Optimal. Leaf size=24 \[ \frac{\left (b x^3+c x^6\right )^{p+1}}{3 (p+1)} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0126921, antiderivative size = 24, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.04 \[ \frac{\left (b x^3+c x^6\right )^{p+1}}{3 (p+1)} \]
Antiderivative was successfully verified.
[In] Int[x^2*(b + 2*c*x^3)*(b*x^3 + c*x^6)^p,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 5.01885, size = 17, normalized size = 0.71 \[ \frac{\left (b x^{3} + c x^{6}\right )^{p + 1}}{3 \left (p + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2*(2*c*x**3+b)*(c*x**6+b*x**3)**p,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0454302, size = 24, normalized size = 1. \[ \frac{\left (x^3 \left (b+c x^3\right )\right )^{p+1}}{3 (p+1)} \]
Antiderivative was successfully verified.
[In] Integrate[x^2*(b + 2*c*x^3)*(b*x^3 + c*x^6)^p,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.005, size = 31, normalized size = 1.3 \[{\frac{{x}^{3} \left ( c{x}^{3}+b \right ) \left ( c{x}^{6}+b{x}^{3} \right ) ^{p}}{3+3\,p}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2*(2*c*x^3+b)*(c*x^6+b*x^3)^p,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.922656, size = 47, normalized size = 1.96 \[ \frac{{\left (c x^{6} + b x^{3}\right )} e^{\left (p \log \left (c x^{3} + b\right ) + 3 \, p \log \left (x\right )\right )}}{3 \,{\left (p + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x^3 + b)*(c*x^6 + b*x^3)^p*x^2,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.280533, size = 42, normalized size = 1.75 \[ \frac{{\left (c x^{6} + b x^{3}\right )}{\left (c x^{6} + b x^{3}\right )}^{p}}{3 \,{\left (p + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x^3 + b)*(c*x^6 + b*x^3)^p*x^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**2*(2*c*x**3+b)*(c*x**6+b*x**3)**p,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.270885, size = 65, normalized size = 2.71 \[ \frac{c x^{6} e^{\left (p{\rm ln}\left (c x^{6} + b x^{3}\right )\right )} + b x^{3} e^{\left (p{\rm ln}\left (c x^{6} + b x^{3}\right )\right )}}{3 \,{\left (p + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x^3 + b)*(c*x^6 + b*x^3)^p*x^2,x, algorithm="giac")
[Out]