Optimal. Leaf size=51 \[ -\frac{2 a^3}{3 x^{3/2}}+\frac{6}{5} a^2 c x^{5/2}+\frac{6}{13} a c^2 x^{13/2}+\frac{2}{21} c^3 x^{21/2} \]
[Out]
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Rubi [A] time = 0.0364448, 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 \[ -\frac{2 a^3}{3 x^{3/2}}+\frac{6}{5} a^2 c x^{5/2}+\frac{6}{13} a c^2 x^{13/2}+\frac{2}{21} c^3 x^{21/2} \]
Antiderivative was successfully verified.
[In] Int[(a + c*x^4)^3/x^(5/2),x]
[Out]
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Rubi in Sympy [A] time = 5.76896, size = 49, normalized size = 0.96 \[ - \frac{2 a^{3}}{3 x^{\frac{3}{2}}} + \frac{6 a^{2} c x^{\frac{5}{2}}}{5} + \frac{6 a c^{2} x^{\frac{13}{2}}}{13} + \frac{2 c^{3} x^{\frac{21}{2}}}{21} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**4+a)**3/x**(5/2),x)
[Out]
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Mathematica [A] time = 0.0159259, size = 41, normalized size = 0.8 \[ \frac{2 \left (-455 a^3+819 a^2 c x^4+315 a c^2 x^8+65 c^3 x^{12}\right )}{1365 x^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + c*x^4)^3/x^(5/2),x]
[Out]
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Maple [A] time = 0.008, size = 38, normalized size = 0.8 \[ -{\frac{-130\,{c}^{3}{x}^{12}-630\,a{c}^{2}{x}^{8}-1638\,{a}^{2}c{x}^{4}+910\,{a}^{3}}{1365}{x}^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^4+a)^3/x^(5/2),x)
[Out]
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Maxima [A] time = 1.44151, size = 47, normalized size = 0.92 \[ \frac{2}{21} \, c^{3} x^{\frac{21}{2}} + \frac{6}{13} \, a c^{2} x^{\frac{13}{2}} + \frac{6}{5} \, a^{2} c x^{\frac{5}{2}} - \frac{2 \, a^{3}}{3 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + a)^3/x^(5/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.228134, size = 50, normalized size = 0.98 \[ \frac{2 \,{\left (65 \, c^{3} x^{12} + 315 \, a c^{2} x^{8} + 819 \, a^{2} c x^{4} - 455 \, a^{3}\right )}}{1365 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + a)^3/x^(5/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 78.7912, size = 49, normalized size = 0.96 \[ - \frac{2 a^{3}}{3 x^{\frac{3}{2}}} + \frac{6 a^{2} c x^{\frac{5}{2}}}{5} + \frac{6 a c^{2} x^{\frac{13}{2}}}{13} + \frac{2 c^{3} x^{\frac{21}{2}}}{21} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**4+a)**3/x**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.216936, size = 47, normalized size = 0.92 \[ \frac{2}{21} \, c^{3} x^{\frac{21}{2}} + \frac{6}{13} \, a c^{2} x^{\frac{13}{2}} + \frac{6}{5} \, a^{2} c x^{\frac{5}{2}} - \frac{2 \, a^{3}}{3 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + a)^3/x^(5/2),x, algorithm="giac")
[Out]