Integrand size = 58, antiderivative size = 32 \[ \int \frac {-15 x^2+96 x^3+50 x^4+6 x^5+e^{-5+x} \left (10 x-67 x^2-64 x^3-15 x^4-x^5\right )}{-6+\log (4)} \, dx=\frac {x (5+x) \left (-e^{-5+x}+x\right ) \left (x-x^2 (5+x)\right )}{6-\log (4)} \]
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Leaf count is larger than twice the leaf count of optimal. \(124\) vs. \(2(32)=64\).
Time = 0.14 (sec) , antiderivative size = 124, normalized size of antiderivative = 3.88, number of steps used = 24, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.069, Rules used = {12, 2227, 2207, 2225} \[ \int \frac {-15 x^2+96 x^3+50 x^4+6 x^5+e^{-5+x} \left (10 x-67 x^2-64 x^3-15 x^4-x^5\right )}{-6+\log (4)} \, dx=-\frac {x^6}{6-\log (4)}+\frac {e^{x-5} x^5}{6-\log (4)}-\frac {10 x^5}{6-\log (4)}+\frac {10 e^{x-5} x^4}{6-\log (4)}-\frac {24 x^4}{6-\log (4)}+\frac {24 e^{x-5} x^3}{6-\log (4)}+\frac {5 x^3}{6-\log (4)}-\frac {5 e^{x-5} x^2}{6-\log (4)} \]
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Rule 12
Rule 2207
Rule 2225
Rule 2227
Rubi steps \begin{align*} \text {integral}& = \frac {\int \left (-15 x^2+96 x^3+50 x^4+6 x^5+e^{-5+x} \left (10 x-67 x^2-64 x^3-15 x^4-x^5\right )\right ) \, dx}{-6+\log (4)} \\ & = \frac {5 x^3}{6-\log (4)}-\frac {24 x^4}{6-\log (4)}-\frac {10 x^5}{6-\log (4)}-\frac {x^6}{6-\log (4)}+\frac {\int e^{-5+x} \left (10 x-67 x^2-64 x^3-15 x^4-x^5\right ) \, dx}{-6+\log (4)} \\ & = \frac {5 x^3}{6-\log (4)}-\frac {24 x^4}{6-\log (4)}-\frac {10 x^5}{6-\log (4)}-\frac {x^6}{6-\log (4)}+\frac {\int \left (10 e^{-5+x} x-67 e^{-5+x} x^2-64 e^{-5+x} x^3-15 e^{-5+x} x^4-e^{-5+x} x^5\right ) \, dx}{-6+\log (4)} \\ & = \frac {5 x^3}{6-\log (4)}-\frac {24 x^4}{6-\log (4)}-\frac {10 x^5}{6-\log (4)}-\frac {x^6}{6-\log (4)}-\frac {10 \int e^{-5+x} x \, dx}{6-\log (4)}+\frac {15 \int e^{-5+x} x^4 \, dx}{6-\log (4)}+\frac {64 \int e^{-5+x} x^3 \, dx}{6-\log (4)}+\frac {67 \int e^{-5+x} x^2 \, dx}{6-\log (4)}-\frac {\int e^{-5+x} x^5 \, dx}{-6+\log (4)} \\ & = -\frac {10 e^{-5+x} x}{6-\log (4)}+\frac {67 e^{-5+x} x^2}{6-\log (4)}+\frac {5 x^3}{6-\log (4)}+\frac {64 e^{-5+x} x^3}{6-\log (4)}-\frac {24 x^4}{6-\log (4)}+\frac {15 e^{-5+x} x^4}{6-\log (4)}-\frac {10 x^5}{6-\log (4)}+\frac {e^{-5+x} x^5}{6-\log (4)}-\frac {x^6}{6-\log (4)}-\frac {5 \int e^{-5+x} x^4 \, dx}{6-\log (4)}+\frac {10 \int e^{-5+x} \, dx}{6-\log (4)}-\frac {60 \int e^{-5+x} x^3 \, dx}{6-\log (4)}-\frac {134 \int e^{-5+x} x \, dx}{6-\log (4)}-\frac {192 \int e^{-5+x} x^2 \, dx}{6-\log (4)} \\ & = \frac {10 e^{-5+x}}{6-\log (4)}-\frac {144 e^{-5+x} x}{6-\log (4)}-\frac {125 e^{-5+x} x^2}{6-\log (4)}+\frac {5 x^3}{6-\log (4)}+\frac {4 e^{-5+x} x^3}{6-\log (4)}-\frac {24 x^4}{6-\log (4)}+\frac {10 e^{-5+x} x^4}{6-\log (4)}-\frac {10 x^5}{6-\log (4)}+\frac {e^{-5+x} x^5}{6-\log (4)}-\frac {x^6}{6-\log (4)}+\frac {20 \int e^{-5+x} x^3 \, dx}{6-\log (4)}+\frac {134 \int e^{-5+x} \, dx}{6-\log (4)}+\frac {180 \int e^{-5+x} x^2 \, dx}{6-\log (4)}+\frac {384 \int e^{-5+x} x \, dx}{6-\log (4)} \\ & = \frac {144 e^{-5+x}}{6-\log (4)}+\frac {240 e^{-5+x} x}{6-\log (4)}+\frac {55 e^{-5+x} x^2}{6-\log (4)}+\frac {5 x^3}{6-\log (4)}+\frac {24 e^{-5+x} x^3}{6-\log (4)}-\frac {24 x^4}{6-\log (4)}+\frac {10 e^{-5+x} x^4}{6-\log (4)}-\frac {10 x^5}{6-\log (4)}+\frac {e^{-5+x} x^5}{6-\log (4)}-\frac {x^6}{6-\log (4)}-\frac {60 \int e^{-5+x} x^2 \, dx}{6-\log (4)}-\frac {360 \int e^{-5+x} x \, dx}{6-\log (4)}-\frac {384 \int e^{-5+x} \, dx}{6-\log (4)} \\ & = -\frac {240 e^{-5+x}}{6-\log (4)}-\frac {120 e^{-5+x} x}{6-\log (4)}-\frac {5 e^{-5+x} x^2}{6-\log (4)}+\frac {5 x^3}{6-\log (4)}+\frac {24 e^{-5+x} x^3}{6-\log (4)}-\frac {24 x^4}{6-\log (4)}+\frac {10 e^{-5+x} x^4}{6-\log (4)}-\frac {10 x^5}{6-\log (4)}+\frac {e^{-5+x} x^5}{6-\log (4)}-\frac {x^6}{6-\log (4)}+\frac {120 \int e^{-5+x} x \, dx}{6-\log (4)}+\frac {360 \int e^{-5+x} \, dx}{6-\log (4)} \\ & = \frac {120 e^{-5+x}}{6-\log (4)}-\frac {5 e^{-5+x} x^2}{6-\log (4)}+\frac {5 x^3}{6-\log (4)}+\frac {24 e^{-5+x} x^3}{6-\log (4)}-\frac {24 x^4}{6-\log (4)}+\frac {10 e^{-5+x} x^4}{6-\log (4)}-\frac {10 x^5}{6-\log (4)}+\frac {e^{-5+x} x^5}{6-\log (4)}-\frac {x^6}{6-\log (4)}-\frac {120 \int e^{-5+x} \, dx}{6-\log (4)} \\ & = -\frac {5 e^{-5+x} x^2}{6-\log (4)}+\frac {5 x^3}{6-\log (4)}+\frac {24 e^{-5+x} x^3}{6-\log (4)}-\frac {24 x^4}{6-\log (4)}+\frac {10 e^{-5+x} x^4}{6-\log (4)}-\frac {10 x^5}{6-\log (4)}+\frac {e^{-5+x} x^5}{6-\log (4)}-\frac {x^6}{6-\log (4)} \\ \end{align*}
Time = 0.72 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.16 \[ \int \frac {-15 x^2+96 x^3+50 x^4+6 x^5+e^{-5+x} \left (10 x-67 x^2-64 x^3-15 x^4-x^5\right )}{-6+\log (4)} \, dx=\frac {x^2 \left (-e^x+e^5 x\right ) \left (-5+24 x+10 x^2+x^3\right )}{e^5 (-6+\log (4))} \]
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Leaf count of result is larger than twice the leaf count of optimal. \(64\) vs. \(2(31)=62\).
