Optimal. Leaf size=23 \[ x^2 \left (a+b x+c x^2+d x^3\right )^{p+1} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0210664, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 49, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.02 \[ x^2 \left (a+b x+c x^2+d x^3\right )^{p+1} \]
Antiderivative was successfully verified.
[In] Int[x*(a + b*x + c*x^2 + d*x^3)^p*(2*a + b*(3 + p)*x + c*(4 + 2*p)*x^2 + d*(5 + 3*p)*x^3),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(d*x**3+c*x**2+b*x+a)**p*(2*a+b*(3+p)*x+c*(4+2*p)*x**2+d*(5+3*p)*x**3),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0590705, size = 21, normalized size = 0.91 \[ x^2 (a+x (b+x (c+d x)))^{p+1} \]
Antiderivative was successfully verified.
[In] Integrate[x*(a + b*x + c*x^2 + d*x^3)^p*(2*a + b*(3 + p)*x + c*(4 + 2*p)*x^2 + d*(5 + 3*p)*x^3),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.009, size = 24, normalized size = 1. \[{x}^{2} \left ( d{x}^{3}+c{x}^{2}+bx+a \right ) ^{1+p} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(d*x^3+c*x^2+b*x+a)^p*(2*a+b*(3+p)*x+c*(4+2*p)*x^2+d*(5+3*p)*x^3),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.90099, size = 53, normalized size = 2.3 \[{\left (d x^{5} + c x^{4} + b x^{3} + a x^{2}\right )}{\left (d x^{3} + c x^{2} + b x + a\right )}^{p} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*(3*p + 5)*x^3 + 2*c*(p + 2)*x^2 + b*(p + 3)*x + 2*a)*(d*x^3 + c*x^2 + b*x + a)^p*x,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.290735, size = 53, normalized size = 2.3 \[{\left (d x^{5} + c x^{4} + b x^{3} + a x^{2}\right )}{\left (d x^{3} + c x^{2} + b x + a\right )}^{p} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*(3*p + 5)*x^3 + 2*c*(p + 2)*x^2 + b*(p + 3)*x + 2*a)*(d*x^3 + c*x^2 + b*x + a)^p*x,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*(d*x**3+c*x**2+b*x+a)**p*(2*a+b*(3+p)*x+c*(4+2*p)*x**2+d*(5+3*p)*x**3),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.328122, size = 131, normalized size = 5.7 \[ d x^{5} e^{\left (p{\rm ln}\left (d x^{3} + c x^{2} + b x + a\right )\right )} + c x^{4} e^{\left (p{\rm ln}\left (d x^{3} + c x^{2} + b x + a\right )\right )} + b x^{3} e^{\left (p{\rm ln}\left (d x^{3} + c x^{2} + b x + a\right )\right )} + a x^{2} e^{\left (p{\rm ln}\left (d x^{3} + c x^{2} + b x + a\right )\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*(3*p + 5)*x^3 + 2*c*(p + 2)*x^2 + b*(p + 3)*x + 2*a)*(d*x^3 + c*x^2 + b*x + a)^p*x,x, algorithm="giac")
[Out]