Optimal. Leaf size=27 \[ 5 \left (x+9 \left (e^{e^2}-e^{1+x}+x-\frac {\log (x)}{x^2}\right )\right ) \]
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Rubi [A]
time = 0.03, antiderivative size = 18, normalized size of antiderivative = 0.67, number of steps
used = 8, number of rules used = 3, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.120, Rules used = {14, 2225, 2341}
\begin {gather*} -\frac {45 \log (x)}{x^2}+50 x-45 e^{x+1} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2225
Rule 2341
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-45 e^{1+x}+\frac {5 \left (-9+10 x^3+18 \log (x)\right )}{x^3}\right ) \, dx\\ &=5 \int \frac {-9+10 x^3+18 \log (x)}{x^3} \, dx-45 \int e^{1+x} \, dx\\ &=-45 e^{1+x}+5 \int \left (\frac {-9+10 x^3}{x^3}+\frac {18 \log (x)}{x^3}\right ) \, dx\\ &=-45 e^{1+x}+5 \int \frac {-9+10 x^3}{x^3} \, dx+90 \int \frac {\log (x)}{x^3} \, dx\\ &=-45 e^{1+x}-\frac {45}{2 x^2}-\frac {45 \log (x)}{x^2}+5 \int \left (10-\frac {9}{x^3}\right ) \, dx\\ &=-45 e^{1+x}+50 x-\frac {45 \log (x)}{x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.04, size = 18, normalized size = 0.67 \begin {gather*} -45 e^{1+x}+50 x-\frac {45 \log (x)}{x^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.25, size = 18, normalized size = 0.67
method | result | size |
default | \(50 x -\frac {45 \ln \left (x \right )}{x^{2}}-45 \,{\mathrm e}^{x +1}\) | \(18\) |
risch | \(50 x -\frac {45 \ln \left (x \right )}{x^{2}}-45 \,{\mathrm e}^{x +1}\) | \(18\) |
norman | \(\frac {50 x^{3}-45 x^{2} {\mathrm e}^{x +1}-45 \ln \left (x \right )}{x^{2}}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 17, normalized size = 0.63 \begin {gather*} 50 \, x - \frac {45 \, \log \left (x\right )}{x^{2}} - 45 \, e^{\left (x + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 24, normalized size = 0.89 \begin {gather*} \frac {5 \, {\left (10 \, x^{3} - 9 \, x^{2} e^{\left (x + 1\right )} - 9 \, \log \left (x\right )\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 17, normalized size = 0.63 \begin {gather*} 50 x - 45 e^{x + 1} - \frac {45 \log {\left (x \right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 24, normalized size = 0.89 \begin {gather*} \frac {5 \, {\left (10 \, x^{3} - 9 \, x^{2} e^{\left (x + 1\right )} - 9 \, \log \left (x\right )\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.64, size = 17, normalized size = 0.63 \begin {gather*} 50\,x-\frac {45\,\ln \left (x\right )}{x^2}-45\,\mathrm {e}\,{\mathrm {e}}^x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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