Optimal. Leaf size=35 \[ -\frac {e^{-4+\frac {5}{1-x}} \left (-4+\frac {x \left (1+x^2\right )}{e}\right )^2}{x}+\log (x) \]
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Rubi [F] time = 45.66, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {e^{-2-\frac {1+4 x}{-1+x}} \left (-x^2-3 x^3-7 x^4+2 x^5-11 x^6+5 x^7-5 x^8+e^2 \left (16-112 x+16 x^2\right )+e^{2+\frac {1+4 x}{-1+x}} \left (x-2 x^2+x^3\right )+e \left (40 x^2+16 x^3+8 x^4+16 x^5\right )\right )}{x^2-2 x^3+x^4} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{-2-\frac {1+4 x}{-1+x}} \left (-x^2-3 x^3-7 x^4+2 x^5-11 x^6+5 x^7-5 x^8+e^2 \left (16-112 x+16 x^2\right )+e^{2+\frac {1+4 x}{-1+x}} \left (x-2 x^2+x^3\right )+e \left (40 x^2+16 x^3+8 x^4+16 x^5\right )\right )}{x^2 \left (1-2 x+x^2\right )} \, dx\\ &=\int \frac {e^{-2-\frac {1+4 x}{-1+x}} \left (-x^2-3 x^3-7 x^4+2 x^5-11 x^6+5 x^7-5 x^8+e^2 \left (16-112 x+16 x^2\right )+e^{2+\frac {1+4 x}{-1+x}} \left (x-2 x^2+x^3\right )+e \left (40 x^2+16 x^3+8 x^4+16 x^5\right )\right )}{(-1+x)^2 x^2} \, dx\\ &=\int \frac {e^{\frac {1-6 x}{-1+x}} \left (-x^2-3 x^3-7 x^4+2 x^5-11 x^6+5 x^7-5 x^8+e^2 \left (16-112 x+16 x^2\right )+e^{2+\frac {1+4 x}{-1+x}} \left (x-2 x^2+x^3\right )+e \left (40 x^2+16 x^3+8 x^4+16 x^5\right )\right )}{(1-x)^2 x^2} \, dx\\ &=\int \left (-\frac {e^{\frac {1-6 x}{-1+x}}}{(-1+x)^2}+\frac {e^{\frac {1-6 x}{-1+x}+\frac {-1+6 x}{-1+x}}}{x}-\frac {3 e^{\frac {1-6 x}{-1+x}} x}{(-1+x)^2}-\frac {7 e^{\frac {1-6 x}{-1+x}} x^2}{(-1+x)^2}+\frac {2 e^{\frac {1-6 x}{-1+x}} x^3}{(-1+x)^2}-\frac {11 e^{\frac {1-6 x}{-1+x}} x^4}{(-1+x)^2}+\frac {5 e^{\frac {1-6 x}{-1+x}} x^5}{(-1+x)^2}-\frac {5 e^{\frac {1-6 x}{-1+x}} x^6}{(-1+x)^2}+\frac {16 e^{2+\frac {1-6 x}{-1+x}} \left (1-7 x+x^2\right )}{(-1+x)^2 x^2}+\frac {8 e^{1+\frac {1-6 x}{-1+x}} \left (5+2 x+x^2+2 x^3\right )}{(-1+x)^2}\right ) \, dx\\ &=2 \int \frac {e^{\frac {1-6 x}{-1+x}} x^3}{(-1+x)^2} \, dx-3 \int \frac {e^{\frac {1-6 x}{-1+x}} x}{(-1+x)^2} \, dx+5 \int \frac {e^{\frac {1-6 x}{-1+x}} x^5}{(-1+x)^2} \, dx-5 \int \frac {e^{\frac {1-6 x}{-1+x}} x^6}{(-1+x)^2} \, dx-7 \int \frac {e^{\frac {1-6 x}{-1+x}} x^2}{(-1+x)^2} \, dx+8 \int \frac {e^{1+\frac {1-6 x}{-1+x}} \left (5+2 x+x^2+2 x^3\right )}{(-1+x)^2} \, dx-11 \int \frac {e^{\frac {1-6 x}{-1+x}} x^4}{(-1+x)^2} \, dx+16 \int \frac {e^{2+\frac {1-6 x}{-1+x}} \left (1-7 x+x^2\right )}{(-1+x)^2 x^2} \, dx-\int \frac {e^{\frac {1-6 x}{-1+x}}}{(-1+x)^2} \, dx+\int \frac {e^{\frac {1-6 x}{-1+x}+\frac {-1+6 x}{-1+x}}}{x} \, dx\\ &=2 \int \left (2 e^{\frac {1-6 x}{-1+x}}+\frac {e^{\frac {1-6 x}{-1+x}}}{(-1+x)^2}+\frac {3 e^{\frac {1-6 x}{-1+x}}}{-1+x}+e^{\frac {1-6 x}{-1+x}} x\right ) \, dx-3 \int \left (\frac {e^{\frac {1-6 x}{-1+x}}}{(-1+x)^2}+\frac {e^{\frac {1-6 x}{-1+x}}}{-1+x}\right ) \, dx+5 \int \left (4 e^{\frac {1-6 