Optimal. Leaf size=38 \[ \frac{\left (a+b x^4\right )^{3/2}}{6 b^2}-\frac{a \sqrt{a+b x^4}}{2 b^2} \]
[Out]
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Rubi [A] time = 0.0629535, antiderivative size = 38, 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 \[ \frac{\left (a+b x^4\right )^{3/2}}{6 b^2}-\frac{a \sqrt{a+b x^4}}{2 b^2} \]
Antiderivative was successfully verified.
[In] Int[x^7/Sqrt[a + b*x^4],x]
[Out]
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Rubi in Sympy [A] time = 7.13061, size = 31, normalized size = 0.82 \[ - \frac{a \sqrt{a + b x^{4}}}{2 b^{2}} + \frac{\left (a + b x^{4}\right )^{\frac{3}{2}}}{6 b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**7/(b*x**4+a)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0221623, size = 27, normalized size = 0.71 \[ \frac{\left (b x^4-2 a\right ) \sqrt{a+b x^4}}{6 b^2} \]
Antiderivative was successfully verified.
[In] Integrate[x^7/Sqrt[a + b*x^4],x]
[Out]
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Maple [A] time = 0.007, size = 25, normalized size = 0.7 \[ -{\frac{-b{x}^{4}+2\,a}{6\,{b}^{2}}\sqrt{b{x}^{4}+a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^7/(b*x^4+a)^(1/2),x)
[Out]
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Maxima [A] time = 1.43814, size = 41, normalized size = 1.08 \[ \frac{{\left (b x^{4} + a\right )}^{\frac{3}{2}}}{6 \, b^{2}} - \frac{\sqrt{b x^{4} + a} a}{2 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^7/sqrt(b*x^4 + a),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.235908, size = 31, normalized size = 0.82 \[ \frac{\sqrt{b x^{4} + a}{\left (b x^{4} - 2 \, a\right )}}{6 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^7/sqrt(b*x^4 + a),x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.58189, size = 42, normalized size = 1.11 \[ \begin{cases} - \frac{a \sqrt{a + b x^{4}}}{3 b^{2}} + \frac{x^{4} \sqrt{a + b x^{4}}}{6 b} & \text{for}\: b \neq 0 \\\frac{x^{8}}{8 \sqrt{a}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**7/(b*x**4+a)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.214511, size = 36, normalized size = 0.95 \[ \frac{{\left (b x^{4} + a\right )}^{\frac{3}{2}} - 3 \, \sqrt{b x^{4} + a} a}{6 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^7/sqrt(b*x^4 + a),x, algorithm="giac")
[Out]