Optimal. Leaf size=38 \[ \frac{b (b x+2)^{3/2}}{15 x^{3/2}}-\frac{(b x+2)^{3/2}}{5 x^{5/2}} \]
[Out]
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Rubi [A] time = 0.0223227, antiderivative size = 38, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{b (b x+2)^{3/2}}{15 x^{3/2}}-\frac{(b x+2)^{3/2}}{5 x^{5/2}} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[2 + b*x]/x^(7/2),x]
[Out]
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Rubi in Sympy [A] time = 2.86492, size = 31, normalized size = 0.82 \[ \frac{b \left (b x + 2\right )^{\frac{3}{2}}}{15 x^{\frac{3}{2}}} - \frac{\left (b x + 2\right )^{\frac{3}{2}}}{5 x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+2)**(1/2)/x**(7/2),x)
[Out]
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Mathematica [A] time = 0.0151269, size = 31, normalized size = 0.82 \[ \frac{\sqrt{b x+2} \left (b^2 x^2-b x-6\right )}{15 x^{5/2}} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[2 + b*x]/x^(7/2),x]
[Out]
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Maple [A] time = 0.005, size = 18, normalized size = 0.5 \[{\frac{bx-3}{15} \left ( bx+2 \right ) ^{{\frac{3}{2}}}{x}^{-{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+2)^(1/2)/x^(7/2),x)
[Out]
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Maxima [A] time = 1.34219, size = 35, normalized size = 0.92 \[ \frac{{\left (b x + 2\right )}^{\frac{3}{2}} b}{6 \, x^{\frac{3}{2}}} - \frac{{\left (b x + 2\right )}^{\frac{5}{2}}}{10 \, x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b*x + 2)/x^(7/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.209882, size = 34, normalized size = 0.89 \[ \frac{{\left (b^{2} x^{2} - b x - 6\right )} \sqrt{b x + 2}}{15 \, x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b*x + 2)/x^(7/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 140.378, size = 56, normalized size = 1.47 \[ \frac{b^{\frac{5}{2}} \sqrt{1 + \frac{2}{b x}}}{15} - \frac{b^{\frac{3}{2}} \sqrt{1 + \frac{2}{b x}}}{15 x} - \frac{2 \sqrt{b} \sqrt{1 + \frac{2}{b x}}}{5 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+2)**(1/2)/x**(7/2),x)
[Out]
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GIAC/XCAS [A] time = 0.208415, size = 57, normalized size = 1.5 \[ \frac{{\left ({\left (b x + 2\right )} b^{5} - 5 \, b^{5}\right )}{\left (b x + 2\right )}^{\frac{3}{2}} b}{15 \,{\left ({\left (b x + 2\right )} b - 2 \, b\right )}^{\frac{5}{2}}{\left | b \right |}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b*x + 2)/x^(7/2),x, algorithm="giac")
[Out]