Optimal. Leaf size=18 \[ 3 x-\frac {x^2}{2}-\frac {10 x^3}{3} \]
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Rubi [A]
time = 0.00, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {45}
\begin {gather*} -\frac {10 x^3}{3}-\frac {x^2}{2}+3 x \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {align*} \int (1-2 x) (3+5 x) \, dx &=\int \left (3-x-10 x^2\right ) \, dx\\ &=3 x-\frac {x^2}{2}-\frac {10 x^3}{3}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 18, normalized size = 1.00 \begin {gather*} 3 x-\frac {x^2}{2}-\frac {10 x^3}{3} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.00, size = 15, normalized size = 0.83
method | result | size |
gosper | \(-\frac {x \left (20 x^{2}+3 x -18\right )}{6}\) | \(14\) |
default | \(3 x -\frac {1}{2} x^{2}-\frac {10}{3} x^{3}\) | \(15\) |
norman | \(3 x -\frac {1}{2} x^{2}-\frac {10}{3} x^{3}\) | \(15\) |
risch | \(3 x -\frac {1}{2} x^{2}-\frac {10}{3} x^{3}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 14, normalized size = 0.78 \begin {gather*} -\frac {10}{3} \, x^{3} - \frac {1}{2} \, x^{2} + 3 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.49, size = 14, normalized size = 0.78 \begin {gather*} -\frac {10}{3} \, x^{3} - \frac {1}{2} \, x^{2} + 3 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 14, normalized size = 0.78 \begin {gather*} - \frac {10 x^{3}}{3} - \frac {x^{2}}{2} + 3 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.60, size = 14, normalized size = 0.78 \begin {gather*} -\frac {10}{3} \, x^{3} - \frac {1}{2} \, x^{2} + 3 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 13, normalized size = 0.72 \begin {gather*} -\frac {x\,\left (20\,x^2+3\,x-18\right )}{6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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