Optimal. Leaf size=74 \[ -\frac{2 b^2 \sqrt{b x+2}}{5 \sqrt{x}}+\frac{2 b \sqrt{b x+2}}{5 x^{3/2}}-\frac{3 \sqrt{b x+2}}{5 x^{5/2}}+\frac{1}{x^{5/2} \sqrt{b x+2}} \]
[Out]
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Rubi [A] time = 0.0532417, antiderivative size = 74, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ -\frac{2 b^2 \sqrt{b x+2}}{5 \sqrt{x}}+\frac{2 b \sqrt{b x+2}}{5 x^{3/2}}-\frac{3 \sqrt{b x+2}}{5 x^{5/2}}+\frac{1}{x^{5/2} \sqrt{b x+2}} \]
Antiderivative was successfully verified.
[In] Int[1/(x^(7/2)*(2 + b*x)^(3/2)),x]
[Out]
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Rubi in Sympy [A] time = 5.93663, size = 70, normalized size = 0.95 \[ - \frac{2 b^{2} \sqrt{b x + 2}}{5 \sqrt{x}} + \frac{2 b \sqrt{b x + 2}}{5 x^{\frac{3}{2}}} - \frac{3 \sqrt{b x + 2}}{5 x^{\frac{5}{2}}} + \frac{1}{x^{\frac{5}{2}} \sqrt{b x + 2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**(7/2)/(b*x+2)**(3/2),x)
[Out]
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Mathematica [A] time = 0.0247523, size = 39, normalized size = 0.53 \[ \frac{-2 b^3 x^3-2 b^2 x^2+b x-1}{5 x^{5/2} \sqrt{b x+2}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^(7/2)*(2 + b*x)^(3/2)),x]
[Out]
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Maple [A] time = 0.007, size = 35, normalized size = 0.5 \[ -{\frac{2\,{b}^{3}{x}^{3}+2\,{b}^{2}{x}^{2}-bx+1}{5}{x}^{-{\frac{5}{2}}}{\frac{1}{\sqrt{bx+2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^(7/2)/(b*x+2)^(3/2),x)
[Out]
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Maxima [A] time = 1.34621, size = 76, normalized size = 1.03 \[ -\frac{b^{3} \sqrt{x}}{8 \, \sqrt{b x + 2}} - \frac{3 \, \sqrt{b x + 2} b^{2}}{8 \, \sqrt{x}} + \frac{{\left (b x + 2\right )}^{\frac{3}{2}} b}{8 \, x^{\frac{3}{2}}} - \frac{{\left (b x + 2\right )}^{\frac{5}{2}}}{40 \, x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + 2)^(3/2)*x^(7/2)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.214832, size = 46, normalized size = 0.62 \[ -\frac{2 \, b^{3} x^{3} + 2 \, b^{2} x^{2} - b x + 1}{5 \, \sqrt{b x + 2} x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + 2)^(3/2)*x^(7/2)),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**(7/2)/(b*x+2)**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.220174, size = 144, normalized size = 1.95 \[ -\frac{b^{\frac{9}{2}}}{2 \,{\left ({\left (\sqrt{b x + 2} \sqrt{b} - \sqrt{{\left (b x + 2\right )} b - 2 \, b}\right )}^{2} + 2 \, b\right )}{\left | b \right |}} - \frac{{\left (\frac{60 \, b^{6}}{{\left | b \right |}} +{\left (\frac{11 \,{\left (b x + 2\right )} b^{6}}{{\left | b \right |}} - \frac{50 \, b^{6}}{{\left | b \right |}}\right )}{\left (b x + 2\right )}\right )} \sqrt{b x + 2}}{40 \,{\left ({\left (b x + 2\right )} b - 2 \, b\right )}^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + 2)^(3/2)*x^(7/2)),x, algorithm="giac")
[Out]