Optimal. Leaf size=24 \[ 3-e^x+(1-2 x) (8+x)-(1+\log (x))^2 \]
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Rubi [A]
time = 0.02, antiderivative size = 24, normalized size of antiderivative = 1.00, number of steps
used = 8, number of rules used = 3, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {14, 2225, 2338}
\begin {gather*} -2 x^2-15 x-e^x-\log ^2(x)-2 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2225
Rule 2338
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-e^x+\frac {-2-15 x-4 x^2-2 \log (x)}{x}\right ) \, dx\\ &=-\int e^x \, dx+\int \frac {-2-15 x-4 x^2-2 \log (x)}{x} \, dx\\ &=-e^x+\int \left (\frac {-2-15 x-4 x^2}{x}-\frac {2 \log (x)}{x}\right ) \, dx\\ &=-e^x-2 \int \frac {\log (x)}{x} \, dx+\int \frac {-2-15 x-4 x^2}{x} \, dx\\ &=-e^x-\log ^2(x)+\int \left (-15-\frac {2}{x}-4 x\right ) \, dx\\ &=-e^x-15 x-2 x^2-2 \log (x)-\log ^2(x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 22, normalized size = 0.92 \begin {gather*} -e^x-15 x-2 x^2-(1+\log (x))^2 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.15, size = 24, normalized size = 1.00
method | result | size |
default | \(-2 x^{2}-15 x -2 \ln \left (x \right )-\ln \left (x \right )^{2}-{\mathrm e}^{x}\) | \(24\) |
norman | \(-2 x^{2}-15 x -2 \ln \left (x \right )-\ln \left (x \right )^{2}-{\mathrm e}^{x}\) | \(24\) |
risch | \(-2 x^{2}-15 x -2 \ln \left (x \right )-\ln \left (x \right )^{2}-{\mathrm e}^{x}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 23, normalized size = 0.96 \begin {gather*} -2 \, x^{2} - \log \left (x\right )^{2} - 15 \, x - e^{x} - 2 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 23, normalized size = 0.96 \begin {gather*} -2 \, x^{2} - \log \left (x\right )^{2} - 15 \, x - e^{x} - 2 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 22, normalized size = 0.92 \begin {gather*} - 2 x^{2} - 15 x - e^{x} - \log {\left (x \right )}^{2} - 2 \log {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 23, normalized size = 0.96 \begin {gather*} -2 \, x^{2} - \log \left (x\right )^{2} - 15 \, x - e^{x} - 2 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.16, size = 23, normalized size = 0.96 \begin {gather*} -15\,x-{\mathrm {e}}^x-2\,\ln \left (x\right )-{\ln \left (x\right )}^2-2\,x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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