Time = 0.23 (sec) , antiderivative size = 65, normalized size of antiderivative = 2.03
method | result | size |
parallelrisch | \(\frac {x^{6}-{\mathrm e}^{-5+x} x^{5}+10 x^{5}-10 \,{\mathrm e}^{-5+x} x^{4}+24 x^{4}-24 \,{\mathrm e}^{-5+x} x^{3}-5 x^{3}+5 x^{2} {\mathrm e}^{-5+x}}{2 \ln \left (2\right )-6}\) | \(65\) |
derivativedivides | \(\frac {-9875 \,{\mathrm e}^{-5+x} \left (-5+x \right )-12250 \,{\mathrm e}^{-5+x}-3105 \,{\mathrm e}^{-5+x} \left (-5+x \right )^{2}-474 \,{\mathrm e}^{-5+x} \left (-5+x \right )^{3}-35 \,{\mathrm e}^{-5+x} \left (-5+x \right )^{4}-{\mathrm e}^{-5+x} \left (-5+x \right )^{5}-5 x^{3}+24 x^{4}+10 x^{5}+x^{6}}{2 \ln \left (2\right )-6}\) | \(87\) |
default | \(\frac {-9875 \,{\mathrm e}^{-5+x} \left (-5+x \right )-12250 \,{\mathrm e}^{-5+x}-3105 \,{\mathrm e}^{-5+x} \left (-5+x \right )^{2}-474 \,{\mathrm e}^{-5+x} \left (-5+x \right )^{3}-35 \,{\mathrm e}^{-5+x} \left (-5+x \right )^{4}-{\mathrm e}^{-5+x} \left (-5+x \right )^{5}-5 x^{3}+24 x^{4}+10 x^{5}+x^{6}}{2 \ln \left (2\right )-6}\) | \(87\) |
risch | \(\frac {x^{6}}{2 \ln \left (2\right )-6}+\frac {10 x^{5}}{2 \ln \left (2\right )-6}+\frac {24 x^{4}}{2 \ln \left (2\right )-6}-\frac {5 x^{3}}{2 \ln \left (2\right )-6}+\frac {\left (-x^{5}-10 x^{4}-24 x^{3}+5 x^{2}\right ) {\mathrm e}^{-5+x}}{2 \ln \left (2\right )-6}\) | \(87\) |
parts | \(\frac {x^{6}+10 x^{5}+24 x^{4}-5 x^{3}}{2 \ln \left (2\right )-6}-\frac {x^{5} {\mathrm e}^{-5+x}}{2 \left (\ln \left (2\right )-3\right )}-\frac {5 x^{4} {\mathrm e}^{-5+x}}{\ln \left (2\right )-3}-\frac {12 x^{3} {\mathrm e}^{-5+x}}{\ln \left (2\right )-3}+\frac {5 x^{2} {\mathrm e}^{-5+x}}{2 \left (\ln \left (2\right )-3\right )}\) | \(89\) |
norman | \(-\frac {5 x^{3}}{2 \left (\ln \left (2\right )-3\right )}+\frac {12 x^{4}}{\ln \left (2\right )-3}+\frac {5 x^{5}}{\ln \left (2\right )-3}+\frac {x^{6}}{2 \ln \left (2\right )-6}+\frac {5 x^{2} {\mathrm e}^{-5+x}}{2 \left (\ln \left (2\right )-3\right )}-\frac {12 x^{3} {\mathrm e}^{-5+x}}{\ln \left (2\right )-3}-\frac {5 x^{4} {\mathrm e}^{-5+x}}{\ln \left (2\right )-3}-\frac {x^{5} {\mathrm e}^{-5+x}}{2 \left (\ln \left (2\right )-3\right )}\) | \(106\) |
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Time = 0.26 (sec) , antiderivative size = 52, normalized size of antiderivative = 1.62 \[ \int \frac {-15 x^2+96 x^3+50 x^4+6 x^5+e^{-5+x} \left (10 x-67 x^2-64 x^3-15 x^4-x^5\right )}{-6+\log (4)} \, dx=\frac {x^{6} + 10 \, x^{5} + 24 \, x^{4} - 5 \, x^{3} - {\left (x^{5} + 10 \, x^{4} + 24 \, x^{3} - 5 \, x^{2}\right )} e^{\left (x - 5\right )}}{2 \, {\left (\log \left (2\right ) - 3\right )}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 71 vs. \(2 (26) = 52\).
