Optimal. Leaf size=25 \[ c d^2 x+c d e x^2+\frac {1}{3} c e^2 x^3 \]
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Rubi [A]
time = 0.00, antiderivative size = 25, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 0, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} c d^2 x+c d e x^2+\frac {1}{3} c e^2 x^3 \end {gather*}
Antiderivative was successfully verified.
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Rubi steps
\begin {align*} \int \left (c d^2+2 c d e x+c e^2 x^2\right ) \, dx &=c d^2 x+c d e x^2+\frac {1}{3} c e^2 x^3\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 25, normalized size = 1.00 \begin {gather*} c d^2 x+c d e x^2+\frac {1}{3} c e^2 x^3 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.04, size = 14, normalized size = 0.56
method | result | size |
default | \(\frac {c \left (e x +d \right )^{3}}{3 e}\) | \(14\) |
gosper | \(\frac {x \left (e^{2} x^{2}+3 d x e +3 d^{2}\right ) c}{3}\) | \(23\) |
norman | \(c \,d^{2} x +c d e \,x^{2}+\frac {1}{3} c \,e^{2} x^{3}\) | \(24\) |
risch | \(c \,d^{2} x +c d e \,x^{2}+\frac {1}{3} c \,e^{2} x^{3}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 23, normalized size = 0.92 \begin {gather*} \frac {1}{3} \, c x^{3} e^{2} + c d x^{2} e + c d^{2} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 2.28, size = 23, normalized size = 0.92 \begin {gather*} \frac {1}{3} \, c x^{3} e^{2} + c d x^{2} e + c d^{2} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 24, normalized size = 0.96 \begin {gather*} c d^{2} x + c d e x^{2} + \frac {c e^{2} x^{3}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 6.12, size = 23, normalized size = 0.92 \begin {gather*} \frac {1}{3} \, c x^{3} e^{2} + c d x^{2} e + c d^{2} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 22, normalized size = 0.88 \begin {gather*} \frac {c\,x\,\left (3\,d^2+3\,d\,e\,x+e^2\,x^2\right )}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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