x}{-1+x}}+\frac {e^{\frac {1-6 x}{-1+x}}}{(-1+x)^2}+\frac {5 e^{\frac {1-6 x}{-1+x}}}{-1+x}+3 e^{\frac {1-6 x}{-1+x}} x+2 e^{\frac {1-6 x}{-1+x}} x^2+e^{\frac {1-6 x}{-1+x}} x^3\right ) \, dx-5 \int \left (5 e^{\frac {1-6 x}{-1+x}}+\frac {e^{\frac {1-6 x}{-1+x}}}{(-1+x)^2}+\frac {6 e^{\frac {1-6 x}{-1+x}}}{-1+x}+4 e^{\frac {1-6 x}{-1+x}} x+3 e^{\frac {1-6 x}{-1+x}} x^2+2 e^{\frac {1-6 x}{-1+x}} x^3+e^{\frac {1-6 x}{-1+x}} x^4\right ) \, dx-7 \int \left (e^{\frac {1-6 x}{-1+x}}+\frac {e^{\frac {1-6 x}{-1+x}}}{(-1+x)^2}+\frac {2 e^{\frac {1-6 x}{-1+x}}}{-1+x}\right ) \, dx+8 \int \frac {e^{-\frac {5 x}{-1+x}} \left (5+2 x+x^2+2 x^3\right )}{(1-x)^2} \, dx-11 \int \left (3 e^{\frac {1-6 x}{-1+x}}+\frac {e^{\frac {1-6 x}{-1+x}}}{(-1+x)^2}+\frac {4 e^{\frac {1-6 x}{-1+x}}}{-1+x}+2 e^{\frac {1-6 x}{-1+x}} x+e^{\frac {1-6 x}{-1+x}} x^2\right ) \, dx+16 \int \frac {e^{\frac {-1-4 x}{-1+x}} \left (1-7 x+x^2\right )}{(1-x)^2 x^2} \, dx-\int \frac {e^{-6-\frac {5}{-1+x}}}{(-1+x)^2} \, dx+\int \frac {1}{x} \, dx\\ &=-\frac {1}{5} e^{-6+\frac {5}{1-x}}+\log (x)+2 \int \frac {e^{\frac {1-6 x}{-1+x}}}{(-1+x)^2} \, dx+2 \int e^{\frac {1-6 x}{-1+x}} x \, dx-3 \int \frac {e^{\frac {1-6 x}{-1+x}}}{(-1+x)^2} \, dx-3 \int \frac {e^{\frac {1-6 x}{-1+x}}}{-1+x} \, dx+4 \int e^{\frac {1-6 x}{-1+x}} \, dx+5 \int e^{\frac {1-6 x}{-1+x}} x^3 \, dx-5 \int e^{\frac {1-6 x}{-1+x}} x^4 \, dx+6 \int \frac {e^{\frac {1-6 x}{-1+x}}}{-1+x} \, dx-7 \int e^{\frac {1-6 x}{-1+x}} \, dx-7 \int \frac {e^{\frac {1-6 x}{-1+x}}}{(-1+x)^2} \, dx+8 \int \left (5 e^{-\frac {5 x}{-1+x}}+\frac {10 e^{-\frac {5 x}{-1+x}}}{(-1+x)^2}+\frac {10 e^{-\frac {5 x}{-1+x}}}{-1+x}+2 e^{-\frac {5 x}{-1+x}} x\right ) \, dx+10 \int e^{\frac {1-6 x}{-1+x}} x^2 \, dx-10 \int e^{\frac {1-6 x}{-1+x}} x^3 \, dx-11 \int \frac {e^{\frac {1-6 x}{-1+x}}}{(-1+x)^2} \, dx-11 \int e^{\frac {1-6 x}{-1+x}} x^2 \, dx-14 \int \frac {e^{\frac {1-6 x}{-1+x}}}{-1+x} \, dx+15 \int e^{\frac {1-6 x}{-1+x}} x \, dx-15 \int e^{\frac {1-6 x}{-1+x}} x^2 \, dx+16 \int \left (-\frac {5 e^{\frac {-1-4 x}{-1+x}}}{(-1+x)^2}+\frac {5 e^{\frac {-1-4 x}{-1+x}}}{-1+x}+\frac {e^{\frac {-1-4 x}{-1+x}}}{x^2}-\frac {5 e^{\frac {-1-4 x}{-1+x}}}{x}\right ) \, dx+20 \int e^{\frac {1-6 x}{-1+x}} \, dx-20 \int e^{\frac {1-6 x}{-1+x}} x \, dx-22 \int e^{\frac {1-6 x}{-1+x}} x \, dx-25 \int e^{\frac {1-6 x}{-1+x}} \, dx+25 \int \frac {e^{\frac {1-6 x}{-1+x}}}{-1+x} \, dx-30 \int \frac {e^{\frac {1-6 x}{-1+x}}}{-1+x} \, dx-33 \int e^{\frac {1-6 x}{-1+x}} \, dx-44 \int \frac {e^{\frac {1-6 x}{-1+x}}}{-1+x} \, dx\\ &=-\frac {1}{5} e^{-6+\frac {5}{1-x}}+\log (x)+2 \int \frac {e^{-6-\frac {5}{-1+x}}}{(-1+x)^2} \, dx+2 \int e^{\frac {1-6 x}{-1+x}} x \, dx-3 \int \frac {e^{-6-\frac {5}{-1+x}}}{(-1+x)^2} \, dx-3 \int \frac {e^{-6-\frac {5}{-1+x}}}{-1+x} \, dx+4 \int e^{\frac {1-6 x}{-1+x}} \, dx+5 \int e^{\frac {1-6 x}{-1+x}} x^3 \, dx-5 \int e^{\frac {1-6 x}{-1+x}} x^4 \, dx+6 \int \frac {e^{-6-\frac {5}{-1+x}}}{-1+x} \, dx-7 \int e^{\frac {1-6 x}{-1+x}} \, dx-7 \int \frac {e^{-6-\frac {5}{-1+x}}}{(-1+x)^2} \, dx+10 \int e^{\frac {1-6 x}{-1+x}} x^2 \, dx-10 \int e^{\frac {1-6 x}{-1+x}} x^3 \, dx-11 \int \frac {e^{-6-\frac {5}{-1+x}}}{(-1+x)^2} \, dx-11 \int e^{\frac {1-6 x}{-1+x}} x^2 \, dx-14 \int \frac {e^{-6-\frac {5}{-1+x}}}{-1+x} \, dx+15 \int e^{\frac {1-6 x}{-1+x}} x \, dx-15 \int e^{\frac {1-6 x}{-1+x}} x^2 \, dx+16 \int \frac {e^{\frac {-1-4 x}{-1+x}}}{x^2} \, dx+16 \int e^{-\frac {5 x}{-1+x}} x \, dx+20 \int e^{\frac {1-6 x}{-1+x}} \, dx-20 \int e^{\frac {1-6 x}{-1+x}} x \, dx-22 \int e^{\frac {1-6 x}{-1+x}} x \, dx-25 \int e^{\frac {1-6 x}{-1+x}} \, dx+25 \int \frac {e^{-6-\frac {5}{-1+x}}}{-1+x} \, dx-30 \int \frac {e^{-6-\frac {5}{-1+x}}}{-1+x} \, dx-33 \int e^{\frac {1-6 x}{-1+x}} \, dx+40 \int e^{-\frac {5 x}{-1+x}} \, dx-44 \int \frac {e^{-6-\frac {5}{-1+x}}}{-1+x} \, dx-80 \int \frac {e^{\frac {-1-4 x}{-1+x}}}{(-1+x)^2} \, dx+80 \int \frac {e^{-\frac {5 x}{-1+x}}}{(-1+x)^2} \, dx+80 \int \frac {e^{\frac {-1-4 x}{-1+x}}}{-1+x} \, dx+80 \int \frac {e^{-\frac {5 x}{-1+x}}}{-1+x} \, dx-80 \int \frac {e^{\frac {-1-4 x}{-1+x}}}{x} \, dx\\ &=-4 e^{-6+\frac {5}{1-x}}-\frac {16 e^{\frac {1+4 x}{1-x}}}{x}+\frac {60 \text {Ei}\left (\frac {5}{1-x}\right )}{e^6}+\log (x)+2 \int e^{\frac {1-6 x}{-1+x}} x \, dx+4 \int e^{\frac {1-6 x}{-1+x}} \, dx+5 \int e^{\frac {1-6 x}{-1+x}} x^3 \, dx-5 \int e^{\frac {1-6 x}{-1+x}} x^4 \, dx-7 \int e^{\frac {1-6 x}{-1+x}} \, dx+10 \int e^{\frac {1-6 x}{-1+x}} x^2 \, dx-10 \int e^{\frac {1-6 x}{-1+x}} x^3 \, dx-11 \int e^{\frac {1-6 x}{-1+x}} x^2 \, dx+15 \int e^{\frac {1-6 x}{-1+x}} x \, dx-15 \int e^{\frac {1-6 x}{-1+x}} x^2 \, dx+16 \int e^{-\frac {5 x}{-1+x}} x \, dx+20 \int e^{\frac {1-6 x}{-1+x}} \, dx-20 \int e^{\frac {1-6 x}{-1+x}} x \, dx-22 \int e^{\frac {1-6 x}{-1+x}} x \, dx-25 \int e^{\frac {1-6 x}{-1+x}} \, dx-33 \int e^{\frac {1-6 x}{-1+x}} \, dx+40 \int e^{-\frac {5 x}{-1+x}} \, dx+80 \int \frac {e^{-5-\frac {5}{-1+x}}}{(-1+x)^2} \, dx-80 \int \frac {e^{-4-\frac {5}{-1+x}}}{(-1+x)^2} \, dx+80 \int \frac {e^{-5-\frac {5}{-1+x}}}{-1+x} \, dx+80 \int \frac {e^{-4-\frac {5}{-1+x}}}{-1+x} \, dx-80 \int \frac {e^{\frac {-1-4 x}{-1+x}}}{-1+x} \, dx+80 \int \frac {e^{\frac {-1-4 x}{-1+x}}}{(-1+x)^2 x} \, dx+80 \int \frac {e^{\frac {-1-4 x}{-1+x}}}{(-1+x) x} \, dx\\ &=-4 e^{-6+\frac {5}{1-x}}+16 e^{-5+\frac {5}{1-x}}-16 e^{-4+\frac {5}{1-x}}-\frac {16 e^{\frac {1+4 x}{1-x}}}{x}+\frac {60 \text {Ei}\left (\frac {5}{1-x}\right )}{e^6}-\frac {80 \text {Ei}\left (\frac {5}{1-x}\right )}{e^5}-\frac {80 \text {Ei}\left (\frac {5}{1-x}\right )}{e^4}+\log (x)+2 \int e^{\frac {1-6 x}{-1+x}} x \, dx+4 \int e^{\frac {1-6 