Time = 0.10 (sec) , antiderivative size = 71, normalized size of antiderivative = 2.22 \[ \int \frac {-15 x^2+96 x^3+50 x^4+6 x^5+e^{-5+x} \left (10 x-67 x^2-64 x^3-15 x^4-x^5\right )}{-6+\log (4)} \, dx=\frac {x^{6}}{-6 + 2 \log {\left (2 \right )}} + \frac {5 x^{5}}{-3 + \log {\left (2 \right )}} + \frac {12 x^{4}}{-3 + \log {\left (2 \right )}} - \frac {5 x^{3}}{-6 + 2 \log {\left (2 \right )}} + \frac {\left (- x^{5} - 10 x^{4} - 24 x^{3} + 5 x^{2}\right ) e^{x - 5}}{-6 + 2 \log {\left (2 \right )}} \]
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Time = 0.20 (sec) , antiderivative size = 52, normalized size of antiderivative = 1.62 \[ \int \frac {-15 x^2+96 x^3+50 x^4+6 x^5+e^{-5+x} \left (10 x-67 x^2-64 x^3-15 x^4-x^5\right )}{-6+\log (4)} \, dx=\frac {x^{6} + 10 \, x^{5} + 24 \, x^{4} - 5 \, x^{3} - {\left (x^{5} + 10 \, x^{4} + 24 \, x^{3} - 5 \, x^{2}\right )} e^{\left (x - 5\right )}}{2 \, {\left (\log \left (2\right ) - 3\right )}} \]
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Time = 0.26 (sec) , antiderivative size = 52, normalized size of antiderivative = 1.62 \[ \int \frac {-15 x^2+96 x^3+50 x^4+6 x^5+e^{-5+x} \left (10 x-67 x^2-64 x^3-15 x^4-x^5\right )}{-6+\log (4)} \, dx=\frac {x^{6} + 10 \, x^{5} + 24 \, x^{4} - 5 \, x^{3} - {\left (x^{5} + 10 \, x^{4} + 24 \, x^{3} - 5 \, x^{2}\right )} e^{\left (x - 5\right )}}{2 \, {\left (\log \left (2\right ) - 3\right )}} \]
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Time = 0.11 (sec) , antiderivative size = 62, normalized size of antiderivative = 1.94 \[ \int \frac {-15 x^2+96 x^3+50 x^4+6 x^5+e^{-5+x} \left (10 x-67 x^2-64 x^3-15 x^4-x^5\right )}{-6+\log (4)} \, dx=\frac {5\,x^2\,{\mathrm {e}}^{x-5}-24\,x^3\,{\mathrm {e}}^{x-5}-10\,x^4\,{\mathrm {e}}^{x-5}-x^5\,{\mathrm {e}}^{x-5}-5\,x^3+24\,x^4+10\,x^5+x^6}{\ln \left (4\right )-6} \]
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