Optimal. Leaf size=36 \[ \frac{2}{13} b^2 x^{13/2}+\frac{4}{17} b c x^{17/2}+\frac{2}{21} c^2 x^{21/2} \]
[Out]
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Rubi [A] time = 0.0358954, antiderivative size = 36, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.105 \[ \frac{2}{13} b^2 x^{13/2}+\frac{4}{17} b c x^{17/2}+\frac{2}{21} c^2 x^{21/2} \]
Antiderivative was successfully verified.
[In] Int[x^(3/2)*(b*x^2 + c*x^4)^2,x]
[Out]
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Rubi in Sympy [A] time = 6.74751, size = 34, normalized size = 0.94 \[ \frac{2 b^{2} x^{\frac{13}{2}}}{13} + \frac{4 b c x^{\frac{17}{2}}}{17} + \frac{2 c^{2} x^{\frac{21}{2}}}{21} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(3/2)*(c*x**4+b*x**2)**2,x)
[Out]
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Mathematica [A] time = 0.0119907, size = 30, normalized size = 0.83 \[ \frac{2 x^{13/2} \left (357 b^2+546 b c x^2+221 c^2 x^4\right )}{4641} \]
Antiderivative was successfully verified.
[In] Integrate[x^(3/2)*(b*x^2 + c*x^4)^2,x]
[Out]
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Maple [A] time = 0.008, size = 27, normalized size = 0.8 \[{\frac{442\,{c}^{2}{x}^{4}+1092\,bc{x}^{2}+714\,{b}^{2}}{4641}{x}^{{\frac{13}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(3/2)*(c*x^4+b*x^2)^2,x)
[Out]
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Maxima [A] time = 0.680109, size = 32, normalized size = 0.89 \[ \frac{2}{21} \, c^{2} x^{\frac{21}{2}} + \frac{4}{17} \, b c x^{\frac{17}{2}} + \frac{2}{13} \, b^{2} x^{\frac{13}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)^2*x^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.263985, size = 39, normalized size = 1.08 \[ \frac{2}{4641} \,{\left (221 \, c^{2} x^{10} + 546 \, b c x^{8} + 357 \, b^{2} x^{6}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)^2*x^(3/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 35.2437, size = 34, normalized size = 0.94 \[ \frac{2 b^{2} x^{\frac{13}{2}}}{13} + \frac{4 b c x^{\frac{17}{2}}}{17} + \frac{2 c^{2} x^{\frac{21}{2}}}{21} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(3/2)*(c*x**4+b*x**2)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.26673, size = 32, normalized size = 0.89 \[ \frac{2}{21} \, c^{2} x^{\frac{21}{2}} + \frac{4}{17} \, b c x^{\frac{17}{2}} + \frac{2}{13} \, b^{2} x^{\frac{13}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)^2*x^(3/2),x, algorithm="giac")
[Out]