Optimal. Leaf size=92 \[ \frac{32 b^3 \sqrt{a+b x}}{35 a^4 \sqrt{x}}-\frac{16 b^2 \sqrt{a+b x}}{35 a^3 x^{3/2}}+\frac{12 b \sqrt{a+b x}}{35 a^2 x^{5/2}}-\frac{2 \sqrt{a+b x}}{7 a x^{7/2}} \]
[Out]
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Rubi [A] time = 0.0686943, antiderivative size = 92, 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 \[ \frac{32 b^3 \sqrt{a+b x}}{35 a^4 \sqrt{x}}-\frac{16 b^2 \sqrt{a+b x}}{35 a^3 x^{3/2}}+\frac{12 b \sqrt{a+b x}}{35 a^2 x^{5/2}}-\frac{2 \sqrt{a+b x}}{7 a x^{7/2}} \]
Antiderivative was successfully verified.
[In] Int[1/(x^(9/2)*Sqrt[a + b*x]),x]
[Out]
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Rubi in Sympy [A] time = 9.33687, size = 87, normalized size = 0.95 \[ - \frac{2 \sqrt{a + b x}}{7 a x^{\frac{7}{2}}} + \frac{12 b \sqrt{a + b x}}{35 a^{2} x^{\frac{5}{2}}} - \frac{16 b^{2} \sqrt{a + b x}}{35 a^{3} x^{\frac{3}{2}}} + \frac{32 b^{3} \sqrt{a + b x}}{35 a^{4} \sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**(9/2)/(b*x+a)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0281607, size = 51, normalized size = 0.55 \[ -\frac{2 \sqrt{a+b x} \left (5 a^3-6 a^2 b x+8 a b^2 x^2-16 b^3 x^3\right )}{35 a^4 x^{7/2}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^(9/2)*Sqrt[a + b*x]),x]
[Out]
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Maple [A] time = 0.007, size = 46, normalized size = 0.5 \[ -{\frac{-32\,{b}^{3}{x}^{3}+16\,a{b}^{2}{x}^{2}-12\,{a}^{2}bx+10\,{a}^{3}}{35\,{a}^{4}}\sqrt{bx+a}{x}^{-{\frac{7}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^(9/2)/(b*x+a)^(1/2),x)
[Out]
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Maxima [A] time = 1.34327, size = 82, normalized size = 0.89 \[ \frac{2 \,{\left (\frac{35 \, \sqrt{b x + a} b^{3}}{\sqrt{x}} - \frac{35 \,{\left (b x + a\right )}^{\frac{3}{2}} b^{2}}{x^{\frac{3}{2}}} + \frac{21 \,{\left (b x + a\right )}^{\frac{5}{2}} b}{x^{\frac{5}{2}}} - \frac{5 \,{\left (b x + a\right )}^{\frac{7}{2}}}{x^{\frac{7}{2}}}\right )}}{35 \, a^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x + a)*x^(9/2)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.233639, size = 61, normalized size = 0.66 \[ \frac{2 \,{\left (16 \, b^{3} x^{3} - 8 \, a b^{2} x^{2} + 6 \, a^{2} b x - 5 \, a^{3}\right )} \sqrt{b x + a}}{35 \, a^{4} x^{\frac{7}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(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(1/x**(9/2)/(b*x+a)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.212779, size = 111, normalized size = 1.21 \[ -\frac{{\left (2 \,{\left (b x + a\right )}{\left (4 \,{\left (b x + a\right )}{\left (\frac{2 \,{\left (b x + a\right )}}{a^{4} b^{5}} - \frac{7}{a^{3} b^{5}}\right )} + \frac{35}{a^{2} b^{5}}\right )} - \frac{35}{a b^{5}}\right )} \sqrt{b x + a} b}{13440 \,{\left ({\left (b x + a\right )} b - a b\right )}^{\frac{7}{2}}{\left | b \right |}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x + a)*x^(9/2)),x, algorithm="giac")
[Out]