Optimal. Leaf size=23 \[ x^3 \left (a+b x+c x^2+d x^3\right )^{p+1} \]
[Out]
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Rubi [A] time = 0.0232666, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 51, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.02 \[ x^3 \left (a+b x+c x^2+d x^3\right )^{p+1} \]
Antiderivative was successfully verified.
[In] Int[x^2*(a + b*x + c*x^2 + d*x^3)^p*(3*a + b*(4 + p)*x + c*(5 + 2*p)*x^2 + d*(6 + 3*p)*x^3),x]
[Out]
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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**2*(d*x**3+c*x**2+b*x+a)**p*(3*a+b*(4+p)*x+c*(5+2*p)*x**2+d*(6+3*p)*x**3),x)
[Out]
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Mathematica [A] time = 0.063995, size = 21, normalized size = 0.91 \[ x^3 (a+x (b+x (c+d x)))^{p+1} \]
Antiderivative was successfully verified.
[In] Integrate[x^2*(a + b*x + c*x^2 + d*x^3)^p*(3*a + b*(4 + p)*x + c*(5 + 2*p)*x^2 + d*(6 + 3*p)*x^3),x]
[Out]
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Maple [A] time = 0.011, size = 24, normalized size = 1. \[{x}^{3} \left ( d{x}^{3}+c{x}^{2}+bx+a \right ) ^{1+p} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2*(d*x^3+c*x^2+b*x+a)^p*(3*a+b*(4+p)*x+c*(5+2*p)*x^2+d*(6+3*p)*x^3),x)
[Out]
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Maxima [A] time = 0.939416, size = 53, normalized size = 2.3 \[{\left (d x^{6} + c x^{5} + b x^{4} + a x^{3}\right )}{\left (d x^{3} + c x^{2} + b x + a\right )}^{p} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*d*(p + 2)*x^3 + c*(2*p + 5)*x^2 + b*(p + 4)*x + 3*a)*(d*x^3 + c*x^2 + b*x + a)^p*x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.293899, size = 53, normalized size = 2.3 \[{\left (d x^{6} + c x^{5} + b x^{4} + a x^{3}\right )}{\left (d x^{3} + c x^{2} + b x + a\right )}^{p} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*d*(p + 2)*x^3 + c*(2*p + 5)*x^2 + b*(p + 4)*x + 3*a)*(d*x^3 + c*x^2 + b*x + a)^p*x^2,x, algorithm="fricas")
[Out]
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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*(d*x**3+c*x**2+b*x+a)**p*(3*a+b*(4+p)*x+c*(5+2*p)*x**2+d*(6+3*p)*x**3),x)
[Out]
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GIAC/XCAS [A] time = 0.469378, size = 131, normalized size = 5.7 \[ d x^{6} e^{\left (p{\rm ln}\left (d x^{3} + c x^{2} + b x + a\right )\right )} + c x^{5} e^{\left (p{\rm ln}\left (d x^{3} + c x^{2} + b x + a\right )\right )} + b x^{4} e^{\left (p{\rm ln}\left (d x^{3} + c x^{2} + b x + a\right )\right )} + a x^{3} e^{\left (p{\rm ln}\left (d x^{3} + c x^{2} + b x + a\right )\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*d*(p + 2)*x^3 + c*(2*p + 5)*x^2 + b*(p + 4)*x + 3*a)*(d*x^3 + c*x^2 + b*x + a)^p*x^2,x, algorithm="giac")
[Out]