Optimal. Leaf size=59 \[ \frac{a^2 \sqrt{a+b x^4}}{2 b^3}+\frac{\left (a+b x^4\right )^{5/2}}{10 b^3}-\frac{a \left (a+b x^4\right )^{3/2}}{3 b^3} \]
[Out]
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Rubi [A] time = 0.0889194, 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 \[ \frac{a^2 \sqrt{a+b x^4}}{2 b^3}+\frac{\left (a+b x^4\right )^{5/2}}{10 b^3}-\frac{a \left (a+b x^4\right )^{3/2}}{3 b^3} \]
Antiderivative was successfully verified.
[In] Int[x^11/Sqrt[a + b*x^4],x]
[Out]
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Rubi in Sympy [A] time = 10.6649, size = 49, normalized size = 0.83 \[ \frac{a^{2} \sqrt{a + b x^{4}}}{2 b^{3}} - \frac{a \left (a + b x^{4}\right )^{\frac{3}{2}}}{3 b^{3}} + \frac{\left (a + b x^{4}\right )^{\frac{5}{2}}}{10 b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**11/(b*x**4+a)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0288769, size = 39, normalized size = 0.66 \[ \frac{\sqrt{a+b x^4} \left (8 a^2-4 a b x^4+3 b^2 x^8\right )}{30 b^3} \]
Antiderivative was successfully verified.
[In] Integrate[x^11/Sqrt[a + b*x^4],x]
[Out]
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Maple [A] time = 0.009, size = 36, normalized size = 0.6 \[{\frac{3\,{b}^{2}{x}^{8}-4\,ab{x}^{4}+8\,{a}^{2}}{30\,{b}^{3}}\sqrt{b{x}^{4}+a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^11/(b*x^4+a)^(1/2),x)
[Out]
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Maxima [A] time = 1.4227, size = 63, normalized size = 1.07 \[ \frac{{\left (b x^{4} + a\right )}^{\frac{5}{2}}}{10 \, b^{3}} - \frac{{\left (b x^{4} + a\right )}^{\frac{3}{2}} a}{3 \, b^{3}} + \frac{\sqrt{b x^{4} + a} a^{2}}{2 \, b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/sqrt(b*x^4 + a),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.247733, size = 47, normalized size = 0.8 \[ \frac{{\left (3 \, b^{2} x^{8} - 4 \, a b x^{4} + 8 \, a^{2}\right )} \sqrt{b x^{4} + a}}{30 \, b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/sqrt(b*x^4 + a),x, algorithm="fricas")
[Out]
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Sympy [A] time = 8.9373, size = 68, normalized size = 1.15 \[ \begin{cases} \frac{4 a^{2} \sqrt{a + b x^{4}}}{15 b^{3}} - \frac{2 a x^{4} \sqrt{a + b x^{4}}}{15 b^{2}} + \frac{x^{8} \sqrt{a + b x^{4}}}{10 b} & \text{for}\: b \neq 0 \\\frac{x^{12}}{12 \sqrt{a}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**11/(b*x**4+a)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.215425, size = 58, normalized size = 0.98 \[ \frac{3 \,{\left (b x^{4} + a\right )}^{\frac{5}{2}} - 10 \,{\left (b x^{4} + a\right )}^{\frac{3}{2}} a + 15 \, \sqrt{b x^{4} + a} a^{2}}{30 \, b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/sqrt(b*x^4 + a),x, algorithm="giac")
[Out]