Optimal. Leaf size=18 \[ \frac{x^{3/2}}{3 (b x+2)^{3/2}} \]
[Out]
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Rubi [A] time = 0.0104337, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ \frac{x^{3/2}}{3 (b x+2)^{3/2}} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[x]/(2 + b*x)^(5/2),x]
[Out]
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Rubi in Sympy [A] time = 2.13042, size = 14, normalized size = 0.78 \[ \frac{x^{\frac{3}{2}}}{3 \left (b x + 2\right )^{\frac{3}{2}}} \]
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 = 0.0158017, size = 18, normalized size = 1. \[ \frac{x^{3/2}}{3 (b x+2)^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[x]/(2 + b*x)^(5/2),x]
[Out]
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Maple [A] time = 0.006, size = 13, 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 = 1.34672, size = 16, normalized size = 0.89 \[ \frac{x^{\frac{3}{2}}}{3 \,{\left (b x + 2\right )}^{\frac{3}{2}}} \]
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 = 0.208844, size = 16, normalized size = 0.89 \[ \frac{x^{\frac{3}{2}}}{3 \,{\left (b x + 2\right )}^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x)/(b*x + 2)^(5/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 13.0641, size = 27, normalized size = 1.5 \[ \frac{x^{\frac{3}{2}}}{3 b x \sqrt{b x + 2} + 6 \sqrt{b x + 2}} \]
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 = 0.219529, size = 111, normalized size = 6.17 \[ \frac{4 \,{\left (3 \,{\left (\sqrt{b x + 2} \sqrt{b} - \sqrt{{\left (b x + 2\right )} b - 2 \, b}\right )}^{4} \sqrt{b} + 4 \, b^{\frac{5}{2}}\right )}{\left | b \right |}}{3 \,{\left ({\left (\sqrt{b x + 2} \sqrt{b} - \sqrt{{\left (b x + 2\right )} b - 2 \, b}\right )}^{2} + 2 \, b\right )}^{3} b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x)/(b*x + 2)^(5/2),x, algorithm="giac")
[Out]