Optimal. Leaf size=22 \[ 7-e^{\frac {1}{27} x^3 \left (5+x^2\right )}-\log (2) \]
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Rubi [A]
time = 0.09, antiderivative size = 17, normalized size of antiderivative = 0.77, number of steps
used = 3, number of rules used = 3, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {12, 1607, 6838}
\begin {gather*} -e^{\frac {1}{27} \left (x^5+5 x^3\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 1607
Rule 6838
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{27} \int e^{\frac {1}{27} \left (5 x^3+x^5\right )} \left (-15 x^2-5 x^4\right ) \, dx\\ &=\frac {1}{27} \int e^{\frac {1}{27} \left (5 x^3+x^5\right )} x^2 \left (-15-5 x^2\right ) \, dx\\ &=-e^{\frac {1}{27} \left (5 x^3+x^5\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 16, normalized size = 0.73 \begin {gather*} -e^{\frac {1}{27} x^3 \left (5+x^2\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 14, normalized size = 0.64
method | result | size |
risch | \(-{\mathrm e}^{\frac {x^{3} \left (x^{2}+5\right )}{27}}\) | \(14\) |
gosper | \(-{\mathrm e}^{\frac {1}{27} x^{5}+\frac {5}{27} x^{3}}\) | \(15\) |
norman | \(-{\mathrm e}^{\frac {1}{27} x^{5}+\frac {5}{27} x^{3}}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 14, normalized size = 0.64 \begin {gather*} -e^{\left (\frac {1}{27} \, x^{5} + \frac {5}{27} \, x^{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 14, normalized size = 0.64 \begin {gather*} -e^{\left (\frac {1}{27} \, x^{5} + \frac {5}{27} \, x^{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 14, normalized size = 0.64 \begin {gather*} - e^{\frac {x^{5}}{27} + \frac {5 x^{3}}{27}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 14, normalized size = 0.64 \begin {gather*} -e^{\left (\frac {1}{27} \, x^{5} + \frac {5}{27} \, x^{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.15, size = 14, normalized size = 0.64 \begin {gather*} -{\mathrm {e}}^{\frac {x^5}{27}+\frac {5\,x^3}{27}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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