Optimal. Leaf size=21 \[ -1+\left (e^5+4 x-\frac {x^4}{-10+x}\right )^2 \]
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Rubi [B] time = 0.14, antiderivative size = 73, normalized size of antiderivative = 3.48, number of steps used = 2, number of rules used = 1, integrand size = 84, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.012, Rules used = {2074} \begin {gather*} x^6+20 x^5+292 x^4+2 \left (1960-e^5\right ) x^3+4 \left (12304-5 e^5\right ) x^2+64 \left (9250-3 e^5\right ) x-\frac {20000 \left (3960-e^5\right )}{10-x}+\frac {100000000}{(10-x)^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 2074
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-64 \left (-9250+3 e^5\right )-\frac {200000000}{(-10+x)^3}+\frac {20000 \left (-3960+e^5\right )}{(-10+x)^2}-8 \left (-12304+5 e^5\right ) x-6 \left (-1960+e^5\right ) x^2+1168 x^3+100 x^4+6 x^5\right ) \, dx\\ &=\frac {100000000}{(10-x)^2}-\frac {20000 \left (3960-e^5\right )}{10-x}+64 \left (9250-3 e^5\right ) x+4 \left (12304-5 e^5\right ) x^2+2 \left (1960-e^5\right ) x^3+292 x^4+20 x^5+x^6\\ \end {aligned} \end {gather*}
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Mathematica [B] time = 0.04, size = 68, normalized size = 3.24 \begin {gather*} \frac {-2760160000+552032000 x-27600000 x^2-320 x^3+16 x^4+80 x^5-8 x^6+x^8+e^5 \left (792000-157600 x+7760 x^2+8 x^3+20 x^4-2 x^5\right )}{(-10+x)^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.50, size = 71, normalized size = 3.38 \begin {gather*} \frac {x^{8} - 8 \, x^{6} + 80 \, x^{5} + 16 \, x^{4} - 320 \, x^{3} - 6918400 \, x^{2} - 2 \, {\left (x^{5} - 10 \, x^{4} - 4 \, x^{3} - 920 \, x^{2} + 19600 \, x - 100000\right )} e^{5} + 138400000 \, x - 692000000}{x^{2} - 20 \, x + 100} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.13, size = 66, normalized size = 3.14 \begin {gather*} x^{6} + 20 \, x^{5} + 292 \, x^{4} - 2 \, x^{3} e^{5} + 3920 \, x^{3} - 20 \, x^{2} e^{5} + 49216 \, x^{2} - 192 \, x e^{5} + 592000 \, x - \frac {20000 \, {\left (x e^{5} - 3960 \, x - 10 \, e^{5} + 34600\right )}}{{\left (x - 10\right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.06, size = 59, normalized size = 2.81
method | result | size |
norman | \(\frac {x^{8}+\left (-320+8 \,{\mathrm e}^{5}\right ) x^{3}+\left (80-2 \,{\mathrm e}^{5}\right ) x^{5}+\left (20 \,{\mathrm e}^{5}+16\right ) x^{4}+\left (32000-2400 \,{\mathrm e}^{5}\right ) x -8 x^{6}-160000+16000 \,{\mathrm e}^{5}}{\left (x -10\right )^{2}}\) | \(59\) |
default | \(x^{6}+20 x^{5}-2 x^{3} {\mathrm e}^{5}+292 x^{4}-20 x^{2} {\mathrm e}^{5}+3920 x^{3}-192 x \,{\mathrm e}^{5}+49216 x^{2}+592000 x -\frac {2 \left (-39600000+10000 \,{\mathrm e}^{5}\right )}{x -10}+\frac {100000000}{\left (x -10\right )^{2}}\) | \(67\) |
risch | \(x^{6}+20 x^{5}-2 x^{3} {\mathrm e}^{5}+292 x^{4}-20 x^{2} {\mathrm e}^{5}+3920 x^{3}-192 x \,{\mathrm e}^{5}+49216 x^{2}+592000 x +\frac {\left (79200000-20000 \,{\mathrm e}^{5}\right ) x -692000000+200000 \,{\mathrm e}^{5}}{x^{2}-20 x +100}\) | \(72\) |
gosper | \(-\frac {-x^{8}+2 x^{5} {\mathrm e}^{5}+8 x^{6}-20 x^{4} {\mathrm e}^{5}-80 x^{5}-8 x^{3} {\mathrm e}^{5}-16 x^{4}+320 x^{3}+2400 x \,{\mathrm e}^{5}-16000 \,{\mathrm e}^{5}-32000 x +160000}{x^{2}-20 x +100}\) | \(73\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.37, size = 67, normalized size = 3.19 \begin {gather*} x^{6} + 20 \, x^{5} + 292 \, x^{4} - 2 \, x^{3} {\left (e^{5} - 1960\right )} - 4 \, x^{2} {\left (5 \, e^{5} - 12304\right )} - 64 \, x {\left (3 \, e^{5} - 9250\right )} - \frac {20000 \, {\left (x {\left (e^{5} - 3960\right )} - 10 \, e^{5} + 34600\right )}}{x^{2} - 20 \, x + 100} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.09, size = 71, normalized size = 3.38 \begin {gather*} 292\,x^4-x^3\,\left (2\,{\mathrm {e}}^5-3920\right )-x^2\,\left (20\,{\mathrm {e}}^5-49216\right )-\frac {x\,\left (20000\,{\mathrm {e}}^5-79200000\right )-200000\,{\mathrm {e}}^5+692000000}{x^2-20\,x+100}+20\,x^5+x^6-x\,\left (192\,{\mathrm {e}}^5-592000\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.28, size = 65, normalized size = 3.10 \begin {gather*} x^{6} + 20 x^{5} + 292 x^{4} + x^{3} \left (3920 - 2 e^{5}\right ) + x^{2} \left (49216 - 20 e^{5}\right ) + x \left (592000 - 192 e^{5}\right ) + \frac {x \left (79200000 - 20000 e^{5}\right ) - 692000000 + 200000 e^{5}}{x^{2} - 20 x + 100} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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