Optimal. Leaf size=53 \[ -\frac{a^3 \log \left (a+b x^5\right )}{5 b^4}+\frac{a^2 x^5}{5 b^3}-\frac{a x^{10}}{10 b^2}+\frac{x^{15}}{15 b} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0772589, antiderivative size = 53, 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 \[ -\frac{a^3 \log \left (a+b x^5\right )}{5 b^4}+\frac{a^2 x^5}{5 b^3}-\frac{a x^{10}}{10 b^2}+\frac{x^{15}}{15 b} \]
Antiderivative was successfully verified.
[In] Int[x^19/(a + b*x^5),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{a^{3} \log{\left (a + b x^{5} \right )}}{5 b^{4}} - \frac{a \int ^{x^{5}} x\, dx}{5 b^{2}} + \frac{x^{15}}{15 b} + \frac{\int ^{x^{5}} a^{2}\, dx}{5 b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**19/(b*x**5+a),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00960077, size = 53, normalized size = 1. \[ -\frac{a^3 \log \left (a+b x^5\right )}{5 b^4}+\frac{a^2 x^5}{5 b^3}-\frac{a x^{10}}{10 b^2}+\frac{x^{15}}{15 b} \]
Antiderivative was successfully verified.
[In] Integrate[x^19/(a + b*x^5),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.004, size = 46, normalized size = 0.9 \[{\frac{{x}^{5}{a}^{2}}{5\,{b}^{3}}}-{\frac{a{x}^{10}}{10\,{b}^{2}}}+{\frac{{x}^{15}}{15\,b}}-{\frac{{a}^{3}\ln \left ( b{x}^{5}+a \right ) }{5\,{b}^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^19/(b*x^5+a),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.4278, size = 62, normalized size = 1.17 \[ -\frac{a^{3} \log \left (b x^{5} + a\right )}{5 \, b^{4}} + \frac{2 \, b^{2} x^{15} - 3 \, a b x^{10} + 6 \, a^{2} x^{5}}{30 \, b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^19/(b*x^5 + a),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.215513, size = 61, normalized size = 1.15 \[ \frac{2 \, b^{3} x^{15} - 3 \, a b^{2} x^{10} + 6 \, a^{2} b x^{5} - 6 \, a^{3} \log \left (b x^{5} + a\right )}{30 \, b^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^19/(b*x^5 + a),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.51254, size = 44, normalized size = 0.83 \[ - \frac{a^{3} \log{\left (a + b x^{5} \right )}}{5 b^{4}} + \frac{a^{2} x^{5}}{5 b^{3}} - \frac{a x^{10}}{10 b^{2}} + \frac{x^{15}}{15 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**19/(b*x**5+a),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.227641, size = 63, normalized size = 1.19 \[ -\frac{a^{3}{\rm ln}\left ({\left | b x^{5} + a \right |}\right )}{5 \, b^{4}} + \frac{2 \, b^{2} x^{15} - 3 \, a b x^{10} + 6 \, a^{2} x^{5}}{30 \, b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^19/(b*x^5 + a),x, algorithm="giac")
[Out]