Optimal. Leaf size=21 \[ 4+e^{\frac {1}{4} x^2 (7+x)^2 \log ^2(4)}+x \]
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Rubi [A]
time = 0.18, antiderivative size = 26, normalized size of antiderivative = 1.24, number of steps
used = 4, number of rules used = 3, integrand size = 49, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.061, Rules used = {12, 1608, 6838}
\begin {gather*} e^{\frac {1}{4} \left (x^4+14 x^3+49 x^2\right ) \log ^2(4)}+x \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 1608
Rule 6838
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \int \left (2+e^{\frac {1}{4} \left (49 x^2+14 x^3+x^4\right ) \log ^2(4)} \left (49 x+21 x^2+2 x^3\right ) \log ^2(4)\right ) \, dx\\ &=x+\frac {1}{2} \log ^2(4) \int e^{\frac {1}{4} \left (49 x^2+14 x^3+x^4\right ) \log ^2(4)} \left (49 x+21 x^2+2 x^3\right ) \, dx\\ &=x+\frac {1}{2} \log ^2(4) \int e^{\frac {1}{4} \left (49 x^2+14 x^3+x^4\right ) \log ^2(4)} x \left (49+21 x+2 x^2\right ) \, dx\\ &=e^{\frac {1}{4} \left (49 x^2+14 x^3+x^4\right ) \log ^2(4)}+x\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.20, size = 20, normalized size = 0.95 \begin {gather*} e^{\frac {1}{4} x^2 (7+x)^2 \log ^2(4)}+x \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.71, size = 23, normalized size = 1.10
method | result | size |
risch | \(x +{\mathrm e}^{\left (x +7\right )^{2} \ln \left (2\right )^{2} x^{2}}\) | \(17\) |
default | \(x +{\mathrm e}^{\left (x^{4}+14 x^{3}+49 x^{2}\right ) \ln \left (2\right )^{2}}\) | \(23\) |
norman | \(x +{\mathrm e}^{\left (x^{4}+14 x^{3}+49 x^{2}\right ) \ln \left (2\right )^{2}}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.58, size = 30, normalized size = 1.43 \begin {gather*} x + e^{\left (x^{4} \log \left (2\right )^{2} + 14 \, x^{3} \log \left (2\right )^{2} + 49 \, x^{2} \log \left (2\right )^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 22, normalized size = 1.05 \begin {gather*} x + e^{\left ({\left (x^{4} + 14 \, x^{3} + 49 \, x^{2}\right )} \log \left (2\right )^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 20, normalized size = 0.95 \begin {gather*} x + e^{\left (x^{4} + 14 x^{3} + 49 x^{2}\right ) \log {\left (2 \right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 30, normalized size = 1.43 \begin {gather*} x + e^{\left (x^{4} \log \left (2\right )^{2} + 14 \, x^{3} \log \left (2\right )^{2} + 49 \, x^{2} \log \left (2\right )^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.12, size = 32, normalized size = 1.52 \begin {gather*} x+{\mathrm {e}}^{x^4\,{\ln \left (2\right )}^2}\,{\mathrm {e}}^{14\,x^3\,{\ln \left (2\right )}^2}\,{\mathrm {e}}^{49\,x^2\,{\ln \left (2\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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