Optimal. Leaf size=20 \[ 5 e^{15/4} x \left (x-x^2\right )-\log (4) \]
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Rubi [A]
time = 0.01, antiderivative size = 21, normalized size of antiderivative = 1.05, number of steps
used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {12}
\begin {gather*} 5 e^{15/4} x^2-5 e^{15/4} x^3 \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=e^{15/4} \int \left (10 x-15 x^2\right ) \, dx\\ &=5 e^{15/4} x^2-5 e^{15/4} x^3\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 16, normalized size = 0.80 \begin {gather*} -5 e^{15/4} \left (-x^2+x^3\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.66, size = 15, normalized size = 0.75
method | result | size |
gosper | \(-5 \,{\mathrm e}^{\frac {15}{4}} x^{2} \left (x -1\right )\) | \(11\) |
default | \({\mathrm e}^{\frac {15}{4}} \left (-5 x^{3}+5 x^{2}\right )\) | \(15\) |
norman | \(5 \,{\mathrm e}^{\frac {15}{4}} x^{2}-5 \,{\mathrm e}^{\frac {15}{4}} x^{3}\) | \(16\) |
risch | \(5 \,{\mathrm e}^{\frac {15}{4}} x^{2}-5 \,{\mathrm e}^{\frac {15}{4}} x^{3}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.25, size = 13, normalized size = 0.65 \begin {gather*} -5 \, {\left (x^{3} - x^{2}\right )} e^{\frac {15}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 13, normalized size = 0.65 \begin {gather*} -5 \, {\left (x^{3} - x^{2}\right )} e^{\frac {15}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 19, normalized size = 0.95 \begin {gather*} - 5 x^{3} e^{\frac {15}{4}} + 5 x^{2} e^{\frac {15}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 13, normalized size = 0.65 \begin {gather*} -5 \, {\left (x^{3} - x^{2}\right )} e^{\frac {15}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 10, normalized size = 0.50 \begin {gather*} -5\,x^2\,{\mathrm {e}}^{15/4}\,\left (x-1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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