Optimal. Leaf size=74 \[ \frac{16 b^2 x^{3/2} \left (a+\frac{b}{x}\right )^{3/2}}{105 a^3}-\frac{8 b x^{5/2} \left (a+\frac{b}{x}\right )^{3/2}}{35 a^2}+\frac{2 x^{7/2} \left (a+\frac{b}{x}\right )^{3/2}}{7 a} \]
[Out]
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Rubi [A] time = 0.0823326, antiderivative size = 74, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118 \[ \frac{16 b^2 x^{3/2} \left (a+\frac{b}{x}\right )^{3/2}}{105 a^3}-\frac{8 b x^{5/2} \left (a+\frac{b}{x}\right )^{3/2}}{35 a^2}+\frac{2 x^{7/2} \left (a+\frac{b}{x}\right )^{3/2}}{7 a} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[a + b/x]*x^(5/2),x]
[Out]
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Rubi in Sympy [A] time = 6.71071, size = 63, normalized size = 0.85 \[ \frac{2 x^{\frac{7}{2}} \left (a + \frac{b}{x}\right )^{\frac{3}{2}}}{7 a} - \frac{8 b x^{\frac{5}{2}} \left (a + \frac{b}{x}\right )^{\frac{3}{2}}}{35 a^{2}} + \frac{16 b^{2} x^{\frac{3}{2}} \left (a + \frac{b}{x}\right )^{\frac{3}{2}}}{105 a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x)**(1/2)*x**(5/2),x)
[Out]
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Mathematica [A] time = 0.038405, size = 53, normalized size = 0.72 \[ \frac{2 \sqrt{x} \sqrt{a+\frac{b}{x}} \left (15 a^3 x^3+3 a^2 b x^2-4 a b^2 x+8 b^3\right )}{105 a^3} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[a + b/x]*x^(5/2),x]
[Out]
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Maple [A] time = 0.007, size = 44, normalized size = 0.6 \[{\frac{ \left ( 2\,ax+2\,b \right ) \left ( 15\,{a}^{2}{x}^{2}-12\,abx+8\,{b}^{2} \right ) }{105\,{a}^{3}}\sqrt{x}\sqrt{{\frac{ax+b}{x}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x)^(1/2)*x^(5/2),x)
[Out]
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Maxima [A] time = 1.42952, size = 70, normalized size = 0.95 \[ \frac{2 \,{\left (15 \,{\left (a + \frac{b}{x}\right )}^{\frac{7}{2}} x^{\frac{7}{2}} - 42 \,{\left (a + \frac{b}{x}\right )}^{\frac{5}{2}} b x^{\frac{5}{2}} + 35 \,{\left (a + \frac{b}{x}\right )}^{\frac{3}{2}} b^{2} x^{\frac{3}{2}}\right )}}{105 \, a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(a + b/x)*x^(5/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.247368, size = 66, normalized size = 0.89 \[ \frac{2 \,{\left (15 \, a^{3} x^{3} + 3 \, a^{2} b x^{2} - 4 \, a b^{2} x + 8 \, b^{3}\right )} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{105 \, a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(a + b/x)*x^(5/2),x, algorithm="fricas")
[Out]
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x)**(1/2)*x**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.235461, size = 68, normalized size = 0.92 \[ -\frac{2}{105} \,{\left (\frac{8 \, b^{\frac{7}{2}}}{a^{3}} - \frac{15 \,{\left (a x + b\right )}^{\frac{7}{2}} - 42 \,{\left (a x + b\right )}^{\frac{5}{2}} b + 35 \,{\left (a x + b\right )}^{\frac{3}{2}} b^{2}}{a^{3}}\right )}{\rm sign}\left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(a + b/x)*x^(5/2),x, algorithm="giac")
[Out]