Optimal. Leaf size=59 \[ -\frac{2 b^2 \sqrt{b x+2}}{15 \sqrt{x}}+\frac{2 b \sqrt{b x+2}}{15 x^{3/2}}-\frac{\sqrt{b x+2}}{5 x^{5/2}} \]
[Out]
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Rubi [A] time = 0.0363981, antiderivative size = 59, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ -\frac{2 b^2 \sqrt{b x+2}}{15 \sqrt{x}}+\frac{2 b \sqrt{b x+2}}{15 x^{3/2}}-\frac{\sqrt{b x+2}}{5 x^{5/2}} \]
Antiderivative was successfully verified.
[In] Int[1/(x^(7/2)*Sqrt[2 + b*x]),x]
[Out]
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Rubi in Sympy [A] time = 4.43052, size = 53, normalized size = 0.9 \[ - \frac{2 b^{2} \sqrt{b x + 2}}{15 \sqrt{x}} + \frac{2 b \sqrt{b x + 2}}{15 x^{\frac{3}{2}}} - \frac{\sqrt{b x + 2}}{5 x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**(7/2)/(b*x+2)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0194562, size = 32, normalized size = 0.54 \[ -\frac{\sqrt{b x+2} \left (2 b^2 x^2-2 b x+3\right )}{15 x^{5/2}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^(7/2)*Sqrt[2 + b*x]),x]
[Out]
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Maple [A] time = 0.007, size = 27, normalized size = 0.5 \[ -{\frac{2\,{b}^{2}{x}^{2}-2\,bx+3}{15}\sqrt{bx+2}{x}^{-{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^(7/2)/(b*x+2)^(1/2),x)
[Out]
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Maxima [A] time = 1.34078, size = 55, normalized size = 0.93 \[ -\frac{\sqrt{b x + 2} b^{2}}{4 \, \sqrt{x}} + \frac{{\left (b x + 2\right )}^{\frac{3}{2}} b}{6 \, x^{\frac{3}{2}}} - \frac{{\left (b x + 2\right )}^{\frac{5}{2}}}{20 \, x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x + 2)*x^(7/2)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.208186, size = 35, normalized size = 0.59 \[ -\frac{{\left (2 \, b^{2} x^{2} - 2 \, b x + 3\right )} \sqrt{b x + 2}}{15 \, x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x + 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)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.213216, size = 74, normalized size = 1.25 \[ -\frac{{\left (15 \, b^{5} + 2 \,{\left ({\left (b x + 2\right )} b^{5} - 5 \, b^{5}\right )}{\left (b x + 2\right )}\right )} \sqrt{b x + 2} b}{15 \,{\left ({\left (b x + 2\right )} b - 2 \, b\right )}^{\frac{5}{2}}{\left | b \right |}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x + 2)*x^(7/2)),x, algorithm="giac")
[Out]