Optimal. Leaf size=43 \[ \frac{4 \log \left (b x^n+2\right )}{b^3 n}-\frac{2 x^n}{b^2 n}+\frac{x^{2 n}}{2 b n} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0593684, antiderivative size = 43, 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 \[ \frac{4 \log \left (b x^n+2\right )}{b^3 n}-\frac{2 x^n}{b^2 n}+\frac{x^{2 n}}{2 b n} \]
Antiderivative was successfully verified.
[In] Int[x^(-1 + 3*n)/(2 + b*x^n),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{\int ^{x^{n}} x\, dx}{b n} - \frac{2 x^{n}}{b^{2} n} + \frac{4 \log{\left (b x^{n} + 2 \right )}}{b^{3} n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(-1+3*n)/(2+b*x**n),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0220743, size = 33, normalized size = 0.77 \[ \frac{b x^n \left (b x^n-4\right )+8 \log \left (b x^n+2\right )}{2 b^3 n} \]
Antiderivative was successfully verified.
[In] Integrate[x^(-1 + 3*n)/(2 + b*x^n),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.032, size = 48, normalized size = 1.1 \[ -2\,{\frac{{{\rm e}^{n\ln \left ( x \right ) }}}{{b}^{2}n}}+{\frac{ \left ({{\rm e}^{n\ln \left ( x \right ) }} \right ) ^{2}}{2\,bn}}+4\,{\frac{\ln \left ( 2+b{{\rm e}^{n\ln \left ( x \right ) }} \right ) }{{b}^{3}n}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(-1+3*n)/(2+b*x^n),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.44422, size = 57, normalized size = 1.33 \[ \frac{b x^{2 \, n} - 4 \, x^{n}}{2 \, b^{2} n} + \frac{4 \, \log \left (\frac{b x^{n} + 2}{b}\right )}{b^{3} n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^(3*n - 1)/(b*x^n + 2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.225858, size = 46, normalized size = 1.07 \[ \frac{b^{2} x^{2 \, n} - 4 \, b x^{n} + 8 \, \log \left (b x^{n} + 2\right )}{2 \, b^{3} n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^(3*n - 1)/(b*x^n + 2),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)/(2+b*x**n),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x^{3 \, n - 1}}{b x^{n} + 2}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^(3*n - 1)/(b*x^n + 2),x, algorithm="giac")
[Out]