Optimal. Leaf size=27 \[ \frac{\left (a+b x^{m+1}\right )^{n+1}}{b (m+1) (n+1)} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0287156, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ \frac{\left (a+b x^{m+1}\right )^{n+1}}{b (m+1) (n+1)} \]
Antiderivative was successfully verified.
[In] Int[x^m*(a + b*x^(1 + m))^n,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 3.3963, size = 19, normalized size = 0.7 \[ \frac{\left (a + b x^{m + 1}\right )^{n + 1}}{b \left (m + 1\right ) \left (n + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**m*(a+b*x**(1+m))**n,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0451166, size = 28, normalized size = 1.04 \[ \frac{\left (a+b x^{m+1}\right )^{n+1}}{b m n+b m+b n+b} \]
Antiderivative was successfully verified.
[In] Integrate[x^m*(a + b*x^(1 + m))^n,x]
[Out]
_______________________________________________________________________________________
Maple [B] time = 0.044, size = 60, normalized size = 2.2 \[{\frac{a{{\rm e}^{n\ln \left ( a+bx{{\rm e}^{m\ln \left ( x \right ) }} \right ) }}}{b \left ( nm+m+n+1 \right ) }}+{\frac{x{{\rm e}^{m\ln \left ( x \right ) }}{{\rm e}^{n\ln \left ( a+bx{{\rm e}^{m\ln \left ( x \right ) }} \right ) }}}{nm+m+n+1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^m*(a+b*x^(1+m))^n,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^(m + 1) + a)^n*x^m,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.236822, size = 47, normalized size = 1.74 \[ \frac{{\left (b x^{m + 1} + a\right )}{\left (b x^{m + 1} + a\right )}^{n}}{b m +{\left (b m + b\right )} n + b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(m + 1) + a)^n*x^m,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**m*(a+b*x**(1+m))**n,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.214024, size = 36, normalized size = 1.33 \[ \frac{{\left (b x^{m + 1} + a\right )}^{n + 1}}{b{\left (m + 1\right )}{\left (n + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(m + 1) + a)^n*x^m,x, algorithm="giac")
[Out]