Optimal. Leaf size=31 \[ -e^{2 x}+x^2 \left (-4+e^5 (5+x) \left (-3+4 x \left (1+x^2\right )\right )\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 53, normalized size of antiderivative = 1.71, number of steps used = 3, number of rules used = 1, integrand size = 39, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.026, Rules used = {2194} \begin {gather*} 4 e^5 x^6+20 e^5 x^5+4 e^5 x^4+17 e^5 x^3-15 e^5 x^2-4 x^2-e^{2 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-4 x^2-2 \int e^{2 x} \, dx+e^5 \int \left (-30 x+51 x^2+16 x^3+100 x^4+24 x^5\right ) \, dx\\ &=-e^{2 x}-4 x^2-15 e^5 x^2+17 e^5 x^3+4 e^5 x^4+20 e^5 x^5+4 e^5 x^6\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 53, normalized size = 1.71 \begin {gather*} -e^{2 x}-4 x^2-15 e^5 x^2+17 e^5 x^3+4 e^5 x^4+20 e^5 x^5+4 e^5 x^6 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.65, size = 41, normalized size = 1.32 \begin {gather*} -4 \, x^{2} + {\left (4 \, x^{6} + 20 \, x^{5} + 4 \, x^{4} + 17 \, x^{3} - 15 \, x^{2}\right )} e^{5} - e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 41, normalized size = 1.32 \begin {gather*} -4 \, x^{2} + {\left (4 \, x^{6} + 20 \, x^{5} + 4 \, x^{4} + 17 \, x^{3} - 15 \, x^{2}\right )} e^{5} - e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 42, normalized size = 1.35
method | result | size |
default | \({\mathrm e}^{5} \left (4 x^{6}+20 x^{5}+4 x^{4}+17 x^{3}-15 x^{2}\right )-4 x^{2}-{\mathrm e}^{2 x}\) | \(42\) |
norman | \(\left (-15 \,{\mathrm e}^{5}-4\right ) x^{2}-{\mathrm e}^{2 x}+17 x^{3} {\mathrm e}^{5}+4 x^{4} {\mathrm e}^{5}+20 x^{5} {\mathrm e}^{5}+4 x^{6} {\mathrm e}^{5}\) | \(46\) |
risch | \(-{\mathrm e}^{2 x}+4 x^{6} {\mathrm e}^{5}+20 x^{5} {\mathrm e}^{5}+4 x^{4} {\mathrm e}^{5}+17 x^{3} {\mathrm e}^{5}-15 x^{2} {\mathrm e}^{5}-4 x^{2}\) | \(48\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 41, normalized size = 1.32 \begin {gather*} -4 \, x^{2} + {\left (4 \, x^{6} + 20 \, x^{5} + 4 \, x^{4} + 17 \, x^{3} - 15 \, x^{2}\right )} e^{5} - e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.41, size = 46, normalized size = 1.48 \begin {gather*} 17\,x^3\,{\mathrm {e}}^5-x^2\,\left (15\,{\mathrm {e}}^5+4\right )-{\mathrm {e}}^{2\,x}+4\,x^4\,{\mathrm {e}}^5+20\,x^5\,{\mathrm {e}}^5+4\,x^6\,{\mathrm {e}}^5 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 49, normalized size = 1.58 \begin {gather*} 4 x^{6} e^{5} + 20 x^{5} e^{5} + 4 x^{4} e^{5} + 17 x^{3} e^{5} + x^{2} \left (- 15 e^{5} - 4\right ) - e^{2 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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