Optimal. Leaf size=22 \[ \frac{\left (a+c x^2+d x^3\right )^{n+1}}{n+1} \]
[Out]
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Rubi [A] time = 0.0153291, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.042 \[ \frac{\left (a+c x^2+d x^3\right )^{n+1}}{n+1} \]
Antiderivative was successfully verified.
[In] Int[x*(2*c + 3*d*x)*(a + c*x^2 + d*x^3)^n,x]
[Out]
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Rubi in Sympy [A] time = 4.93662, size = 17, normalized size = 0.77 \[ \frac{\left (a + c x^{2} + d x^{3}\right )^{n + 1}}{n + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(3*d*x+2*c)*(d*x**3+c*x**2+a)**n,x)
[Out]
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Mathematica [A] time = 0.0210146, size = 21, normalized size = 0.95 \[ \frac{\left (a+x^2 (c+d x)\right )^{n+1}}{n+1} \]
Antiderivative was successfully verified.
[In] Integrate[x*(2*c + 3*d*x)*(a + c*x^2 + d*x^3)^n,x]
[Out]
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Maple [A] time = 0.004, size = 23, normalized size = 1.1 \[{\frac{ \left ( d{x}^{3}+c{x}^{2}+a \right ) ^{1+n}}{1+n}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(3*d*x+2*c)*(d*x^3+c*x^2+a)^n,x)
[Out]
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Maxima [A] time = 0.864532, size = 43, normalized size = 1.95 \[ \frac{{\left (d x^{3} + c x^{2} + a\right )}{\left (d x^{3} + c x^{2} + a\right )}^{n}}{n + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*d*x + 2*c)*(d*x^3 + c*x^2 + a)^n*x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.267711, size = 43, normalized size = 1.95 \[ \frac{{\left (d x^{3} + c x^{2} + a\right )}{\left (d x^{3} + c x^{2} + a\right )}^{n}}{n + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*d*x + 2*c)*(d*x^3 + c*x^2 + a)^n*x,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*(3*d*x+2*c)*(d*x**3+c*x**2+a)**n,x)
[Out]
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GIAC/XCAS [A] time = 0.272057, size = 90, normalized size = 4.09 \[ \frac{d x^{3} e^{\left (n{\rm ln}\left (d x^{3} + c x^{2} + a\right )\right )} + c x^{2} e^{\left (n{\rm ln}\left (d x^{3} + c x^{2} + a\right )\right )} + a e^{\left (n{\rm ln}\left (d x^{3} + c x^{2} + a\right )\right )}}{n + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*d*x + 2*c)*(d*x^3 + c*x^2 + a)^n*x,x, algorithm="giac")
[Out]