Optimal. Leaf size=34 \[ \frac{2}{5} a^2 x^{5/2}+\frac{4}{3} a b x^{3/2}+2 b^2 \sqrt{x} \]
[Out]
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Rubi [A] time = 0.0335745, antiderivative size = 34, 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 \[ \frac{2}{5} a^2 x^{5/2}+\frac{4}{3} a b x^{3/2}+2 b^2 \sqrt{x} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x)^2*x^(3/2),x]
[Out]
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Rubi in Sympy [A] time = 5.45849, size = 32, normalized size = 0.94 \[ \frac{2 a^{2} x^{\frac{5}{2}}}{5} + \frac{4 a b x^{\frac{3}{2}}}{3} + 2 b^{2} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x)**2*x**(3/2),x)
[Out]
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Mathematica [A] time = 0.010315, size = 28, normalized size = 0.82 \[ \frac{2}{15} \sqrt{x} \left (3 a^2 x^2+10 a b x+15 b^2\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x)^2*x^(3/2),x]
[Out]
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Maple [A] time = 0.006, size = 25, normalized size = 0.7 \[{\frac{6\,{a}^{2}{x}^{2}+20\,abx+30\,{b}^{2}}{15}\sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x)^2*x^(3/2),x)
[Out]
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Maxima [A] time = 1.4503, size = 35, normalized size = 1.03 \[ \frac{2}{15} \,{\left (3 \, a^{2} + \frac{10 \, a b}{x} + \frac{15 \, b^{2}}{x^{2}}\right )} x^{\frac{5}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^2*x^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.227482, size = 32, normalized size = 0.94 \[ \frac{2}{15} \,{\left (3 \, a^{2} x^{2} + 10 \, a b x + 15 \, b^{2}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^2*x^(3/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.29041, size = 32, normalized size = 0.94 \[ \frac{2 a^{2} x^{\frac{5}{2}}}{5} + \frac{4 a b x^{\frac{3}{2}}}{3} + 2 b^{2} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x)**2*x**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.228209, size = 32, normalized size = 0.94 \[ \frac{2}{5} \, a^{2} x^{\frac{5}{2}} + \frac{4}{3} \, a b x^{\frac{3}{2}} + 2 \, b^{2} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^2*x^(3/2),x, algorithm="giac")
[Out]