Optimal. Leaf size=71 \[ -\frac{16 b^2 (a-b x)^{3/2}}{105 a^3 x^{3/2}}-\frac{8 b (a-b x)^{3/2}}{35 a^2 x^{5/2}}-\frac{2 (a-b x)^{3/2}}{7 a x^{7/2}} \]
[Out]
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Rubi [A] time = 0.0452699, antiderivative size = 71, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ -\frac{16 b^2 (a-b x)^{3/2}}{105 a^3 x^{3/2}}-\frac{8 b (a-b x)^{3/2}}{35 a^2 x^{5/2}}-\frac{2 (a-b x)^{3/2}}{7 a x^{7/2}} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[a - b*x]/x^(9/2),x]
[Out]
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Rubi in Sympy [A] time = 6.43434, size = 65, normalized size = 0.92 \[ - \frac{2 \left (a - b x\right )^{\frac{3}{2}}}{7 a x^{\frac{7}{2}}} - \frac{8 b \left (a - b x\right )^{\frac{3}{2}}}{35 a^{2} x^{\frac{5}{2}}} - \frac{16 b^{2} \left (a - b x\right )^{\frac{3}{2}}}{105 a^{3} x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((-b*x+a)**(1/2)/x**(9/2),x)
[Out]
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Mathematica [A] time = 0.0230026, size = 52, normalized size = 0.73 \[ -\frac{2 \sqrt{a-b x} \left (15 a^3-3 a^2 b x-4 a b^2 x^2-8 b^3 x^3\right )}{105 a^3 x^{7/2}} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[a - b*x]/x^(9/2),x]
[Out]
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Maple [A] time = 0.006, size = 36, normalized size = 0.5 \[ -{\frac{16\,{b}^{2}{x}^{2}+24\,abx+30\,{a}^{2}}{105\,{a}^{3}} \left ( -bx+a \right ) ^{{\frac{3}{2}}}{x}^{-{\frac{7}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((-b*x+a)^(1/2)/x^(9/2),x)
[Out]
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Maxima [A] time = 1.33332, size = 66, normalized size = 0.93 \[ -\frac{2 \,{\left (\frac{35 \,{\left (-b x + a\right )}^{\frac{3}{2}} b^{2}}{x^{\frac{3}{2}}} + \frac{42 \,{\left (-b x + a\right )}^{\frac{5}{2}} b}{x^{\frac{5}{2}}} + \frac{15 \,{\left (-b x + a\right )}^{\frac{7}{2}}}{x^{\frac{7}{2}}}\right )}}{105 \, a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-b*x + a)/x^(9/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.2161, size = 62, normalized size = 0.87 \[ \frac{2 \,{\left (8 \, b^{3} x^{3} + 4 \, a b^{2} x^{2} + 3 \, a^{2} b x - 15 \, a^{3}\right )} \sqrt{-b x + a}}{105 \, a^{3} x^{\frac{7}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-b*x + a)/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((-b*x+a)**(1/2)/x**(9/2),x)
[Out]
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GIAC/XCAS [A] time = 0.212143, size = 107, normalized size = 1.51 \[ \frac{{\left (b x - a\right )} \sqrt{-b x + a}{\left (4 \,{\left (b x - a\right )}{\left (\frac{2 \,{\left (b x - a\right )}}{a^{4} b^{5}} + \frac{7}{a^{3} b^{5}}\right )} + \frac{35}{a^{2} b^{5}}\right )} b}{40320 \,{\left ({\left (b x - a\right )} b + a b\right )}^{\frac{7}{2}}{\left | b \right |}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-b*x + a)/x^(9/2),x, algorithm="giac")
[Out]