Optimal. Leaf size=38 \[ \frac{b \sqrt{b x+2}}{3 \sqrt{x}}-\frac{\sqrt{b x+2}}{3 x^{3/2}} \]
[Out]
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Rubi [A] time = 0.0230381, antiderivative size = 38, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{b \sqrt{b x+2}}{3 \sqrt{x}}-\frac{\sqrt{b x+2}}{3 x^{3/2}} \]
Antiderivative was successfully verified.
[In] Int[1/(x^(5/2)*Sqrt[2 + b*x]),x]
[Out]
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Rubi in Sympy [A] time = 3.06112, size = 31, normalized size = 0.82 \[ \frac{b \sqrt{b x + 2}}{3 \sqrt{x}} - \frac{\sqrt{b x + 2}}{3 x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**(5/2)/(b*x+2)**(1/2),x)
[Out]
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Mathematica [A] time = 0.015859, size = 23, normalized size = 0.61 \[ \frac{(b x-1) \sqrt{b x+2}}{3 x^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^(5/2)*Sqrt[2 + b*x]),x]
[Out]
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Maple [A] time = 0.006, size = 18, normalized size = 0.5 \[{\frac{bx-1}{3}\sqrt{bx+2}{x}^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^(5/2)/(b*x+2)^(1/2),x)
[Out]
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Maxima [A] time = 1.3405, size = 35, normalized size = 0.92 \[ \frac{\sqrt{b x + 2} b}{2 \, \sqrt{x}} - \frac{{\left (b x + 2\right )}^{\frac{3}{2}}}{6 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x + 2)*x^(5/2)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.209167, size = 23, normalized size = 0.61 \[ \frac{\sqrt{b x + 2}{\left (b x - 1\right )}}{3 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x + 2)*x^(5/2)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 23.9987, size = 34, normalized size = 0.89 \[ \frac{b^{\frac{3}{2}} \sqrt{1 + \frac{2}{b x}}}{3} - \frac{\sqrt{b} \sqrt{1 + \frac{2}{b x}}}{3 x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**(5/2)/(b*x+2)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.216265, size = 57, normalized size = 1.5 \[ \frac{{\left ({\left (b x + 2\right )} b^{3} - 3 \, b^{3}\right )} \sqrt{b x + 2} b}{3 \,{\left ({\left (b x + 2\right )} b - 2 \, b\right )}^{\frac{3}{2}}{\left | b \right |}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x + 2)*x^(5/2)),x, algorithm="giac")
[Out]