Optimal. Leaf size=51 \[ \frac{2}{3} a^3 x^{3/2}+\frac{6}{11} a^2 c x^{11/2}+\frac{6}{19} a c^2 x^{19/2}+\frac{2}{27} c^3 x^{27/2} \]
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Rubi [A] time = 0.0349735, antiderivative size = 51, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ \frac{2}{3} a^3 x^{3/2}+\frac{6}{11} a^2 c x^{11/2}+\frac{6}{19} a c^2 x^{19/2}+\frac{2}{27} c^3 x^{27/2} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[x]*(a + c*x^4)^3,x]
[Out]
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Rubi in Sympy [A] time = 5.79958, size = 49, normalized size = 0.96 \[ \frac{2 a^{3} x^{\frac{3}{2}}}{3} + \frac{6 a^{2} c x^{\frac{11}{2}}}{11} + \frac{6 a c^{2} x^{\frac{19}{2}}}{19} + \frac{2 c^{3} x^{\frac{27}{2}}}{27} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**4+a)**3*x**(1/2),x)
[Out]
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Mathematica [A] time = 0.0137471, size = 41, normalized size = 0.8 \[ \frac{2 x^{3/2} \left (1881 a^3+1539 a^2 c x^4+891 a c^2 x^8+209 c^3 x^{12}\right )}{5643} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[x]*(a + c*x^4)^3,x]
[Out]
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Maple [A] time = 0.009, size = 38, normalized size = 0.8 \[{\frac{418\,{c}^{3}{x}^{12}+1782\,a{c}^{2}{x}^{8}+3078\,{a}^{2}c{x}^{4}+3762\,{a}^{3}}{5643}{x}^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^4+a)^3*x^(1/2),x)
[Out]
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Maxima [A] time = 1.42841, size = 47, normalized size = 0.92 \[ \frac{2}{27} \, c^{3} x^{\frac{27}{2}} + \frac{6}{19} \, a c^{2} x^{\frac{19}{2}} + \frac{6}{11} \, a^{2} c x^{\frac{11}{2}} + \frac{2}{3} \, a^{3} x^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + a)^3*sqrt(x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.227585, size = 51, normalized size = 1. \[ \frac{2}{5643} \,{\left (209 \, c^{3} x^{13} + 891 \, a c^{2} x^{9} + 1539 \, a^{2} c x^{5} + 1881 \, a^{3} x\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + a)^3*sqrt(x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 29.1991, size = 49, normalized size = 0.96 \[ \frac{2 a^{3} x^{\frac{3}{2}}}{3} + \frac{6 a^{2} c x^{\frac{11}{2}}}{11} + \frac{6 a c^{2} x^{\frac{19}{2}}}{19} + \frac{2 c^{3} x^{\frac{27}{2}}}{27} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**4+a)**3*x**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.212428, size = 47, normalized size = 0.92 \[ \frac{2}{27} \, c^{3} x^{\frac{27}{2}} + \frac{6}{19} \, a c^{2} x^{\frac{19}{2}} + \frac{6}{11} \, a^{2} c x^{\frac{11}{2}} + \frac{2}{3} \, a^{3} x^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + a)^3*sqrt(x),x, algorithm="giac")
[Out]