Optimal. Leaf size=15 \[ 5 (-4+x) \left (1-e^8 x\right )^2 \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(32\) vs. \(2(15)=30\).
time = 0.01, antiderivative size = 32, normalized size of antiderivative = 2.13, number of steps
used = 2, number of rules used = 0, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} 5 e^{16} x^3-20 e^{16} x^2+5 x-10 e^8 (2-x)^2 \end {gather*}
Antiderivative was successfully verified.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-10 e^8 (2-x)^2+5 x+e^{16} \int \left (-40 x+15 x^2\right ) \, dx\\ &=-10 e^8 (2-x)^2+5 x-20 e^{16} x^2+5 e^{16} x^3\\ \end {aligned} \end {gather*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(34\) vs. \(2(15)=30\).
time = 0.00, size = 34, normalized size = 2.27 \begin {gather*} 5 x+40 e^8 x-10 e^8 x^2-20 e^{16} x^2+5 e^{16} x^3 \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(45\) vs.
\(2(17)=34\).
time = 0.41, size = 46, normalized size = 3.07
method | result | size |
risch | \(5 x^{3} {\mathrm e}^{16}-20 x^{2} {\mathrm e}^{16}-10 x^{2} {\mathrm e}^{8}+40 x \,{\mathrm e}^{8}+5 x\) | \(31\) |
gosper | \(5 x \left (x^{2} {\mathrm e}^{16}-4 x \,{\mathrm e}^{16}-2 x \,{\mathrm e}^{8}+8 \,{\mathrm e}^{8}+1\right )\) | \(34\) |
norman | \(\left (40 \,{\mathrm e}^{8}+5\right ) x +\left (-20 \,{\mathrm e}^{16}-10 \,{\mathrm e}^{8}\right ) x^{2}+5 x^{3} {\mathrm e}^{16}\) | \(38\) |
default | \(5 x^{3} {\mathrm e}^{16}+\frac {5 \left (-3 \,{\mathrm e}^{8}+{\mathrm e}^{8} \left (-8 \,{\mathrm e}^{8}-1\right )\right ) x^{2}}{2}+40 x \,{\mathrm e}^{8}+5 x\) | \(46\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 28 vs.
\(2 (13) = 26\).
time = 0.25, size = 28, normalized size = 1.87 \begin {gather*} 5 \, {\left (x^{3} - 4 \, x^{2}\right )} e^{16} - 10 \, {\left (x^{2} - 4 \, x\right )} e^{8} + 5 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 28 vs.
\(2 (13) = 26\).
time = 0.40, size = 28, normalized size = 1.87 \begin {gather*} 5 \, {\left (x^{3} - 4 \, x^{2}\right )} e^{16} - 10 \, {\left (x^{2} - 4 \, x\right )} e^{8} + 5 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 31 vs.
\(2 (12) = 24\).
time = 0.01, size = 31, normalized size = 2.07 \begin {gather*} 5 x^{3} e^{16} + x^{2} \left (- 20 e^{16} - 10 e^{8}\right ) + x \left (5 + 40 e^{8}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 28 vs.
\(2 (13) = 26\).
time = 0.41, size = 28, normalized size = 1.87 \begin {gather*} 5 \, {\left (x^{3} - 4 \, x^{2}\right )} e^{16} - 10 \, {\left (x^{2} - 4 \, x\right )} e^{8} + 5 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 30, normalized size = 2.00 \begin {gather*} 5\,{\mathrm {e}}^{16}\,x^3+\left (-10\,{\mathrm {e}}^8-20\,{\mathrm {e}}^{16}\right )\,x^2+\left (40\,{\mathrm {e}}^8+5\right )\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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