Optimal. Leaf size=62 \[ -\frac{a^2 \left (a-b x^4\right )^{3/4}}{3 b^3}-\frac{\left (a-b x^4\right )^{11/4}}{11 b^3}+\frac{2 a \left (a-b x^4\right )^{7/4}}{7 b^3} \]
[Out]
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Rubi [A] time = 0.0892385, antiderivative size = 62, 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 \[ -\frac{a^2 \left (a-b x^4\right )^{3/4}}{3 b^3}-\frac{\left (a-b x^4\right )^{11/4}}{11 b^3}+\frac{2 a \left (a-b x^4\right )^{7/4}}{7 b^3} \]
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 = 11.5577, size = 51, normalized size = 0.82 \[ - \frac{a^{2} \left (a - b x^{4}\right )^{\frac{3}{4}}}{3 b^{3}} + \frac{2 a \left (a - b x^{4}\right )^{\frac{7}{4}}}{7 b^{3}} - \frac{\left (a - b x^{4}\right )^{\frac{11}{4}}}{11 b^{3}} \]
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 = 0.0314233, size = 40, normalized size = 0.65 \[ -\frac{\left (a-b x^4\right )^{3/4} \left (32 a^2+24 a b x^4+21 b^2 x^8\right )}{231 b^3} \]
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 = 37, 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 = 1.43841, size = 68, normalized size = 1.1 \[ -\frac{{\left (-b x^{4} + a\right )}^{\frac{11}{4}}}{11 \, b^{3}} + \frac{2 \,{\left (-b x^{4} + a\right )}^{\frac{7}{4}} a}{7 \, b^{3}} - \frac{{\left (-b x^{4} + a\right )}^{\frac{3}{4}} a^{2}}{3 \, b^{3}} \]
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 = 0.230098, size = 49, normalized size = 0.79 \[ -\frac{{\left (21 \, b^{2} x^{8} + 24 \, a b x^{4} + 32 \, a^{2}\right )}{\left (-b x^{4} + a\right )}^{\frac{3}{4}}}{231 \, b^{3}} \]
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 = 11.0313, size = 70, normalized size = 1.13 \[ \begin{cases} - \frac{32 a^{2} \left (a - b x^{4}\right )^{\frac{3}{4}}}{231 b^{3}} - \frac{8 a x^{4} \left (a - b x^{4}\right )^{\frac{3}{4}}}{77 b^{2}} - \frac{x^{8} \left (a - b x^{4}\right )^{\frac{3}{4}}}{11 b} & \text{for}\: b \neq 0 \\\frac{x^{12}}{12 \sqrt [4]{a}} & \text{otherwise} \end{cases} \]
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 = 0.216756, size = 77, normalized size = 1.24 \[ -\frac{21 \,{\left (b x^{4} - a\right )}^{2}{\left (-b x^{4} + a\right )}^{\frac{3}{4}} - 66 \,{\left (-b x^{4} + a\right )}^{\frac{7}{4}} a + 77 \,{\left (-b x^{4} + a\right )}^{\frac{3}{4}} a^{2}}{231 \, b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/(-b*x^4 + a)^(1/4),x, algorithm="giac")
[Out]