Integrand size = 37, antiderivative size = 22 \[ \int \frac {-3840+e^5 (-3840-1280 x)-1280 x+e^{10} \left (11520+9600 x+2880 x^2+320 x^3\right )}{e^{10}} \, dx=80 \left (-4+\left (1+\frac {2}{e^5}\right )^2-(3+x)^2\right )^2 \]
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Time = 0.01 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.95, number of steps used = 3, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.027, Rules used = {12} \[ \int \frac {-3840+e^5 (-3840-1280 x)-1280 x+e^{10} \left (11520+9600 x+2880 x^2+320 x^3\right )}{e^{10}} \, dx=80 x^4+960 x^3-\frac {640 x^2}{e^{10}}+4800 x^2-\frac {3840 x}{e^{10}}+11520 x-\frac {640 (x+3)^2}{e^5} \]
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Rule 12
Rubi steps \begin{align*} \text {integral}& = \frac {\int \left (-3840+e^5 (-3840-1280 x)-1280 x+e^{10} \left (11520+9600 x+2880 x^2+320 x^3\right )\right ) \, dx}{e^{10}} \\ & = -\frac {3840 x}{e^{10}}-\frac {640 x^2}{e^{10}}-\frac {640 (3+x)^2}{e^5}+\int \left (11520+9600 x+2880 x^2+320 x^3\right ) \, dx \\ & = 11520 x-\frac {3840 x}{e^{10}}+4800 x^2-\frac {640 x^2}{e^{10}}+960 x^3+80 x^4-\frac {640 (3+x)^2}{e^5} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.27 \[ \int \frac {-3840+e^5 (-3840-1280 x)-1280 x+e^{10} \left (11520+9600 x+2880 x^2+320 x^3\right )}{e^{10}} \, dx=\frac {80 x (6+x) \left (-8-8 e^5+e^{10} \left (24+6 x+x^2\right )\right )}{e^{10}} \]
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Time = 0.14 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.64
method | result | size |
default | \(80 \,{\mathrm e}^{-20} \left (x^{2} {\mathrm e}^{10}+6 x \,{\mathrm e}^{10}+12 \,{\mathrm e}^{10}-4 \,{\mathrm e}^{5}-4\right )^{2}\) | \(36\) |
gosper | \(80 x \left (x^{3} {\mathrm e}^{10}+12 x^{2} {\mathrm e}^{10}+60 x \,{\mathrm e}^{10}+144 \,{\mathrm e}^{10}-8 x \,{\mathrm e}^{5}-48 \,{\mathrm e}^{5}-8 x -48\right ) {\mathrm e}^{-10}\) | \(52\) |
norman | \(\left (960 x^{3} {\mathrm e}^{5}+80 x^{4} {\mathrm e}^{5}+3840 \left (3 \,{\mathrm e}^{10}-{\mathrm e}^{5}-1\right ) {\mathrm e}^{-5} x +320 \left (15 \,{\mathrm e}^{10}-2 \,{\mathrm e}^{5}-2\right ) {\mathrm e}^{-5} x^{2}\right ) {\mathrm e}^{-5}\) | \(61\) |
parallelrisch | \({\mathrm e}^{-10} \left (80 x^{4} {\mathrm e}^{10}+960 x^{3} {\mathrm e}^{10}+4800 x^{2} {\mathrm e}^{10}+11520 x \,{\mathrm e}^{10}-640 x^{2} {\mathrm e}^{5}-3840 x \,{\mathrm e}^{5}-640 x^{2}-3840 x \right )\) | \(61\) |
risch | \(80 \,{\mathrm e}^{-20} {\mathrm e}^{20} x^{4}+960 \,{\mathrm e}^{-20} {\mathrm e}^{20} x^{3}-640 \,{\mathrm e}^{5} {\mathrm e}^{-20} {\mathrm e}^{10} x^{2}+4800 \,{\mathrm e}^{-20} {\mathrm e}^{20} x^{2}-3840 \,{\mathrm e}^{5} {\mathrm e}^{-20} {\mathrm e}^{10} x +11520 \,{\mathrm e}^{-20} {\mathrm e}^{20} x -640 \,{\mathrm e}^{-20} {\mathrm e}^{10} x^{2}-6400 \,{\mathrm e}^{-20} {\mathrm e}^{10}-7680 \,{\mathrm e}^{5} {\mathrm e}^{-20} {\mathrm e}^{10}+11520 \,{\mathrm e}^{-20} {\mathrm e}^{20}-3840 \,{\mathrm e}^{-20} {\mathrm e}^{10} x +2560 \,{\mathrm e}^{5} {\mathrm e}^{-20}+1280 \,{\mathrm e}^{-20}\) | \(120\) |
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Leaf count of result is larger than twice the leaf count of optimal. 45 vs. \(2 (21) = 42\).
