Optimal. Leaf size=21 \[ \frac{\left (c x^2+d x^3\right )^{n+1}}{n+1} \]
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Rubi [A] time = 0.0145531, antiderivative size = 21, 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 \[ \frac{\left (c x^2+d x^3\right )^{n+1}}{n+1} \]
Antiderivative was successfully verified.
[In] Int[(2*c*x + 3*d*x^2)*(c*x^2 + d*x^3)^n,x]
[Out]
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Rubi in Sympy [A] time = 6.41581, size = 15, normalized size = 0.71 \[ \frac{\left (c x^{2} + d x^{3}\right )^{n + 1}}{n + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((3*d*x**2+2*c*x)*(d*x**3+c*x**2)**n,x)
[Out]
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Mathematica [A] time = 0.0381455, size = 19, normalized size = 0.9 \[ \frac{\left (x^2 (c+d x)\right )^{n+1}}{n+1} \]
Antiderivative was successfully verified.
[In] Integrate[(2*c*x + 3*d*x^2)*(c*x^2 + d*x^3)^n,x]
[Out]
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Maple [A] time = 0.005, size = 28, normalized size = 1.3 \[{\frac{ \left ( d{x}^{3}+c{x}^{2} \right ) ^{n}{x}^{2} \left ( dx+c \right ) }{1+n}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((3*d*x^2+2*c*x)*(d*x^3+c*x^2)^n,x)
[Out]
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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((3*d*x^2 + 2*c*x)*(d*x^3 + c*x^2)^n,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.278936, size = 41, normalized size = 1.95 \[ \frac{{\left (d x^{3} + c x^{2}\right )}{\left (d x^{3} + c x^{2}\right )}^{n}}{n + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*d*x^2 + 2*c*x)*(d*x^3 + c*x^2)^n,x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.42592, size = 53, normalized size = 2.52 \[ \begin{cases} \frac{c x^{2} \left (c x^{2} + d x^{3}\right )^{n}}{n + 1} + \frac{d x^{3} \left (c x^{2} + d x^{3}\right )^{n}}{n + 1} & \text{for}\: n \neq -1 \\2 \log{\left (x \right )} + \log{\left (\frac{c}{d} + x \right )} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*d*x**2+2*c*x)*(d*x**3+c*x**2)**n,x)
[Out]
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GIAC/XCAS [A] time = 0.277027, size = 63, normalized size = 3. \[ \frac{d x^{3} e^{\left (n{\rm ln}\left (d x^{3} + c x^{2}\right )\right )} + c x^{2} e^{\left (n{\rm ln}\left (d x^{3} + c x^{2}\right )\right )}}{n + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*d*x^2 + 2*c*x)*(d*x^3 + c*x^2)^n,x, algorithm="giac")
[Out]