Optimal. Leaf size=57 \[ -\frac{a^2}{b^3 \sqrt [4]{a+b x^4}}-\frac{2 a \left (a+b x^4\right )^{3/4}}{3 b^3}+\frac{\left (a+b x^4\right )^{7/4}}{7 b^3} \]
[Out]
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Rubi [A] time = 0.0839911, antiderivative size = 57, 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 \[ -\frac{a^2}{b^3 \sqrt [4]{a+b x^4}}-\frac{2 a \left (a+b x^4\right )^{3/4}}{3 b^3}+\frac{\left (a+b x^4\right )^{7/4}}{7 b^3} \]
Antiderivative was successfully verified.
[In] Int[x^11/(a + b*x^4)^(5/4),x]
[Out]
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Rubi in Sympy [A] time = 10.5703, size = 49, normalized size = 0.86 \[ - \frac{a^{2}}{b^{3} \sqrt [4]{a + b x^{4}}} - \frac{2 a \left (a + b x^{4}\right )^{\frac{3}{4}}}{3 b^{3}} + \frac{\left (a + b x^{4}\right )^{\frac{7}{4}}}{7 b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**11/(b*x**4+a)**(5/4),x)
[Out]
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Mathematica [A] time = 0.0331995, size = 39, normalized size = 0.68 \[ \frac{-32 a^2-8 a b x^4+3 b^2 x^8}{21 b^3 \sqrt [4]{a+b x^4}} \]
Antiderivative was successfully verified.
[In] Integrate[x^11/(a + b*x^4)^(5/4),x]
[Out]
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Maple [A] time = 0.008, size = 36, normalized size = 0.6 \[ -{\frac{-3\,{b}^{2}{x}^{8}+8\,ab{x}^{4}+32\,{a}^{2}}{21\,{b}^{3}}{\frac{1}{\sqrt [4]{b{x}^{4}+a}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^11/(b*x^4+a)^(5/4),x)
[Out]
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Maxima [A] time = 1.41638, size = 63, normalized size = 1.11 \[ \frac{{\left (b x^{4} + a\right )}^{\frac{7}{4}}}{7 \, b^{3}} - \frac{2 \,{\left (b x^{4} + a\right )}^{\frac{3}{4}} a}{3 \, b^{3}} - \frac{a^{2}}{{\left (b x^{4} + a\right )}^{\frac{1}{4}} b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/(b*x^4 + a)^(5/4),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.231002, size = 47, normalized size = 0.82 \[ \frac{3 \, b^{2} x^{8} - 8 \, a b x^{4} - 32 \, a^{2}}{21 \,{\left (b x^{4} + a\right )}^{\frac{1}{4}} b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/(b*x^4 + a)^(5/4),x, algorithm="fricas")
[Out]
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Sympy [A] time = 10.2773, size = 68, normalized size = 1.19 \[ \begin{cases} - \frac{32 a^{2}}{21 b^{3} \sqrt [4]{a + b x^{4}}} - \frac{8 a x^{4}}{21 b^{2} \sqrt [4]{a + b x^{4}}} + \frac{x^{8}}{7 b \sqrt [4]{a + b x^{4}}} & \text{for}\: b \neq 0 \\\frac{x^{12}}{12 a^{\frac{5}{4}}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**11/(b*x**4+a)**(5/4),x)
[Out]
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GIAC/XCAS [A] time = 0.214441, size = 58, normalized size = 1.02 \[ \frac{3 \,{\left (b x^{4} + a\right )}^{\frac{7}{4}} - 14 \,{\left (b x^{4} + a\right )}^{\frac{3}{4}} a - \frac{21 \, a^{2}}{{\left (b x^{4} + a\right )}^{\frac{1}{4}}}}{21 \, b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/(b*x^4 + a)^(5/4),x, algorithm="giac")
[Out]