Time = 0.23 (sec) , antiderivative size = 45, normalized size of antiderivative = 2.05 \[ \int \frac {-3840+e^5 (-3840-1280 x)-1280 x+e^{10} \left (11520+9600 x+2880 x^2+320 x^3\right )}{e^{10}} \, dx=-80 \, {\left (8 \, x^{2} - {\left (x^{4} + 12 \, x^{3} + 60 \, x^{2} + 144 \, x\right )} e^{10} + 8 \, {\left (x^{2} + 6 \, x\right )} e^{5} + 48 \, x\right )} e^{\left (-10\right )} \]
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Time = 0.03 (sec) , antiderivative size = 44, normalized size of antiderivative = 2.00 \[ \int \frac {-3840+e^5 (-3840-1280 x)-1280 x+e^{10} \left (11520+9600 x+2880 x^2+320 x^3\right )}{e^{10}} \, dx=80 x^{4} + 960 x^{3} + \frac {x^{2} \left (- 640 e^{5} - 640 + 4800 e^{10}\right )}{e^{10}} + \frac {x \left (- 3840 e^{5} - 3840 + 11520 e^{10}\right )}{e^{10}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 45 vs. \(2 (21) = 42\).
Time = 0.19 (sec) , antiderivative size = 45, normalized size of antiderivative = 2.05 \[ \int \frac {-3840+e^5 (-3840-1280 x)-1280 x+e^{10} \left (11520+9600 x+2880 x^2+320 x^3\right )}{e^{10}} \, dx=-80 \, {\left (8 \, x^{2} - {\left (x^{4} + 12 \, x^{3} + 60 \, x^{2} + 144 \, x\right )} e^{10} + 8 \, {\left (x^{2} + 6 \, x\right )} e^{5} + 48 \, x\right )} e^{\left (-10\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 45 vs. \(2 (21) = 42\).
Time = 0.26 (sec) , antiderivative size = 45, normalized size of antiderivative = 2.05 \[ \int \frac {-3840+e^5 (-3840-1280 x)-1280 x+e^{10} \left (11520+9600 x+2880 x^2+320 x^3\right )}{e^{10}} \, dx=-80 \, {\left (8 \, x^{2} - {\left (x^{4} + 12 \, x^{3} + 60 \, x^{2} + 144 \, x\right )} e^{10} + 8 \, {\left (x^{2} + 6 \, x\right )} e^{5} + 48 \, x\right )} e^{\left (-10\right )} \]
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Time = 9.29 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.95 \[ \int \frac {-3840+e^5 (-3840-1280 x)-1280 x+e^{10} \left (11520+9600 x+2880 x^2+320 x^3\right )}{e^{10}} \, dx=80\,x^4+960\,x^3-\frac {{\mathrm {e}}^{-10}\,\left (1280\,{\mathrm {e}}^5-9600\,{\mathrm {e}}^{10}+1280\right )\,x^2}{2}-{\mathrm {e}}^{-10}\,\left (3840\,{\mathrm {e}}^5-11520\,{\mathrm {e}}^{10}+3840\right )\,x \]
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