Optimal. Leaf size=68 \[ \frac{b^{7/2} \tan ^{-1}\left (\frac{\sqrt{c} x}{\sqrt{b}}\right )}{c^{9/2}}-\frac{b^3 x}{c^4}+\frac{b^2 x^3}{3 c^3}-\frac{b x^5}{5 c^2}+\frac{x^7}{7 c} \]
[Out]
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Rubi [A] time = 0.0867442, antiderivative size = 68, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.176 \[ \frac{b^{7/2} \tan ^{-1}\left (\frac{\sqrt{c} x}{\sqrt{b}}\right )}{c^{9/2}}-\frac{b^3 x}{c^4}+\frac{b^2 x^3}{3 c^3}-\frac{b x^5}{5 c^2}+\frac{x^7}{7 c} \]
Antiderivative was successfully verified.
[In] Int[x^10/(b*x^2 + c*x^4),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{b^{\frac{7}{2}} \operatorname{atan}{\left (\frac{\sqrt{c} x}{\sqrt{b}} \right )}}{c^{\frac{9}{2}}} + \frac{b^{2} x^{3}}{3 c^{3}} - \frac{b x^{5}}{5 c^{2}} + \frac{x^{7}}{7 c} - \frac{\int b^{3}\, dx}{c^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**10/(c*x**4+b*x**2),x)
[Out]
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Mathematica [A] time = 0.0465441, size = 68, normalized size = 1. \[ \frac{b^{7/2} \tan ^{-1}\left (\frac{\sqrt{c} x}{\sqrt{b}}\right )}{c^{9/2}}-\frac{b^3 x}{c^4}+\frac{b^2 x^3}{3 c^3}-\frac{b x^5}{5 c^2}+\frac{x^7}{7 c} \]
Antiderivative was successfully verified.
[In] Integrate[x^10/(b*x^2 + c*x^4),x]
[Out]
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Maple [A] time = 0.008, size = 60, normalized size = 0.9 \[{\frac{{x}^{7}}{7\,c}}-{\frac{b{x}^{5}}{5\,{c}^{2}}}+{\frac{{b}^{2}{x}^{3}}{3\,{c}^{3}}}-{\frac{{b}^{3}x}{{c}^{4}}}+{\frac{{b}^{4}}{{c}^{4}}\arctan \left ({cx{\frac{1}{\sqrt{bc}}}} \right ){\frac{1}{\sqrt{bc}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^10/(c*x^4+b*x^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^10/(c*x^4 + b*x^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.260012, size = 1, normalized size = 0.01 \[ \left [\frac{30 \, c^{3} x^{7} - 42 \, b c^{2} x^{5} + 70 \, b^{2} c x^{3} + 105 \, b^{3} \sqrt{-\frac{b}{c}} \log \left (\frac{c x^{2} + 2 \, c x \sqrt{-\frac{b}{c}} - b}{c x^{2} + b}\right ) - 210 \, b^{3} x}{210 \, c^{4}}, \frac{15 \, c^{3} x^{7} - 21 \, b c^{2} x^{5} + 35 \, b^{2} c x^{3} + 105 \, b^{3} \sqrt{\frac{b}{c}} \arctan \left (\frac{x}{\sqrt{\frac{b}{c}}}\right ) - 105 \, b^{3} x}{105 \, c^{4}}\right ] \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^10/(c*x^4 + b*x^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.33467, size = 107, normalized size = 1.57 \[ - \frac{b^{3} x}{c^{4}} + \frac{b^{2} x^{3}}{3 c^{3}} - \frac{b x^{5}}{5 c^{2}} - \frac{\sqrt{- \frac{b^{7}}{c^{9}}} \log{\left (x - \frac{c^{4} \sqrt{- \frac{b^{7}}{c^{9}}}}{b^{3}} \right )}}{2} + \frac{\sqrt{- \frac{b^{7}}{c^{9}}} \log{\left (x + \frac{c^{4} \sqrt{- \frac{b^{7}}{c^{9}}}}{b^{3}} \right )}}{2} + \frac{x^{7}}{7 c} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**10/(c*x**4+b*x**2),x)
[Out]
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GIAC/XCAS [A] time = 0.268679, size = 88, normalized size = 1.29 \[ \frac{b^{4} \arctan \left (\frac{c x}{\sqrt{b c}}\right )}{\sqrt{b c} c^{4}} + \frac{15 \, c^{6} x^{7} - 21 \, b c^{5} x^{5} + 35 \, b^{2} c^{4} x^{3} - 105 \, b^{3} c^{3} x}{105 \, c^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^10/(c*x^4 + b*x^2),x, algorithm="giac")
[Out]