Optimal. Leaf size=25 \[ 6 x+\frac {7 x^2}{2}-\frac {23 x^3}{3}-\frac {15 x^4}{2} \]
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Rubi [A]
time = 0.01, antiderivative size = 25, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {78}
\begin {gather*} -\frac {15 x^4}{2}-\frac {23 x^3}{3}+\frac {7 x^2}{2}+6 x \end {gather*}
Antiderivative was successfully verified.
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Rule 78
Rubi steps
\begin {align*} \int (1-2 x) (2+3 x) (3+5 x) \, dx &=\int \left (6+7 x-23 x^2-30 x^3\right ) \, dx\\ &=6 x+\frac {7 x^2}{2}-\frac {23 x^3}{3}-\frac {15 x^4}{2}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 25, normalized size = 1.00 \begin {gather*} 6 x+\frac {7 x^2}{2}-\frac {23 x^3}{3}-\frac {15 x^4}{2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.00, size = 20, normalized size = 0.80
method | result | size |
gosper | \(-\frac {x \left (45 x^{3}+46 x^{2}-21 x -36\right )}{6}\) | \(19\) |
default | \(6 x +\frac {7}{2} x^{2}-\frac {23}{3} x^{3}-\frac {15}{2} x^{4}\) | \(20\) |
norman | \(6 x +\frac {7}{2} x^{2}-\frac {23}{3} x^{3}-\frac {15}{2} x^{4}\) | \(20\) |
risch | \(6 x +\frac {7}{2} x^{2}-\frac {23}{3} x^{3}-\frac {15}{2} x^{4}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.35, size = 19, normalized size = 0.76 \begin {gather*} -\frac {15}{2} \, x^{4} - \frac {23}{3} \, x^{3} + \frac {7}{2} \, x^{2} + 6 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.44, size = 19, normalized size = 0.76 \begin {gather*} -\frac {15}{2} \, x^{4} - \frac {23}{3} \, x^{3} + \frac {7}{2} \, x^{2} + 6 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 22, normalized size = 0.88 \begin {gather*} - \frac {15 x^{4}}{2} - \frac {23 x^{3}}{3} + \frac {7 x^{2}}{2} + 6 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.61, size = 19, normalized size = 0.76 \begin {gather*} -\frac {15}{2} \, x^{4} - \frac {23}{3} \, x^{3} + \frac {7}{2} \, x^{2} + 6 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 19, normalized size = 0.76 \begin {gather*} -\frac {15\,x^4}{2}-\frac {23\,x^3}{3}+\frac {7\,x^2}{2}+6\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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