Optimal. Leaf size=19 \[ \frac {1}{e^4}+625 e^9 x^4 \left (\frac {1}{4}+x\right )^2 \]
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Rubi [A] time = 0.01, antiderivative size = 29, normalized size of antiderivative = 1.53, number of steps used = 2, number of rules used = 1, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {12} \begin {gather*} 625 e^9 x^6+\frac {625 e^9 x^5}{2}+\frac {625 e^9 x^4}{16} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} e^9 \int \left (625 x^3+6250 x^4+15000 x^5\right ) \, dx\\ &=\frac {625 e^9 x^4}{16}+\frac {625 e^9 x^5}{2}+625 e^9 x^6\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 25, normalized size = 1.32 \begin {gather*} \frac {625}{4} e^9 \left (\frac {x^4}{4}+2 x^5+4 x^6\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.66, size = 18, normalized size = 0.95 \begin {gather*} \frac {625}{16} \, {\left (16 \, x^{6} + 8 \, x^{5} + x^{4}\right )} e^{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.34, size = 18, normalized size = 0.95 \begin {gather*} \frac {625}{16} \, {\left (16 \, x^{6} + 8 \, x^{5} + x^{4}\right )} e^{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 15, normalized size = 0.79
method | result | size |
gosper | \(\frac {625 x^{4} \left (4 x +1\right )^{2} {\mathrm e}^{9}}{16}\) | \(15\) |
default | \(\frac {{\mathrm e}^{9} \left (2500 x^{6}+1250 x^{5}+\frac {625}{4} x^{4}\right )}{4}\) | \(21\) |
norman | \(\frac {625 x^{4} {\mathrm e}^{9}}{16}+\frac {625 \,{\mathrm e}^{9} x^{5}}{2}+625 \,{\mathrm e}^{9} x^{6}\) | \(23\) |
risch | \(\frac {625 x^{4} {\mathrm e}^{9}}{16}+\frac {625 \,{\mathrm e}^{9} x^{5}}{2}+625 \,{\mathrm e}^{9} x^{6}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 18, normalized size = 0.95 \begin {gather*} \frac {625}{16} \, {\left (16 \, x^{6} + 8 \, x^{5} + x^{4}\right )} e^{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 14, normalized size = 0.74 \begin {gather*} \frac {625\,x^4\,{\mathrm {e}}^9\,{\left (4\,x+1\right )}^2}{16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 27, normalized size = 1.42 \begin {gather*} 625 x^{6} e^{9} + \frac {625 x^{5} e^{9}}{2} + \frac {625 x^{4} e^{9}}{16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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