Optimal. Leaf size=47 \[ -\frac{2 a^3}{3 x^{3/2}}-\frac{6 a^2 b}{\sqrt{x}}+6 a b^2 \sqrt{x}+\frac{2}{3} b^3 x^{3/2} \]
[Out]
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Rubi [A] time = 0.0305014, antiderivative size = 47, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ -\frac{2 a^3}{3 x^{3/2}}-\frac{6 a^2 b}{\sqrt{x}}+6 a b^2 \sqrt{x}+\frac{2}{3} b^3 x^{3/2} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^3/x^(5/2),x]
[Out]
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Rubi in Sympy [A] time = 5.24496, size = 46, normalized size = 0.98 \[ - \frac{2 a^{3}}{3 x^{\frac{3}{2}}} - \frac{6 a^{2} b}{\sqrt{x}} + 6 a b^{2} \sqrt{x} + \frac{2 b^{3} x^{\frac{3}{2}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**3/x**(5/2),x)
[Out]
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Mathematica [A] time = 0.0129769, size = 38, normalized size = 0.81 \[ \frac{2 \left (-a^3-9 a^2 b x+9 a b^2 x^2+b^3 x^3\right )}{3 x^{3/2}} \]
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 = 34, normalized size = 0.7 \[ -{\frac{-2\,{b}^{3}{x}^{3}-18\,a{b}^{2}{x}^{2}+18\,{a}^{2}bx+2\,{a}^{3}}{3}{x}^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^3/x^(5/2),x)
[Out]
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Maxima [A] time = 1.35102, size = 46, normalized size = 0.98 \[ \frac{2}{3} \, b^{3} x^{\frac{3}{2}} + 6 \, a b^{2} \sqrt{x} - \frac{2 \,{\left (9 \, a^{2} b x + a^{3}\right )}}{3 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^3/x^(5/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.208721, size = 46, normalized size = 0.98 \[ \frac{2 \,{\left (b^{3} x^{3} + 9 \, a b^{2} x^{2} - 9 \, a^{2} b x - a^{3}\right )}}{3 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^3/x^(5/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.32839, size = 46, normalized size = 0.98 \[ - \frac{2 a^{3}}{3 x^{\frac{3}{2}}} - \frac{6 a^{2} b}{\sqrt{x}} + 6 a b^{2} \sqrt{x} + \frac{2 b^{3} x^{\frac{3}{2}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**3/x**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.201015, size = 46, normalized size = 0.98 \[ \frac{2}{3} \, b^{3} x^{\frac{3}{2}} + 6 \, a b^{2} \sqrt{x} - \frac{2 \,{\left (9 \, a^{2} b x + a^{3}\right )}}{3 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^3/x^(5/2),x, algorithm="giac")
[Out]