Optimal. Leaf size=46 \[ -\frac{a^2}{4 c^3 \left (a+c x^4\right )}-\frac{a \log \left (a+c x^4\right )}{2 c^3}+\frac{x^4}{4 c^2} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0758085, antiderivative size = 46, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ -\frac{a^2}{4 c^3 \left (a+c x^4\right )}-\frac{a \log \left (a+c x^4\right )}{2 c^3}+\frac{x^4}{4 c^2} \]
Antiderivative was successfully verified.
[In] Int[x^11/(a + c*x^4)^2,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{a^{2}}{4 c^{3} \left (a + c x^{4}\right )} - \frac{a \log{\left (a + c x^{4} \right )}}{2 c^{3}} + \frac{\int ^{x^{4}} \frac{1}{c^{2}}\, dx}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**11/(c*x**4+a)**2,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0344519, size = 38, normalized size = 0.83 \[ \frac{-\frac{a^2}{a+c x^4}-2 a \log \left (a+c x^4\right )+c x^4}{4 c^3} \]
Antiderivative was successfully verified.
[In] Integrate[x^11/(a + c*x^4)^2,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.019, size = 41, normalized size = 0.9 \[{\frac{{x}^{4}}{4\,{c}^{2}}}-{\frac{{a}^{2}}{4\,{c}^{3} \left ( c{x}^{4}+a \right ) }}-{\frac{a\ln \left ( c{x}^{4}+a \right ) }{2\,{c}^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^11/(c*x^4+a)^2,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.43671, size = 58, normalized size = 1.26 \[ \frac{x^{4}}{4 \, c^{2}} - \frac{a^{2}}{4 \,{\left (c^{4} x^{4} + a c^{3}\right )}} - \frac{a \log \left (c x^{4} + a\right )}{2 \, c^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/(c*x^4 + a)^2,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.224977, size = 76, normalized size = 1.65 \[ \frac{c^{2} x^{8} + a c x^{4} - a^{2} - 2 \,{\left (a c x^{4} + a^{2}\right )} \log \left (c x^{4} + a\right )}{4 \,{\left (c^{4} x^{4} + a c^{3}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/(c*x^4 + a)^2,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 2.04735, size = 41, normalized size = 0.89 \[ - \frac{a^{2}}{4 a c^{3} + 4 c^{4} x^{4}} - \frac{a \log{\left (a + c x^{4} \right )}}{2 c^{3}} + \frac{x^{4}}{4 c^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**11/(c*x**4+a)**2,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.22016, size = 66, normalized size = 1.43 \[ \frac{x^{4}}{4 \, c^{2}} - \frac{a{\rm ln}\left ({\left | c x^{4} + a \right |}\right )}{2 \, c^{3}} + \frac{2 \, a c x^{4} + a^{2}}{4 \,{\left (c x^{4} + a\right )} c^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/(c*x^4 + a)^2,x, algorithm="giac")
[Out]