Optimal. Leaf size=45 \[ -\frac{a^3}{4 x^4}-\frac{6 a^2 b}{7 x^{7/2}}-\frac{a b^2}{x^3}-\frac{2 b^3}{5 x^{5/2}} \]
[Out]
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Rubi [A] time = 0.0550816, antiderivative size = 45, 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 \[ -\frac{a^3}{4 x^4}-\frac{6 a^2 b}{7 x^{7/2}}-\frac{a b^2}{x^3}-\frac{2 b^3}{5 x^{5/2}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*Sqrt[x])^3/x^5,x]
[Out]
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Rubi in Sympy [A] time = 8.58788, size = 42, normalized size = 0.93 \[ - \frac{a^{3}}{4 x^{4}} - \frac{6 a^{2} b}{7 x^{\frac{7}{2}}} - \frac{a b^{2}}{x^{3}} - \frac{2 b^{3}}{5 x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**(1/2))**3/x**5,x)
[Out]
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Mathematica [A] time = 0.0160295, size = 41, normalized size = 0.91 \[ -\frac{35 a^3+120 a^2 b \sqrt{x}+140 a b^2 x+56 b^3 x^{3/2}}{140 x^4} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*Sqrt[x])^3/x^5,x]
[Out]
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Maple [A] time = 0.003, size = 36, normalized size = 0.8 \[ -{\frac{{a}^{3}}{4\,{x}^{4}}}-{\frac{6\,{a}^{2}b}{7}{x}^{-{\frac{7}{2}}}}-{\frac{a{b}^{2}}{{x}^{3}}}-{\frac{2\,{b}^{3}}{5}{x}^{-{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^(1/2))^3/x^5,x)
[Out]
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Maxima [A] time = 1.43958, size = 47, normalized size = 1.04 \[ -\frac{56 \, b^{3} x^{\frac{3}{2}} + 140 \, a b^{2} x + 120 \, a^{2} b \sqrt{x} + 35 \, a^{3}}{140 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^3/x^5,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.241591, size = 49, normalized size = 1.09 \[ -\frac{140 \, a b^{2} x + 35 \, a^{3} + 8 \,{\left (7 \, b^{3} x + 15 \, a^{2} b\right )} \sqrt{x}}{140 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^3/x^5,x, algorithm="fricas")
[Out]
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Sympy [A] time = 5.04537, size = 42, normalized size = 0.93 \[ - \frac{a^{3}}{4 x^{4}} - \frac{6 a^{2} b}{7 x^{\frac{7}{2}}} - \frac{a b^{2}}{x^{3}} - \frac{2 b^{3}}{5 x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*x**(1/2))**3/x**5,x)
[Out]
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GIAC/XCAS [A] time = 0.215818, size = 47, normalized size = 1.04 \[ -\frac{56 \, b^{3} x^{\frac{3}{2}} + 140 \, a b^{2} x + 120 \, a^{2} b \sqrt{x} + 35 \, a^{3}}{140 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^3/x^5,x, algorithm="giac")
[Out]