Optimal. Leaf size=17 \[ e^{1+4 x}+x \left (-5+x+\log \left (x^3\right )\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 20, normalized size of antiderivative = 1.18, number of steps used = 3, number of rules used = 2, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {2194, 2295} \begin {gather*} x \log \left (x^3\right )+x^2-5 x+e^{4 x+1} \end {gather*}
Antiderivative was successfully verified.
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Rule 2194
Rule 2295
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-2 x+x^2+4 \int e^{1+4 x} \, dx+\int \log \left (x^3\right ) \, dx\\ &=e^{1+4 x}-5 x+x^2+x \log \left (x^3\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 20, normalized size = 1.18 \begin {gather*} e^{1+4 x}-5 x+x^2+x \log \left (x^3\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.66, size = 19, normalized size = 1.12 \begin {gather*} x^{2} + x \log \left (x^{3}\right ) - 5 \, x + e^{\left (4 \, x + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 19, normalized size = 1.12 \begin {gather*} x^{2} + x \log \left (x^{3}\right ) - 5 \, x + e^{\left (4 \, x + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 20, normalized size = 1.18
method | result | size |
default | \(x^{2}-5 x +{\mathrm e}^{4 x +1}+x \ln \left (x^{3}\right )\) | \(20\) |
norman | \(x^{2}-5 x +{\mathrm e}^{4 x +1}+x \ln \left (x^{3}\right )\) | \(20\) |
risch | \(x^{2}-5 x +{\mathrm e}^{4 x +1}+x \ln \left (x^{3}\right )\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.39, size = 19, normalized size = 1.12 \begin {gather*} x^{2} + x \log \left (x^{3}\right ) - 5 \, x + e^{\left (4 \, x + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.10, size = 19, normalized size = 1.12 \begin {gather*} {\mathrm {e}}^{4\,x+1}-5\,x+x\,\ln \left (x^3\right )+x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.25, size = 19, normalized size = 1.12 \begin {gather*} x^{2} + x \log {\left (x^{3} \right )} - 5 x + e^{4 x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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