Optimal. Leaf size=19 \[ 9 x \left (4+x^4 \left (-4+3 e^3+x\right )^2\right ) \]
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Rubi [B] time = 0.01, antiderivative size = 42, normalized size of antiderivative = 2.21, number of steps used = 3, number of rules used = 1, integrand size = 40, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.025, Rules used = {6} \begin {gather*} 9 x^7+54 e^3 x^6-72 x^6+9 \left (16+9 e^6\right ) x^5-216 e^3 x^5+36 x \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (36+\left (720+405 e^6\right ) x^4-432 x^5+63 x^6+e^3 \left (-1080 x^4+324 x^5\right )\right ) \, dx\\ &=36 x+9 \left (16+9 e^6\right ) x^5-72 x^6+9 x^7+e^3 \int \left (-1080 x^4+324 x^5\right ) \, dx\\ &=36 x-216 e^3 x^5+9 \left (16+9 e^6\right ) x^5-72 x^6+54 e^3 x^6+9 x^7\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 34, normalized size = 1.79 \begin {gather*} 9 \left (4 x+\left (-4+3 e^3\right )^2 x^5+2 \left (-4+3 e^3\right ) x^6+x^7\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.58, size = 39, normalized size = 2.05 \begin {gather*} 9 \, x^{7} - 72 \, x^{6} + 81 \, x^{5} e^{6} + 144 \, x^{5} + 54 \, {\left (x^{6} - 4 \, x^{5}\right )} e^{3} + 36 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.55, size = 39, normalized size = 2.05 \begin {gather*} 9 \, x^{7} - 72 \, x^{6} + 81 \, x^{5} e^{6} + 144 \, x^{5} + 54 \, {\left (x^{6} - 4 \, x^{5}\right )} e^{3} + 36 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 36, normalized size = 1.89
method | result | size |
norman | \(\left (54 \,{\mathrm e}^{3}-72\right ) x^{6}+\left (81 \,{\mathrm e}^{6}-216 \,{\mathrm e}^{3}+144\right ) x^{5}+36 x +9 x^{7}\) | \(36\) |
risch | \(81 x^{5} {\mathrm e}^{6}+54 x^{6} {\mathrm e}^{3}-216 x^{5} {\mathrm e}^{3}+9 x^{7}-72 x^{6}+144 x^{5}+36 x\) | \(41\) |
gosper | \(9 x \left (9 x^{4} {\mathrm e}^{6}+6 x^{5} {\mathrm e}^{3}+x^{6}-24 x^{4} {\mathrm e}^{3}-8 x^{5}+16 x^{4}+4\right )\) | \(42\) |
default | \(81 x^{5} {\mathrm e}^{6}+{\mathrm e}^{3} \left (54 x^{6}-216 x^{5}\right )+9 x^{7}-72 x^{6}+144 x^{5}+36 x\) | \(43\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.48, size = 39, normalized size = 2.05 \begin {gather*} 9 \, x^{7} - 72 \, x^{6} + 81 \, x^{5} e^{6} + 144 \, x^{5} + 54 \, {\left (x^{6} - 4 \, x^{5}\right )} e^{3} + 36 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 33, normalized size = 1.74 \begin {gather*} 9\,x^7+\left (54\,{\mathrm {e}}^3-72\right )\,x^6+\left (81\,{\mathrm {e}}^6-216\,{\mathrm {e}}^3+144\right )\,x^5+36\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 32, normalized size = 1.68 \begin {gather*} 9 x^{7} + x^{6} \left (-72 + 54 e^{3}\right ) + x^{5} \left (- 216 e^{3} + 144 + 81 e^{6}\right ) + 36 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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