Optimal. Leaf size=34 \[ a d e x+\frac {1}{2} \left (c d^2+a e^2\right ) x^2+\frac {1}{3} c d e x^3 \]
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Rubi [A]
time = 0.01, antiderivative size = 34, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 0, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \frac {1}{2} x^2 \left (a e^2+c d^2\right )+a d e x+\frac {1}{3} c d e x^3 \end {gather*}
Antiderivative was successfully verified.
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Rubi steps
\begin {align*} \int \left (a d e+\left (c d^2+a e^2\right ) x+c d e x^2\right ) \, dx &=a d e x+\frac {1}{2} \left (c d^2+a e^2\right ) x^2+\frac {1}{3} c d e x^3\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 38, normalized size = 1.12 \begin {gather*} a d e x+\frac {1}{2} c d^2 x^2+\frac {1}{2} a e^2 x^2+\frac {1}{3} c d e x^3 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.03, size = 31, normalized size = 0.91
method | result | size |
default | \(a d e x +\frac {\left (e^{2} a +c \,d^{2}\right ) x^{2}}{2}+\frac {c d e \,x^{3}}{3}\) | \(31\) |
gosper | \(\frac {x \left (2 c d e \,x^{2}+3 a \,e^{2} x +3 c \,d^{2} x +6 a d e \right )}{6}\) | \(32\) |
norman | \(\frac {c d e \,x^{3}}{3}+\left (\frac {e^{2} a}{2}+\frac {c \,d^{2}}{2}\right ) x^{2}+a d e x\) | \(32\) |
risch | \(a d e x +\frac {1}{2} a \,e^{2} x^{2}+\frac {1}{2} c \,d^{2} x^{2}+\frac {1}{3} c d e \,x^{3}\) | \(33\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 31, normalized size = 0.91 \begin {gather*} \frac {1}{3} \, c d x^{3} e + a d x e + \frac {1}{2} \, {\left (c d^{2} + a e^{2}\right )} x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 2.33, size = 34, normalized size = 1.00 \begin {gather*} \frac {1}{2} \, c d^{2} x^{2} + \frac {1}{2} \, a x^{2} e^{2} + \frac {1}{3} \, {\left (c d x^{3} + 3 \, a d x\right )} e \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 32, normalized size = 0.94 \begin {gather*} a d e x + \frac {c d e x^{3}}{3} + x^{2} \left (\frac {a e^{2}}{2} + \frac {c d^{2}}{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.45, size = 31, normalized size = 0.91 \begin {gather*} \frac {1}{3} \, c d x^{3} e + a d x e + \frac {1}{2} \, {\left (c d^{2} + a e^{2}\right )} x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 31, normalized size = 0.91 \begin {gather*} \frac {c\,d\,e\,x^3}{3}+\left (\frac {c\,d^2}{2}+\frac {a\,e^2}{2}\right )\,x^2+a\,d\,e\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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