Optimal. Leaf size=44 \[ \frac{c \left (a+c x^4\right )^{3/2}}{15 a^2 x^6}-\frac{\left (a+c x^4\right )^{3/2}}{10 a x^{10}} \]
[Out]
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Rubi [A] time = 0.039715, antiderivative size = 44, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{c \left (a+c x^4\right )^{3/2}}{15 a^2 x^6}-\frac{\left (a+c x^4\right )^{3/2}}{10 a x^{10}} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[a + c*x^4]/x^11,x]
[Out]
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Rubi in Sympy [A] time = 4.28462, size = 36, normalized size = 0.82 \[ - \frac{\left (a + c x^{4}\right )^{\frac{3}{2}}}{10 a x^{10}} + \frac{c \left (a + c x^{4}\right )^{\frac{3}{2}}}{15 a^{2} x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**4+a)**(1/2)/x**11,x)
[Out]
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Mathematica [A] time = 0.0236378, size = 41, normalized size = 0.93 \[ -\frac{\sqrt{a+c x^4} \left (3 a^2+a c x^4-2 c^2 x^8\right )}{30 a^2 x^{10}} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[a + c*x^4]/x^11,x]
[Out]
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Maple [A] time = 0.007, size = 28, normalized size = 0.6 \[ -{\frac{-2\,c{x}^{4}+3\,a}{30\,{x}^{10}{a}^{2}} \left ( c{x}^{4}+a \right ) ^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^4+a)^(1/2)/x^11,x)
[Out]
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Maxima [A] time = 1.44049, size = 47, normalized size = 1.07 \[ \frac{\frac{5 \,{\left (c x^{4} + a\right )}^{\frac{3}{2}} c}{x^{6}} - \frac{3 \,{\left (c x^{4} + a\right )}^{\frac{5}{2}}}{x^{10}}}{30 \, a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(c*x^4 + a)/x^11,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.278824, size = 51, normalized size = 1.16 \[ \frac{{\left (2 \, c^{2} x^{8} - a c x^{4} - 3 \, a^{2}\right )} \sqrt{c x^{4} + a}}{30 \, a^{2} x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(c*x^4 + a)/x^11,x, algorithm="fricas")
[Out]
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Sympy [A] time = 6.08287, size = 66, normalized size = 1.5 \[ - \frac{\sqrt{c} \sqrt{\frac{a}{c x^{4}} + 1}}{10 x^{8}} - \frac{c^{\frac{3}{2}} \sqrt{\frac{a}{c x^{4}} + 1}}{30 a x^{4}} + \frac{c^{\frac{5}{2}} \sqrt{\frac{a}{c x^{4}} + 1}}{15 a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**4+a)**(1/2)/x**11,x)
[Out]
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GIAC/XCAS [A] time = 0.216665, size = 39, normalized size = 0.89 \[ -\frac{3 \,{\left (c + \frac{a}{x^{4}}\right )}^{\frac{5}{2}} - 5 \,{\left (c + \frac{a}{x^{4}}\right )}^{\frac{3}{2}} c}{30 \, a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(c*x^4 + a)/x^11,x, algorithm="giac")
[Out]