Optimal. Leaf size=23 \[ 9 x+6 x^2-\frac {35 x^3}{3}-\frac {25 x^4}{2} \]
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Rubi [A]
time = 0.01, antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {45}
\begin {gather*} -\frac {25 x^4}{2}-\frac {35 x^3}{3}+6 x^2+9 x \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {align*} \int (1-2 x) (3+5 x)^2 \, dx &=\int \left (9+12 x-35 x^2-50 x^3\right ) \, dx\\ &=9 x+6 x^2-\frac {35 x^3}{3}-\frac {25 x^4}{2}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 23, normalized size = 1.00 \begin {gather*} 9 x+6 x^2-\frac {35 x^3}{3}-\frac {25 x^4}{2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 20, normalized size = 0.87
method | result | size |
gosper | \(-\frac {x \left (75 x^{3}+70 x^{2}-36 x -54\right )}{6}\) | \(19\) |
default | \(9 x +6 x^{2}-\frac {35}{3} x^{3}-\frac {25}{2} x^{4}\) | \(20\) |
norman | \(9 x +6 x^{2}-\frac {35}{3} x^{3}-\frac {25}{2} x^{4}\) | \(20\) |
risch | \(9 x +6 x^{2}-\frac {35}{3} x^{3}-\frac {25}{2} x^{4}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 19, normalized size = 0.83 \begin {gather*} -\frac {25}{2} \, x^{4} - \frac {35}{3} \, x^{3} + 6 \, x^{2} + 9 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.64, size = 19, normalized size = 0.83 \begin {gather*} -\frac {25}{2} \, x^{4} - \frac {35}{3} \, x^{3} + 6 \, x^{2} + 9 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 20, normalized size = 0.87 \begin {gather*} - \frac {25 x^{4}}{2} - \frac {35 x^{3}}{3} + 6 x^{2} + 9 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.24, size = 19, normalized size = 0.83 \begin {gather*} -\frac {25}{2} \, x^{4} - \frac {35}{3} \, x^{3} + 6 \, x^{2} + 9 \, 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 = 0.83 \begin {gather*} -\frac {25\,x^4}{2}-\frac {35\,x^3}{3}+6\,x^2+9\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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