Optimal. Leaf size=47 \[ \frac{2}{7} a^3 x^{7/2}+\frac{6}{5} a^2 b x^{5/2}+2 a b^2 x^{3/2}+2 b^3 \sqrt{x} \]
[Out]
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Rubi [A] time = 0.0454168, antiderivative size = 47, 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 \[ \frac{2}{7} a^3 x^{7/2}+\frac{6}{5} a^2 b x^{5/2}+2 a b^2 x^{3/2}+2 b^3 \sqrt{x} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x)^3*x^(5/2),x]
[Out]
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Rubi in Sympy [A] time = 6.84821, size = 46, normalized size = 0.98 \[ \frac{2 a^{3} x^{\frac{7}{2}}}{7} + \frac{6 a^{2} b x^{\frac{5}{2}}}{5} + 2 a b^{2} x^{\frac{3}{2}} + 2 b^{3} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x)**3*x**(5/2),x)
[Out]
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Mathematica [A] time = 0.013087, size = 39, normalized size = 0.83 \[ \frac{2}{35} \sqrt{x} \left (5 a^3 x^3+21 a^2 b x^2+35 a b^2 x+35 b^3\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x)^3*x^(5/2),x]
[Out]
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Maple [A] time = 0.007, size = 36, normalized size = 0.8 \[{\frac{10\,{a}^{3}{x}^{3}+42\,{a}^{2}b{x}^{2}+70\,a{b}^{2}x+70\,{b}^{3}}{35}\sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x)^3*x^(5/2),x)
[Out]
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Maxima [A] time = 1.44526, size = 50, normalized size = 1.06 \[ \frac{2}{35} \,{\left (5 \, a^{3} + \frac{21 \, a^{2} b}{x} + \frac{35 \, a b^{2}}{x^{2}} + \frac{35 \, b^{3}}{x^{3}}\right )} x^{\frac{7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^3*x^(5/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.228466, size = 47, normalized size = 1. \[ \frac{2}{35} \,{\left (5 \, a^{3} x^{3} + 21 \, a^{2} b x^{2} + 35 \, a b^{2} x + 35 \, b^{3}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^3*x^(5/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 14.8014, size = 46, normalized size = 0.98 \[ \frac{2 a^{3} x^{\frac{7}{2}}}{7} + \frac{6 a^{2} b x^{\frac{5}{2}}}{5} + 2 a b^{2} x^{\frac{3}{2}} + 2 b^{3} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x)**3*x**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.223068, size = 47, normalized size = 1. \[ \frac{2}{7} \, a^{3} x^{\frac{7}{2}} + \frac{6}{5} \, a^{2} b x^{\frac{5}{2}} + 2 \, a b^{2} x^{\frac{3}{2}} + 2 \, b^{3} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^3*x^(5/2),x, algorithm="giac")
[Out]