Optimal. Leaf size=75 \[ -\frac{2 \sqrt{2-b x}}{3 x^{3/2}}+\frac{1}{x^{3/2} \sqrt{2-b x}}+\frac{1}{3 x^{3/2} (2-b x)^{3/2}}-\frac{2 b \sqrt{2-b x}}{3 \sqrt{x}} \]
[Out]
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Rubi [A] time = 0.0478922, antiderivative size = 75, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 2, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ -\frac{2 \sqrt{2-b x}}{3 x^{3/2}}+\frac{1}{x^{3/2} \sqrt{2-b x}}+\frac{1}{3 x^{3/2} (2-b x)^{3/2}}-\frac{2 b \sqrt{2-b x}}{3 \sqrt{x}} \]
Antiderivative was successfully verified.
[In] Int[1/(x^(5/2)*(2 - b*x)^(5/2)),x]
[Out]
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Rubi in Sympy [A] time = 6.17764, size = 66, normalized size = 0.88 \[ - \frac{2 b \sqrt{- b x + 2}}{3 \sqrt{x}} - \frac{2 \sqrt{- b x + 2}}{3 x^{\frac{3}{2}}} + \frac{1}{x^{\frac{3}{2}} \sqrt{- b x + 2}} + \frac{1}{3 x^{\frac{3}{2}} \left (- b x + 2\right )^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**(5/2)/(-b*x+2)**(5/2),x)
[Out]
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Mathematica [A] time = 0.0331432, size = 41, normalized size = 0.55 \[ -\frac{2 b^3 x^3-6 b^2 x^2+3 b x+1}{3 x^{3/2} (2-b x)^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^(5/2)*(2 - b*x)^(5/2)),x]
[Out]
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Maple [A] time = 0.006, size = 36, normalized size = 0.5 \[ -{\frac{2\,{b}^{3}{x}^{3}-6\,{b}^{2}{x}^{2}+3\,bx+1}{3}{x}^{-{\frac{3}{2}}} \left ( -bx+2 \right ) ^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^(5/2)/(-b*x+2)^(5/2),x)
[Out]
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Maxima [A] time = 1.3435, size = 78, normalized size = 1.04 \[ -\frac{3 \, \sqrt{-b x + 2} b}{8 \, \sqrt{x}} + \frac{{\left (b^{3} - \frac{9 \,{\left (b x - 2\right )} b^{2}}{x}\right )} x^{\frac{3}{2}}}{24 \,{\left (-b x + 2\right )}^{\frac{3}{2}}} - \frac{{\left (-b x + 2\right )}^{\frac{3}{2}}}{24 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((-b*x + 2)^(5/2)*x^(5/2)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.24165, size = 62, normalized size = 0.83 \[ \frac{2 \, b^{3} x^{3} - 6 \, b^{2} x^{2} + 3 \, b x + 1}{3 \,{\left (b x^{2} - 2 \, x\right )} \sqrt{-b x + 2} \sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((-b*x + 2)^(5/2)*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(1/x**(5/2)/(-b*x+2)**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.228596, size = 247, normalized size = 3.29 \[ -\frac{{\left (4 \,{\left (b x - 2\right )} b^{2}{\left | b \right |} + 9 \, b^{2}{\left | b \right |}\right )} \sqrt{-b x + 2}}{12 \,{\left ({\left (b x - 2\right )} b + 2 \, b\right )}^{\frac{3}{2}}} - \frac{3 \,{\left (\sqrt{-b x + 2} \sqrt{-b} - \sqrt{{\left (b x - 2\right )} b + 2 \, b}\right )}^{4} \sqrt{-b} b^{3} - 18 \,{\left (\sqrt{-b x + 2} \sqrt{-b} - \sqrt{{\left (b x - 2\right )} b + 2 \, b}\right )}^{2} \sqrt{-b} b^{4} + 16 \, \sqrt{-b} b^{5}}{3 \,{\left ({\left (\sqrt{-b x + 2} \sqrt{-b} - \sqrt{{\left (b x - 2\right )} b + 2 \, b}\right )}^{2} - 2 \, b\right )}^{3}{\left | b \right |}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((-b*x + 2)^(5/2)*x^(5/2)),x, algorithm="giac")
[Out]