Optimal. Leaf size=80 \[ \frac{2 b^3 \sqrt{b x+2}}{35 \sqrt{x}}-\frac{2 b^2 \sqrt{b x+2}}{35 x^{3/2}}+\frac{3 b \sqrt{b x+2}}{35 x^{5/2}}-\frac{\sqrt{b x+2}}{7 x^{7/2}} \]
[Out]
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Rubi [A] time = 0.0522062, antiderivative size = 80, 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 \[ \frac{2 b^3 \sqrt{b x+2}}{35 \sqrt{x}}-\frac{2 b^2 \sqrt{b x+2}}{35 x^{3/2}}+\frac{3 b \sqrt{b x+2}}{35 x^{5/2}}-\frac{\sqrt{b x+2}}{7 x^{7/2}} \]
Antiderivative was successfully verified.
[In] Int[1/(x^(9/2)*Sqrt[2 + b*x]),x]
[Out]
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Rubi in Sympy [A] time = 5.96022, size = 73, normalized size = 0.91 \[ \frac{2 b^{3} \sqrt{b x + 2}}{35 \sqrt{x}} - \frac{2 b^{2} \sqrt{b x + 2}}{35 x^{\frac{3}{2}}} + \frac{3 b \sqrt{b x + 2}}{35 x^{\frac{5}{2}}} - \frac{\sqrt{b x + 2}}{7 x^{\frac{7}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**(9/2)/(b*x+2)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0205807, size = 40, normalized size = 0.5 \[ \frac{\sqrt{b x+2} \left (2 b^3 x^3-2 b^2 x^2+3 b x-5\right )}{35 x^{7/2}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^(9/2)*Sqrt[2 + b*x]),x]
[Out]
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Maple [A] time = 0.006, size = 35, normalized size = 0.4 \[{\frac{2\,{b}^{3}{x}^{3}-2\,{b}^{2}{x}^{2}+3\,bx-5}{35}\sqrt{bx+2}{x}^{-{\frac{7}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^(9/2)/(b*x+2)^(1/2),x)
[Out]
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Maxima [A] time = 1.34723, size = 76, normalized size = 0.95 \[ \frac{\sqrt{b x + 2} b^{3}}{8 \, \sqrt{x}} - \frac{{\left (b x + 2\right )}^{\frac{3}{2}} b^{2}}{8 \, x^{\frac{3}{2}}} + \frac{3 \,{\left (b x + 2\right )}^{\frac{5}{2}} b}{40 \, x^{\frac{5}{2}}} - \frac{{\left (b x + 2\right )}^{\frac{7}{2}}}{56 \, x^{\frac{7}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x + 2)*x^(9/2)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.246375, size = 46, normalized size = 0.57 \[ \frac{{\left (2 \, b^{3} x^{3} - 2 \, b^{2} x^{2} + 3 \, b x - 5\right )} \sqrt{b x + 2}}{35 \, x^{\frac{7}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x + 2)*x^(9/2)),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**(9/2)/(b*x+2)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.213796, size = 92, normalized size = 1.15 \[ -\frac{{\left (35 \, b^{7} -{\left (35 \, b^{7} + 2 \,{\left ({\left (b x + 2\right )} b^{7} - 7 \, b^{7}\right )}{\left (b x + 2\right )}\right )}{\left (b x + 2\right )}\right )} \sqrt{b x + 2} b}{35 \,{\left ({\left (b x + 2\right )} b - 2 \, b\right )}^{\frac{7}{2}}{\left | b \right |}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x + 2)*x^(9/2)),x, algorithm="giac")
[Out]