Optimal. Leaf size=104 \[ -\frac{a^2 \tanh ^{-1}\left (\frac{\sqrt{b} \sqrt{c+d x^6}}{\sqrt{b c-a d}}\right )}{3 b^{5/2} \sqrt{b c-a d}}-\frac{\sqrt{c+d x^6} (a d+b c)}{3 b^2 d^2}+\frac{\left (c+d x^6\right )^{3/2}}{9 b d^2} \]
[Out]
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Rubi [A] time = 0.291659, antiderivative size = 104, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 4, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.167 \[ -\frac{a^2 \tanh ^{-1}\left (\frac{\sqrt{b} \sqrt{c+d x^6}}{\sqrt{b c-a d}}\right )}{3 b^{5/2} \sqrt{b c-a d}}-\frac{\sqrt{c+d x^6} (a d+b c)}{3 b^2 d^2}+\frac{\left (c+d x^6\right )^{3/2}}{9 b d^2} \]
Antiderivative was successfully verified.
[In] Int[x^17/((a + b*x^6)*Sqrt[c + d*x^6]),x]
[Out]
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Rubi in Sympy [A] time = 30.4419, size = 88, normalized size = 0.85 \[ \frac{a^{2} \operatorname{atan}{\left (\frac{\sqrt{b} \sqrt{c + d x^{6}}}{\sqrt{a d - b c}} \right )}}{3 b^{\frac{5}{2}} \sqrt{a d - b c}} + \frac{\left (c + d x^{6}\right )^{\frac{3}{2}}}{9 b d^{2}} - \frac{\sqrt{c + d x^{6}} \left (a d + b c\right )}{3 b^{2} d^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**17/(b*x**6+a)/(d*x**6+c)**(1/2),x)
[Out]
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Mathematica [A] time = 0.272446, size = 91, normalized size = 0.88 \[ \frac{\sqrt{c+d x^6} \left (-3 a d-2 b c+b d x^6\right )}{9 b^2 d^2}-\frac{a^2 \tanh ^{-1}\left (\frac{\sqrt{b} \sqrt{c+d x^6}}{\sqrt{b c-a d}}\right )}{3 b^{5/2} \sqrt{b c-a d}} \]
Antiderivative was successfully verified.
[In] Integrate[x^17/((a + b*x^6)*Sqrt[c + d*x^6]),x]
[Out]
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Maple [F] time = 0.098, size = 0, normalized size = 0. \[ \int{\frac{{x}^{17}}{b{x}^{6}+a}{\frac{1}{\sqrt{d{x}^{6}+c}}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^17/(b*x^6+a)/(d*x^6+c)^(1/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^17/((b*x^6 + a)*sqrt(d*x^6 + c)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.217275, size = 1, normalized size = 0.01 \[ \left [\frac{3 \, a^{2} d^{2} \log \left (\frac{{\left (b d x^{6} + 2 \, b c - a d\right )} \sqrt{b^{2} c - a b d} - 2 \, \sqrt{d x^{6} + c}{\left (b^{2} c - a b d\right )}}{b x^{6} + a}\right ) + 2 \,{\left (b d x^{6} - 2 \, b c - 3 \, a d\right )} \sqrt{d x^{6} + c} \sqrt{b^{2} c - a b d}}{18 \, \sqrt{b^{2} c - a b d} b^{2} d^{2}}, -\frac{3 \, a^{2} d^{2} \arctan \left (-\frac{b c - a d}{\sqrt{d x^{6} + c} \sqrt{-b^{2} c + a b d}}\right ) -{\left (b d x^{6} - 2 \, b c - 3 \, a d\right )} \sqrt{d x^{6} + c} \sqrt{-b^{2} c + a b d}}{9 \, \sqrt{-b^{2} c + a b d} b^{2} d^{2}}\right ] \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^17/((b*x^6 + a)*sqrt(d*x^6 + c)),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(x**17/(b*x**6+a)/(d*x**6+c)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.217833, size = 143, normalized size = 1.38 \[ \frac{a^{2} \arctan \left (\frac{\sqrt{d x^{6} + c} b}{\sqrt{-b^{2} c + a b d}}\right )}{3 \, \sqrt{-b^{2} c + a b d} b^{2}} + \frac{{\left (d x^{6} + c\right )}^{\frac{3}{2}} b^{2} d^{4} - 3 \, \sqrt{d x^{6} + c} b^{2} c d^{4} - 3 \, \sqrt{d x^{6} + c} a b d^{5}}{9 \, b^{3} d^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^17/((b*x^6 + a)*sqrt(d*x^6 + c)),x, algorithm="giac")
[Out]