x}{-1+x}} \, dx+5 \int e^{\frac {1-6 x}{-1+x}} x^3 \, dx-5 \int e^{\frac {1-6 x}{-1+x}} x^4 \, dx-7 \int e^{\frac {1-6 x}{-1+x}} \, dx+10 \int e^{\frac {1-6 x}{-1+x}} x^2 \, dx-10 \int e^{\frac {1-6 x}{-1+x}} x^3 \, dx-11 \int e^{\frac {1-6 x}{-1+x}} x^2 \, dx+15 \int e^{\frac {1-6 x}{-1+x}} x \, dx-15 \int e^{\frac {1-6 x}{-1+x}} x^2 \, dx+16 \int e^{-\frac {5 x}{-1+x}} x \, dx+20 \int e^{\frac {1-6 x}{-1+x}} \, dx-20 \int e^{\frac {1-6 x}{-1+x}} x \, dx-22 \int e^{\frac {1-6 x}{-1+x}} x \, dx-25 \int e^{\frac {1-6 x}{-1+x}} \, dx-33 \int e^{\frac {1-6 x}{-1+x}} \, dx+40 \int e^{-\frac {5 x}{-1+x}} \, dx+80 \int \left (\frac {e^{\frac {-1-4 x}{-1+x}}}{1-x}+\frac {e^{\frac {-1-4 x}{-1+x}}}{(-1+x)^2}+\frac {e^{\frac {-1-4 x}{-1+x}}}{x}\right ) \, dx-80 \int \frac {e^{-4-\frac {5}{-1+x}}}{-1+x} \, dx-80 \operatorname {Subst}\left (\int \frac {e^{1-5 x}}{x} \, dx,x,\frac {x}{-1+x}\right )\\ &=-4 e^{-6+\frac {5}{1-x}}+16 e^{-5+\frac {5}{1-x}}-16 e^{-4+\frac {5}{1-x}}-\frac {16 e^{\frac {1+4 x}{1-x}}}{x}+\frac {60 \text {Ei}\left (\frac {5}{1-x}\right )}{e^6}-\frac {80 \text {Ei}\left (\frac {5}{1-x}\right )}{e^5}-80 e \text {Ei}\left (\frac {5 x}{1-x}\right )+\log (x)+2 \int e^{\frac {1-6 x}{-1+x}} x \, dx+4 \int e^{\frac {1-6 x}{-1+x}} \, dx+5 \int e^{\frac {1-6 x}{-1+x}} x^3 \, dx-5 \int e^{\frac {1-6 x}{-1+x}} x^4 \, dx-7 \int e^{\frac {1-6 x}{-1+x}} \, dx+10 \int e^{\frac {1-6 x}{-1+x}} x^2 \, dx-10 \int e^{\frac {1-6 x}{-1+x}} x^3 \, dx-11 \int e^{\frac {1-6 x}{-1+x}} x^2 \, dx+15 \int e^{\frac {1-6 x}{-1+x}} x \, dx-15 \int e^{\frac {1-6 x}{-1+x}} x^2 \, dx+16 \int e^{-\frac {5 x}{-1+x}} x \, dx+20 \int e^{\frac {1-6 x}{-1+x}} \, dx-20 \int e^{\frac {1-6 x}{-1+x}} x \, dx-22 \int e^{\frac {1-6 x}{-1+x}} x \, dx-25 \int e^{\frac {1-6 x}{-1+x}} \, dx-33 \int e^{\frac {1-6 x}{-1+x}} \, dx+40 \int e^{-\frac {5 x}{-1+x}} \, dx+80 \int \frac {e^{\frac {-1-4 x}{-1+x}}}{1-x} \, dx+80 \int \frac {e^{\frac {-1-4 x}{-1+x}}}{(-1+x)^2} \, dx+80 \int \frac {e^{\frac {-1-4 x}{-1+x}}}{x} \, dx\\ &=-4 e^{-6+\frac {5}{1-x}}+16 e^{-5+\frac {5}{1-x}}-16 e^{-4+\frac {5}{1-x}}-\frac {16 e^{\frac {1+4 x}{1-x}}}{x}+\frac {60 \text {Ei}\left (\frac {5}{1-x}\right )}{e^6}-\frac {80 \text {Ei}\left (\frac {5}{1-x}\right )}{e^5}-80 e \text {Ei}\left (\frac {5 x}{1-x}\right )+\log (x)+2 \int e^{\frac {1-6 x}{-1+x}} x \, dx+4 \int e^{\frac {1-6 x}{-1+x}} \, dx+5 \int e^{\frac {1-6 x}{-1+x}} x^3 \, dx-5 \int e^{\frac {1-6 x}{-1+x}} x^4 \, dx-7 \int e^{\frac {1-6 x}{-1+x}} \, dx+10 \int e^{\frac {1-6 x}{-1+x}} x^2 \, dx-10 \int e^{\frac {1-6 x}{-1+x}} x^3 \, dx-11 \int e^{\frac {1-6 x}{-1+x}} x^2 \, dx+15 \int e^{\frac {1-6 x}{-1+x}} x \, dx-15 \int e^{\frac {1-6 x}{-1+x}} x^2 \, dx+16 \int e^{-\frac {5 x}{-1+x}} x \, dx+20 \int e^{\frac {1-6 x}{-1+x}} \, dx-20 \int e^{\frac {1-6 x}{-1+x}} x \, dx-22 \int