Optimal. Leaf size=100 \[ -\frac{32 b^3 \sqrt{x} \sqrt{a+\frac{b}{x}}}{35 a^4}+\frac{16 b^2 x^{3/2} \sqrt{a+\frac{b}{x}}}{35 a^3}-\frac{12 b x^{5/2} \sqrt{a+\frac{b}{x}}}{35 a^2}+\frac{2 x^{7/2} \sqrt{a+\frac{b}{x}}}{7 a} \]
[Out]
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Rubi [A] time = 0.114401, antiderivative size = 100, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118 \[ -\frac{32 b^3 \sqrt{x} \sqrt{a+\frac{b}{x}}}{35 a^4}+\frac{16 b^2 x^{3/2} \sqrt{a+\frac{b}{x}}}{35 a^3}-\frac{12 b x^{5/2} \sqrt{a+\frac{b}{x}}}{35 a^2}+\frac{2 x^{7/2} \sqrt{a+\frac{b}{x}}}{7 a} \]
Antiderivative was successfully verified.
[In] Int[x^(5/2)/Sqrt[a + b/x],x]
[Out]
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Rubi in Sympy [A] time = 9.84751, size = 87, normalized size = 0.87 \[ \frac{2 x^{\frac{7}{2}} \sqrt{a + \frac{b}{x}}}{7 a} - \frac{12 b x^{\frac{5}{2}} \sqrt{a + \frac{b}{x}}}{35 a^{2}} + \frac{16 b^{2} x^{\frac{3}{2}} \sqrt{a + \frac{b}{x}}}{35 a^{3}} - \frac{32 b^{3} \sqrt{x} \sqrt{a + \frac{b}{x}}}{35 a^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(5/2)/(a+b/x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0445848, size = 53, normalized size = 0.53 \[ \frac{2 \sqrt{x} \sqrt{a+\frac{b}{x}} \left (5 a^3 x^3-6 a^2 b x^2+8 a b^2 x-16 b^3\right )}{35 a^4} \]
Antiderivative was successfully verified.
[In] Integrate[x^(5/2)/Sqrt[a + b/x],x]
[Out]
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Maple [A] time = 0.007, size = 55, normalized size = 0.6 \[{\frac{ \left ( 2\,ax+2\,b \right ) \left ( 5\,{a}^{3}{x}^{3}-6\,{a}^{2}b{x}^{2}+8\,a{b}^{2}x-16\,{b}^{3} \right ) }{35\,{a}^{4}}{\frac{1}{\sqrt{x}}}{\frac{1}{\sqrt{{\frac{ax+b}{x}}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(5/2)/(a+b/x)^(1/2),x)
[Out]
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Maxima [A] time = 1.44442, size = 93, normalized size = 0.93 \[ \frac{2 \,{\left (5 \,{\left (a + \frac{b}{x}\right )}^{\frac{7}{2}} x^{\frac{7}{2}} - 21 \,{\left (a + \frac{b}{x}\right )}^{\frac{5}{2}} b x^{\frac{5}{2}} + 35 \,{\left (a + \frac{b}{x}\right )}^{\frac{3}{2}} b^{2} x^{\frac{3}{2}} - 35 \, \sqrt{a + \frac{b}{x}} b^{3} \sqrt{x}\right )}}{35 \, a^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^(5/2)/sqrt(a + b/x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.240728, size = 66, normalized size = 0.66 \[ \frac{2 \,{\left (5 \, a^{3} x^{3} - 6 \, a^{2} b x^{2} + 8 \, a b^{2} x - 16 \, b^{3}\right )} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{35 \, a^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^(5/2)/sqrt(a + b/x),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(x**(5/2)/(a+b/x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.232322, size = 78, normalized size = 0.78 \[ \frac{32 \, b^{\frac{7}{2}}}{35 \, a^{4}} + \frac{2 \,{\left (5 \,{\left (a x + b\right )}^{\frac{7}{2}} - 21 \,{\left (a x + b\right )}^{\frac{5}{2}} b + 35 \,{\left (a x + b\right )}^{\frac{3}{2}} b^{2} - 35 \, \sqrt{a x + b} b^{3}\right )}}{35 \, a^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^(5/2)/sqrt(a + b/x),x, algorithm="giac")
[Out]