Optimal. Leaf size=48 \[ \frac{4 b \sqrt{a+b x^5}}{15 a^2 x^{5/2}}-\frac{2 \sqrt{a+b x^5}}{15 a x^{15/2}} \]
[Out]
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Rubi [A] time = 0.0427456, antiderivative size = 48, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118 \[ \frac{4 b \sqrt{a+b x^5}}{15 a^2 x^{5/2}}-\frac{2 \sqrt{a+b x^5}}{15 a x^{15/2}} \]
Antiderivative was successfully verified.
[In] Int[1/(x^(17/2)*Sqrt[a + b*x^5]),x]
[Out]
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Rubi in Sympy [A] time = 4.53086, size = 42, normalized size = 0.88 \[ - \frac{2 \sqrt{a + b x^{5}}}{15 a x^{\frac{15}{2}}} + \frac{4 b \sqrt{a + b x^{5}}}{15 a^{2} x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**(17/2)/(b*x**5+a)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0351076, size = 31, normalized size = 0.65 \[ -\frac{2 \left (a-2 b x^5\right ) \sqrt{a+b x^5}}{15 a^2 x^{15/2}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^(17/2)*Sqrt[a + b*x^5]),x]
[Out]
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Maple [A] time = 0.007, size = 26, normalized size = 0.5 \[ -{\frac{-4\,b{x}^{5}+2\,a}{15\,{a}^{2}}\sqrt{b{x}^{5}+a}{x}^{-{\frac{15}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^(17/2)/(b*x^5+a)^(1/2),x)
[Out]
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Maxima [A] time = 1.43893, size = 47, normalized size = 0.98 \[ \frac{2 \,{\left (\frac{3 \, \sqrt{b x^{5} + a} b}{x^{\frac{5}{2}}} - \frac{{\left (b x^{5} + a\right )}^{\frac{3}{2}}}{x^{\frac{15}{2}}}\right )}}{15 \, a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x^5 + a)*x^(17/2)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.228314, size = 36, normalized size = 0.75 \[ \frac{2 \,{\left (2 \, b x^{5} - a\right )} \sqrt{b x^{5} + a}}{15 \, a^{2} x^{\frac{15}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x^5 + a)*x^(17/2)),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**(17/2)/(b*x**5+a)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.232102, size = 49, normalized size = 1.02 \[ -\frac{4 \, b^{\frac{3}{2}}}{15 \, a^{2}} - \frac{2 \,{\left ({\left (b + \frac{a}{x^{5}}\right )}^{\frac{3}{2}} - 3 \, \sqrt{b + \frac{a}{x^{5}}} b\right )}}{15 \, a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x^5 + a)*x^(17/2)),x, algorithm="giac")
[Out]