Optimal. Leaf size=85 \[ -\frac{a^5 x^{-3 n}}{3 n}-\frac{5 a^4 b x^{-2 n}}{2 n}-\frac{10 a^3 b^2 x^{-n}}{n}+10 a^2 b^3 \log (x)+\frac{5 a b^4 x^n}{n}+\frac{b^5 x^{2 n}}{2 n} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0962733, antiderivative size = 85, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118 \[ -\frac{a^5 x^{-3 n}}{3 n}-\frac{5 a^4 b x^{-2 n}}{2 n}-\frac{10 a^3 b^2 x^{-n}}{n}+10 a^2 b^3 \log (x)+\frac{5 a b^4 x^n}{n}+\frac{b^5 x^{2 n}}{2 n} \]
Antiderivative was successfully verified.
[In] Int[x^(-1 - 3*n)*(a + b*x^n)^5,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{a^{5} x^{- 3 n}}{3 n} - \frac{5 a^{4} b x^{- 2 n}}{2 n} - \frac{10 a^{3} b^{2} x^{- n}}{n} + \frac{10 a^{2} b^{3} \log{\left (x^{n} \right )}}{n} + \frac{5 a b^{4} x^{n}}{n} + \frac{b^{5} \int ^{x^{n}} x\, dx}{n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(-1-3*n)*(a+b*x**n)**5,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0825211, size = 72, normalized size = 0.85 \[ -\frac{2 a^5 x^{-3 n}+15 a^4 b x^{-2 n}+60 a^3 b^2 x^{-n}-60 a^2 b^3 n \log (x)-30 a b^4 x^n-3 b^5 x^{2 n}}{6 n} \]
Antiderivative was successfully verified.
[In] Integrate[x^(-1 - 3*n)*(a + b*x^n)^5,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.028, size = 98, normalized size = 1.2 \[{\frac{1}{ \left ({{\rm e}^{n\ln \left ( x \right ) }} \right ) ^{3}} \left ( 10\,{a}^{2}{b}^{3}\ln \left ( x \right ) \left ({{\rm e}^{n\ln \left ( x \right ) }} \right ) ^{3}-{\frac{{a}^{5}}{3\,n}}+{\frac{{b}^{5} \left ({{\rm e}^{n\ln \left ( x \right ) }} \right ) ^{5}}{2\,n}}+5\,{\frac{a{b}^{4} \left ({{\rm e}^{n\ln \left ( x \right ) }} \right ) ^{4}}{n}}-10\,{\frac{{a}^{3}{b}^{2} \left ({{\rm e}^{n\ln \left ( x \right ) }} \right ) ^{2}}{n}}-{\frac{5\,{a}^{4}b{{\rm e}^{n\ln \left ( x \right ) }}}{2\,n}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(-1-3*n)*(a+b*x^n)^5,x)
[Out]
_______________________________________________________________________________________
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((b*x^n + a)^5*x^(-3*n - 1),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.227236, size = 104, normalized size = 1.22 \[ \frac{60 \, a^{2} b^{3} n x^{3 \, n} \log \left (x\right ) + 3 \, b^{5} x^{5 \, n} + 30 \, a b^{4} x^{4 \, n} - 60 \, a^{3} b^{2} x^{2 \, n} - 15 \, a^{4} b x^{n} - 2 \, a^{5}}{6 \, n x^{3 \, n}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^n + a)^5*x^(-3*n - 1),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
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**(-1-3*n)*(a+b*x**n)**5,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.226243, size = 111, normalized size = 1.31 \[ \frac{{\left (60 \, a^{2} b^{3} n e^{\left (3 \, n{\rm ln}\left (x\right )\right )}{\rm ln}\left (x\right ) + 3 \, b^{5} e^{\left (5 \, n{\rm ln}\left (x\right )\right )} + 30 \, a b^{4} e^{\left (4 \, n{\rm ln}\left (x\right )\right )} - 60 \, a^{3} b^{2} e^{\left (2 \, n{\rm ln}\left (x\right )\right )} - 15 \, a^{4} b e^{\left (n{\rm ln}\left (x\right )\right )} - 2 \, a^{5}\right )} e^{\left (-3 \, n{\rm ln}\left (x\right )\right )}}{6 \, n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^n + a)^5*x^(-3*n - 1),x, algorithm="giac")
[Out]