Optimal. Leaf size=31 \[ \frac{1}{90} \left (3 x^4+5\right )^{5/2}-\frac{5}{54} \left (3 x^4+5\right )^{3/2} \]
[Out]
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Rubi [A] time = 0.0394817, antiderivative size = 31, 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 \[ \frac{1}{90} \left (3 x^4+5\right )^{5/2}-\frac{5}{54} \left (3 x^4+5\right )^{3/2} \]
Antiderivative was successfully verified.
[In] Int[x^7*Sqrt[5 + 3*x^4],x]
[Out]
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Rubi in Sympy [A] time = 4.84401, size = 24, normalized size = 0.77 \[ \frac{\left (3 x^{4} + 5\right )^{\frac{5}{2}}}{90} - \frac{5 \left (3 x^{4} + 5\right )^{\frac{3}{2}}}{54} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**7*(3*x**4+5)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0133727, size = 22, normalized size = 0.71 \[ \frac{1}{270} \left (3 x^4+5\right )^{3/2} \left (9 x^4-10\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^7*Sqrt[5 + 3*x^4],x]
[Out]
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Maple [A] time = 0.006, size = 19, normalized size = 0.6 \[{\frac{9\,{x}^{4}-10}{270} \left ( 3\,{x}^{4}+5 \right ) ^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^7*(3*x^4+5)^(1/2),x)
[Out]
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Maxima [A] time = 1.4372, size = 31, normalized size = 1. \[ \frac{1}{90} \,{\left (3 \, x^{4} + 5\right )}^{\frac{5}{2}} - \frac{5}{54} \,{\left (3 \, x^{4} + 5\right )}^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(3*x^4 + 5)*x^7,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.23149, size = 31, normalized size = 1. \[ \frac{1}{270} \,{\left (27 \, x^{8} + 15 \, x^{4} - 50\right )} \sqrt{3 \, x^{4} + 5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(3*x^4 + 5)*x^7,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.66159, size = 42, normalized size = 1.35 \[ \frac{x^{8} \sqrt{3 x^{4} + 5}}{10} + \frac{x^{4} \sqrt{3 x^{4} + 5}}{18} - \frac{5 \sqrt{3 x^{4} + 5}}{27} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**7*(3*x**4+5)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.215625, size = 31, normalized size = 1. \[ \frac{1}{90} \,{\left (3 \, x^{4} + 5\right )}^{\frac{5}{2}} - \frac{5}{54} \,{\left (3 \, x^{4} + 5\right )}^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(3*x^4 + 5)*x^7,x, algorithm="giac")
[Out]