Optimal. Leaf size=24 \[ 4+e^x-x+3 x \left (3-\frac {16 x^3}{\log \left (x^2\right )}\right ) \]
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Rubi [A]
time = 0.21, antiderivative size = 18, normalized size of antiderivative = 0.75, number of steps
used = 10, number of rules used = 5, integrand size = 34, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.147, Rules used = {6874, 2225,
2343, 2347, 2209} \begin {gather*} -\frac {48 x^4}{\log \left (x^2\right )}+8 x+e^x \end {gather*}
Antiderivative was successfully verified.
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Rule 2209
Rule 2225
Rule 2343
Rule 2347
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (e^x-\frac {8 \left (-12 x^3+24 x^3 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{\log ^2\left (x^2\right )}\right ) \, dx\\ &=-\left (8 \int \frac {-12 x^3+24 x^3 \log \left (x^2\right )-\log ^2\left (x^2\right )}{\log ^2\left (x^2\right )} \, dx\right )+\int e^x \, dx\\ &=e^x-8 \int \left (-1-\frac {12 x^3}{\log ^2\left (x^2\right )}+\frac {24 x^3}{\log \left (x^2\right )}\right ) \, dx\\ &=e^x+8 x+96 \int \frac {x^3}{\log ^2\left (x^2\right )} \, dx-192 \int \frac {x^3}{\log \left (x^2\right )} \, dx\\ &=e^x+8 x-\frac {48 x^4}{\log \left (x^2\right )}-96 \text {Subst}\left (\int \frac {e^{2 x}}{x} \, dx,x,\log \left (x^2\right )\right )+192 \int \frac {x^3}{\log \left (x^2\right )} \, dx\\ &=e^x+8 x-96 \text {Ei}\left (2 \log \left (x^2\right )\right )-\frac {48 x^4}{\log \left (x^2\right )}+96 \text {Subst}\left (\int \frac {e^{2 x}}{x} \, dx,x,\log \left (x^2\right )\right )\\ &=e^x+8 x-\frac {48 x^4}{\log \left (x^2\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.05, size = 18, normalized size = 0.75 \begin {gather*} e^x+8 x-\frac {48 x^4}{\log \left (x^2\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.49, size = 18, normalized size = 0.75
method | result | size |
default | \(8 x -\frac {48 x^{4}}{\ln \left (x^{2}\right )}+{\mathrm e}^{x}\) | \(18\) |
risch | \(8 x +{\mathrm e}^{x}-\frac {96 i x^{4}}{\pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-2 \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+\pi \mathrm {csgn}\left (i x^{2}\right )^{3}+4 i \ln \left (x \right )}\) | \(65\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 15, normalized size = 0.62 \begin {gather*} -\frac {24 \, x^{4}}{\log \left (x\right )} + 8 \, x + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 26, normalized size = 1.08 \begin {gather*} -\frac {48 \, x^{4} - {\left (8 \, x + e^{x}\right )} \log \left (x^{2}\right )}{\log \left (x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 15, normalized size = 0.62 \begin {gather*} - \frac {48 x^{4}}{\log {\left (x^{2} \right )}} + 8 x + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 29, normalized size = 1.21 \begin {gather*} -\frac {48 \, x^{4} - 8 \, x \log \left (x^{2}\right ) - e^{x} \log \left (x^{2}\right )}{\log \left (x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 7.27, size = 17, normalized size = 0.71 \begin {gather*} 8\,x+{\mathrm {e}}^x-\frac {48\,x^4}{\ln \left (x^2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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