Optimal. Leaf size=28 \[ 12 x+16 x^2-\frac {25 x^3}{3}-\frac {129 x^4}{4}-18 x^5 \]
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Rubi [A]
time = 0.01, antiderivative size = 28, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {78}
\begin {gather*} -18 x^5-\frac {129 x^4}{4}-\frac {25 x^3}{3}+16 x^2+12 x \end {gather*}
Antiderivative was successfully verified.
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Rule 78
Rubi steps
\begin {align*} \int (1-2 x) (2+3 x)^2 (3+5 x) \, dx &=\int \left (12+32 x-25 x^2-129 x^3-90 x^4\right ) \, dx\\ &=12 x+16 x^2-\frac {25 x^3}{3}-\frac {129 x^4}{4}-18 x^5\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 28, normalized size = 1.00 \begin {gather*} 12 x+16 x^2-\frac {25 x^3}{3}-\frac {129 x^4}{4}-18 x^5 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 25, normalized size = 0.89
method | result | size |
gosper | \(-\frac {x \left (216 x^{4}+387 x^{3}+100 x^{2}-192 x -144\right )}{12}\) | \(24\) |
default | \(12 x +16 x^{2}-\frac {25}{3} x^{3}-\frac {129}{4} x^{4}-18 x^{5}\) | \(25\) |
norman | \(12 x +16 x^{2}-\frac {25}{3} x^{3}-\frac {129}{4} x^{4}-18 x^{5}\) | \(25\) |
risch | \(12 x +16 x^{2}-\frac {25}{3} x^{3}-\frac {129}{4} x^{4}-18 x^{5}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.32, size = 24, normalized size = 0.86 \begin {gather*} -18 \, x^{5} - \frac {129}{4} \, x^{4} - \frac {25}{3} \, x^{3} + 16 \, x^{2} + 12 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.50, size = 24, normalized size = 0.86 \begin {gather*} -18 \, x^{5} - \frac {129}{4} \, x^{4} - \frac {25}{3} \, x^{3} + 16 \, x^{2} + 12 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 26, normalized size = 0.93 \begin {gather*} - 18 x^{5} - \frac {129 x^{4}}{4} - \frac {25 x^{3}}{3} + 16 x^{2} + 12 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.38, size = 24, normalized size = 0.86 \begin {gather*} -18 \, x^{5} - \frac {129}{4} \, x^{4} - \frac {25}{3} \, x^{3} + 16 \, x^{2} + 12 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.02, size = 24, normalized size = 0.86 \begin {gather*} -18\,x^5-\frac {129\,x^4}{4}-\frac {25\,x^3}{3}+16\,x^2+12\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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