Optimal. Leaf size=19 \[ \frac{x^{3/2}}{3 (2-b x)^{3/2}} \]
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Rubi [A] time = 0.0115242, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062 \[ \frac{x^{3/2}}{3 (2-b x)^{3/2}} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[x]/(2 - b*x)^(5/2),x]
[Out]
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Rubi in Sympy [A] time = 2.40184, size = 14, normalized size = 0.74 \[ \frac{x^{\frac{3}{2}}}{3 \left (- b x + 2\right )^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(1/2)/(-b*x+2)**(5/2),x)
[Out]
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Mathematica [A] time = 0.0199826, size = 19, normalized size = 1. \[ \frac{x^{3/2}}{3 (2-b x)^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[x]/(2 - b*x)^(5/2),x]
[Out]
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Maple [A] time = 0.004, size = 14, normalized size = 0.7 \[{\frac{1}{3}{x}^{{\frac{3}{2}}} \left ( -bx+2 \right ) ^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(1/2)/(-b*x+2)^(5/2),x)
[Out]
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Maxima [A] time = 1.34282, size = 18, normalized size = 0.95 \[ \frac{x^{\frac{3}{2}}}{3 \,{\left (-b x + 2\right )}^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x)/(-b*x + 2)^(5/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.228623, size = 27, normalized size = 1.42 \[ -\frac{x^{\frac{3}{2}}}{3 \,{\left (b x - 2\right )} \sqrt{-b x + 2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x)/(-b*x + 2)^(5/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 13.7715, size = 65, normalized size = 3.42 \[ \begin{cases} \frac{i x^{\frac{3}{2}}}{3 b x \sqrt{b x - 2} - 6 \sqrt{b x - 2}} & \text{for}\: \frac{\left |{b x}\right |}{2} > 1 \\- \frac{x^{\frac{3}{2}}}{3 b x \sqrt{- b x + 2} - 6 \sqrt{- b x + 2}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(1/2)/(-b*x+2)**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.217782, size = 128, normalized size = 6.74 \[ \frac{4 \,{\left (3 \,{\left (\sqrt{-b x + 2} \sqrt{-b} - \sqrt{{\left (b x - 2\right )} b + 2 \, b}\right )}^{4} \sqrt{-b} + 4 \, \sqrt{-b} b^{2}\right )}{\left | b \right |}}{3 \,{\left ({\left (\sqrt{-b x + 2} \sqrt{-b} - \sqrt{{\left (b x - 2\right )} b + 2 \, b}\right )}^{2} - 2 \, b\right )}^{3} b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x)/(-b*x + 2)^(5/2),x, algorithm="giac")
[Out]