e^{\frac {1-6 x}{-1+x}} x \, dx-25 \int e^{\frac {1-6 x}{-1+x}} \, dx-33 \int e^{\frac {1-6 x}{-1+x}} \, dx+40 \int e^{-\frac {5 x}{-1+x}} \, dx+80 \int \frac {e^{-4-\frac {5}{-1+x}}}{1-x} \, dx+80 \int \frac {e^{-4-\frac {5}{-1+x}}}{(-1+x)^2} \, dx+80 \int \frac {e^{\frac {-1-4 x}{-1+x}}}{-1+x} \, dx-80 \int \frac {e^{\frac {-1-4 x}{-1+x}}}{(-1+x) x} \, dx\\ &=-4 e^{-6+\frac {5}{1-x}}+16 e^{-5+\frac {5}{1-x}}-\frac {16 e^{\frac {1+4 x}{1-x}}}{x}+\frac {60 \text {Ei}\left (\frac {5}{1-x}\right )}{e^6}-\frac {80 \text {Ei}\left (\frac {5}{1-x}\right )}{e^5}+\frac {80 \text {Ei}\left (\frac {5}{1-x}\right )}{e^4}-80 e \text {Ei}\left (\frac {5 x}{1-x}\right )+\log (x)+2 \int e^{\frac {1-6 x}{-1+x}} x \, dx+4 \int e^{\frac {1-6 x}{-1+x}} \, dx+5 \int e^{\frac {1-6 x}{-1+x}} x^3 \, dx-5 \int e^{\frac {1-6 x}{-1+x}} x^4 \, dx-7 \int e^{\frac {1-6 x}{-1+x}} \, dx+10 \int e^{\frac {1-6 x}{-1+x}} x^2 \, dx-10 \int e^{\frac {1-6 x}{-1+x}} x^3 \, dx-11 \int e^{\frac {1-6 x}{-1+x}} x^2 \, dx+15 \int e^{\frac {1-6 x}{-1+x}} x \, dx-15 \int e^{\frac {1-6 x}{-1+x}} x^2 \, dx+16 \int e^{-\frac {5 x}{-1+x}} x \, dx+20 \int e^{\frac {1-6 x}{-1+x}} \, dx-20 \int e^{\frac {1-6 x}{-1+x}} x \, dx-22 \int e^{\frac {1-6 x}{-1+x}} x \, dx-25 \int e^{\frac {1-6 x}{-1+x}} \, dx-33 \int e^{\frac {1-6 x}{-1+x}} \, dx+40 \int e^{-\frac {5 x}{-1+x}} \, dx+80 \int \frac {e^{-4-\frac {5}{-1+x}}}{-1+x} \, dx+80 \operatorname {Subst}\left (\int \frac {e^{1-5 x}}{x} \, dx,x,\frac {x}{-1+x}\right )\\ &=-4 e^{-6+\frac {5}{1-x}}+16 e^{-5+\frac {5}{1-x}}-\frac {16 e^{\frac {1+4 x}{1-x}}}{x}+\frac {60 \text {Ei}\left (\frac {5}{1-x}\right )}{e^6}-\frac {80 \text {Ei}\left (\frac {5}{1-x}\right )}{e^5}+\log (x)+2 \int e^{\frac {1-6 x}{-1+x}} x \, dx+4 \int e^{\frac {1-6 x}{-1+x}} \, dx+5 \int e^{\frac {1-6 x}{-1+x}} x^3 \, dx-5 \int e^{\frac {1-6 x}{-1+x}} x^4 \, dx-7 \int e^{\frac {1-6 x}{-1+x}} \, dx+10 \int e^{\frac {1-6 x}{-1+x}} x^2 \, dx-10 \int e^{\frac {1-6 x}{-1+x}} x^3 \, dx-11 \int e^{\frac {1-6 x}{-1+x}} x^2 \, dx+15 \int e^{\frac {1-6 x}{-1+x}} x \, dx-15 \int e^{\frac {1-6 x}{-1+x}} x^2 \, dx+16 \int e^{-\frac {5 x}{-1+x}} x \, dx+20 \int e^{\frac {1-6 x}{-1+x}} \, dx-20 \int e^{\frac {1-6 x}{-1+x}} x \, dx-22 \int e^{\frac {1-6 x}{-1+x}} x \, dx-25 \int e^{\frac {1-6 x}{-1+x}} \, dx-33 \int e^{\frac {1-6 x}{-1+x}} \, dx+40 \int e^{-\frac {5 x}{-1+x}} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.10, size = 43, normalized size = 1.23 \begin {gather*} \frac {e^{-6-\frac {5}{-1+x}} \left (-\left (-4 e+x+x^3\right )^2+e^{6+\frac {5}{-1+x}} x \log (x)\right )}{x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.14, size = 60, normalized size = 1.71 \begin {gather*} -\frac {{\left (x^{6} + 2 \, x^{4} - x e^{\left (\frac {6 \, x - 1}{x - 1}\right )} \log \relax (x) + x^{2} - 8 \, {\left (x^{3} + x\right )} e + 16 \, e^{2}\right )} e^{\left (-\frac {6 \, x - 1}{x - 1}\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.27, size = 98, normalized size = 2.80 \begin {gather*} -\frac {{\left (x^{6} e^{\left (-\frac {5 \, x}{x - 1}\right )} + 2 \, x^{4} e^{\left (-\frac {5 \, x}{x - 1}\right )} - 8 \, x^{3} e^{\left (-\frac {5 \, x}{x - 1} + 1\right )} + x^{2} e^{\left (-\frac {5 \, x}{x - 1}\right )} - x e \log \relax (x) - 8 \, x e^{\left (-\frac {5 \, x}{x - 1} + 1\right )} + 16 \, e^{\left (-\frac {5 \, x}{x - 1} + 2\right )}\right )} e^{\left (-1\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.24, size = 50, normalized size = 1.43
method | result | size |
risch | \(\ln \relax (x )-\frac {\left (x^{6}-8 x^{3} {\mathrm e}+2 x^{4}+16 \,{\mathrm e}^{2}-8 x \,{\mathrm e}+x^{2}\right ) {\mathrm e}^{-\frac {6 x -1}{x -1}}}{x}\) | \(50\) |
norman | \(\frac {\left (\left (-16 \,{\mathrm e}-8\right ) x +{\mathrm e}^{-1} x^{6}+\left (1+8 \,{\mathrm e}\right ) {\mathrm e}^{-1} x^{2}-2 \,{\mathrm e}^{-1} x^{5}-{\mathrm e}^{-1} x^{7}-\left (1+8 \,{\mathrm e}\right ) {\mathrm e}^{-1} x^{3}+2 \left (4 \,{\mathrm e}+1\right ) {\mathrm e}^{-1} x^{4}+16 \,{\mathrm e}\right ) {\mathrm e}^{-1} {\mathrm e}^{-\frac {4 x +1}{x -1}}}{x \left (x -1\right )}+\ln \relax (x )\) | \(114\) |
default | \({\mathrm e}^{-2} \left ({\mathrm e}^{2} \ln \left (5+\frac {5}{x -1}\right )-{\mathrm e}^{2} \ln \left (\frac {5}{x -1}\right )-4 \,{\mathrm e}^{-4-\frac {5}{x -1}}+\frac {920 \,{\mathrm e}^{-4-\frac {5}{x -1}}}{5+\frac {5}{x -1}}-\frac {{\mathrm e}^{-4-\frac {5}{x -1}} \left (353 \left (4+\frac {5}{x -1}\right )^{5}-5640 \left (4+\frac {5}{x -1}\right )^{4}+32685 \left (4+\frac {5}{x -1}\right )^{3}-75200 \left (4+\frac {5}{x -1}\right )^{2}+198728+\frac {109850}{x -1}\right ) \left (x -1\right )^{5}}{1000 \left (5+\frac {5}{x -1}\right )}+\frac {175 \,{\mathrm e}^{-4-\frac {5}{x -1}} \left (\left (4+\frac {5}{x -1}\right )^{4}-12 \left (4+\frac {5}{x -1}\right )^{3}+45 \left (4+\frac {5}{x -1}\right )^{2}-214-\frac {180}{x -1}\right ) \left (x -1\right )^{4}}{24 \left (5+\frac {5}{x -1}\right )}-\frac {58 \,{\mathrm e}^{-4-\frac {5}{x -1}} \left (79 \left (4+\frac {5}{x -1}\right )^{3}-638 \left (4+\frac {5}{x -1}\right )^{2}+5402+\frac {5435}{x -1}\right ) \left (x -1\right )^{3}}{75 \left (5+\frac {5}{x -1}\right )}+\frac {239 \,{\mathrm e}^{-4-\frac {5}{x -1}} \left (11 \left (4+\frac {5}{x -1}\right )^{2}-201-\frac {240}{x -1}\right ) \left (x -1\right )^{2}}{10 \left (5+\frac {5}{x -1}\right )}-\frac {337 \,{\mathrm e}^{-4-\frac {5}{x -1}} \left (5+\frac {10}{x -1}\right ) \left (x -1\right )}{5+\frac {5}{x -1}}-400 \,{\mathrm e} \left (-\frac {{\mathrm e}^{-4-\frac {5}{x -1}}}{25}-\frac {{\mathrm e}^{-4-\frac {5}{x -1}}}{5+\frac {5}{x -1}}+\frac {7 \,{\mathrm e} \expIntegralEi \left (1, 5+\frac {5}{x -1}\right )}{5}\right )+400 \,{\mathrm e}^{2} \left (-\frac {{\mathrm e}^{-4-\frac {5}{x -1}}}{25}-\frac {{\mathrm e}^{-4-\frac {5}{x -1}}}{5+\frac {5}{x -1}}+\frac {7 \,{\mathrm e} \expIntegralEi \left (1, 5+\frac {5}{x -1}\right )}{5}\right )-250000 \,{\mathrm e} \left (\frac {{\mathrm e}^{-4-\frac {5}{x -1}} \left (11 \left (4+\frac {5}{x -1}\right )^{2}-201-\frac {240}{x -1}\right ) \left (x -1\right )^{2}}{781250+\frac {781250}{x -1}}-\frac {2 \,{\mathrm e} \expIntegralEi \left (1, 5+\frac {5}{x -1}\right )}{15625}-\frac {51 \,{\mathrm e}^{-4} \expIntegralEi \left (1, \frac {5}{x -1}\right )}{31250}\right )-275000 \,{\mathrm e} \left (-\frac {{\mathrm e}^{-4-\frac {5}{x -1}} \left (5+\frac {10}{x -1}\right ) \left (x -1\right )}{3125 \left (5+\frac {5}{x -1}\right )}+\frac {3 \,{\mathrm e} \expIntegralEi \left (1, 5+\frac {5}{x -1}\right )}{3125}+\frac {7 \,{\mathrm e}^{-4} \expIntegralEi \left (1, \frac {5}{x -1}\right )}{3125}\right )-130000 \,{\mathrm e} \left (\frac {{\mathrm e}^{-4-\frac {5}{x -1}}}{625+\frac {625}{x -1}}-\frac {4 \,{\mathrm e} \expIntegralEi \left (1, 5+\frac {5}{x -1}\right )}{625}-\frac {{\mathrm e}^{-4} \expIntegralEi \left (1, \frac {5}{x -1}\right )}{625}\right )-37000 \,{\mathrm e} \left (-\frac {{\mathrm e}^{-4-\frac {5}{x -1}}}{25 \left (5+\frac {5}{x -1}\right )}+\frac {{\mathrm e} \expIntegralEi \left (1, 5+\frac {5}{x -1}\right )}{25}\right )-6000 \,{\mathrm e} \left (\frac {{\mathrm e}^{-4-\frac {5}{x -1}}}{25+\frac {25}{x -1}}-\frac {6 \,{\mathrm e} \expIntegralEi \left (1, 5+\frac {5}{x -1}\right )}{25}\right )-2000 \,{\mathrm e}^{2} \left (-\frac {{\mathrm e}^{-4-\frac {5}{x -1}}}{25 \left (5+\frac {5}{x -1}\right )}+\frac {{\mathrm e} \expIntegralEi \left (1, 5+\frac {5}{x -1}\right )}{25}\right )+2000 \,{\mathrm e}^{2} \left (\frac {{\mathrm e}^{-4-\frac {5}{x -1}}}{25+\frac {25}{x -1}}-\frac {6 \,{\mathrm e} \expIntegralEi \left (1, 5+\frac {5}{x -1}\right )}{25}\right )\right )\) | \(877\) |
derivativedivides | \(-{\mathrm e}^{-2} \left (-{\mathrm e}^{2} \ln \left (5+\frac {5}{x -1}\right )+{\mathrm e}^{2} \ln \left (\frac {5}{x -1}\right )+4 \,{\mathrm e}^{-4-\frac {5}{x -1}}-\frac {920 \,{\mathrm e}^{-4-\frac {5}{x -1}}}{5+\frac {5}{x -1}}+\frac {{\mathrm e}^{-4-\frac {5}{x -1}} \left (353 \left (4+\frac {5}{x -1}\right )^{5}-5640 \left (4+\frac {5}{x -1}\right )^{4}+32685 \left (4+\frac {5}{x -1}\right )^{3}-75200 \left (4+\frac {5}{x -1}\right )^{2}+198728+\frac {109850}{x -1}\right ) \left (x -1\right )^{5}}{5000+\frac {5000}{x -1}}-\frac {175 \,{\mathrm e}^{-4-\frac {5}{x -1}} \left (\left (4+\frac {5}{x -1}\right )^{4}-12 \left (4+\frac {5}{x -1}\right )^{3}+45 \left (4+\frac {5}{x -1}\right )^{2}-214-\frac {180}{x -1}\right ) \left (x -1\right )^{4}}{24 \left (5+\frac {5}{x -1}\right )}+\frac {58 \,{\mathrm e}^{-4-\frac {5}{x -1}} \left (79 \left (4+\frac {5}{x -1}\right )^{3}-638 \left (4+\frac {5}{x -1}\right )^{2}+5402+\frac {5435}{x -1}\right ) \left (x -1\right )^{3}}{75 \left (5+\frac {5}{x -1}\right )}-\frac {239 \,{\mathrm e}^{-4-\frac {5}{x -1}} \left (11 \left (4+\frac {5}{x -1}\right )^{2}-201-\frac {240}{x -1}\right ) \left (x -1\right )^{2}}{10 \left (5+\frac {5}{x -1}\right )}+\frac {337 \,{\mathrm e}^{-4-\frac {5}{x -1}} \left (5+\frac {10}{x -1}\right ) \left (x -1\right )}{5+\frac {5}{x -1}}+400 \,{\mathrm e} \left (-\frac {{\mathrm e}^{-4-\frac {5}{x -1}}}{25}-\frac {{\mathrm e}^{-4-\frac {5}{x -1}}}{5+\frac {5}{x -1}}+\frac {7 \,{\mathrm e} \expIntegralEi \left (1, 5+\frac {5}{x -1}\right )}{5}\right )-400 \,{\mathrm e}^{2} \left (-\frac {{\mathrm e}^{-4-\frac {5}{x -1}}}{25}-\frac {{\mathrm e}^{-4-\frac {5}{x -1}}}{5+\frac {5}{x -1}}+\frac {7 \,{\mathrm e} \expIntegralEi \left (1, 5+\frac {5}{x -1}\right )}{5}\right )+250000 \,{\mathrm e} \left (\frac {{\mathrm e}^{-4-\frac {5}{x -1}} \left (11 \left (4+\frac {5}{x -1}\right )^{2}-201-\frac {240}{x -1}\right ) \left (x -1\right )^{2}}{781250+\frac {781250}{x -1}}-\frac {2 \,{\mathrm e} \expIntegralEi \left (1, 5+\frac {5}{x -1}\right )}{15625}-\frac {51 \,{\mathrm e}^{-4} \expIntegralEi \left (1, \frac {5}{x -1}\right )}{31250}\right )+275000 \,{\mathrm e} \left (-\frac {{\mathrm e}^{-4-\frac {5}{x -1}} \left (5+\frac {10}{x -1}\right ) \left (x -1\right )}{3125 \left (5+\frac {5}{x -1}\right )}+\frac {3 \,{\mathrm e} \expIntegralEi \left (1, 5+\frac {5}{x -1}\right )}{3125}+\frac {7 \,{\mathrm e}^{-4} \expIntegralEi \left (1, \frac {5}{x -1}\right )}{3125}\right )+130000 \,{\mathrm e} \left (\frac {{\mathrm e}^{-4-\frac {5}{x -1}}}{625+\frac {625}{x -1}}-\frac {4 \,{\mathrm e} \expIntegralEi \left (1, 5+\frac {5}{x -1}\right )}{625}-\frac {{\mathrm e}^{-4} \expIntegralEi \left (1, \frac {5}{x -1}\right )}{625}\right )+37000 \,{\mathrm e} \left (-\frac {{\mathrm e}^{-4-\frac {5}{x -1}}}{25 \left (5+\frac {5}{x -1}\right )}+\frac {{\mathrm e} \expIntegralEi \left (1, 5+\frac {5}{x -1}\right )}{25}\right )+6000 \,{\mathrm e} \left (\frac {{\mathrm e}^{-4-\frac {5}{x -1}}}{25+\frac {25}{x -1}}-\frac {6 \,{\mathrm e} \expIntegralEi \left (1, 5+\frac {5}{x -1}\right )}{25}\right )+2000 \,{\mathrm e}^{2} \left (-\frac {{\mathrm e}^{-4-\frac {5}{x -1}}}{25 \left (5+\frac {5}{x -1}\right )}+\frac {{\mathrm e} \expIntegralEi \left (1, 5+\frac {5}{x -1}\right )}{25}\right )-2000 \,{\mathrm e}^{2} \left (\frac {{\mathrm e}^{-4-\frac {5}{x -1}}}{25+\frac {25}{x -1}}-\frac {6 \,{\mathrm e} \expIntegralEi \left (1, 5+\frac {5}{x -1}\right )}{25}\right )\right )\) | \(878\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} -\frac {{\left (x^{6} + 2 \, x^{4} - 8 \, x^{3} e + x^{2} + 16 \, e^{2} + 40 \, e + 1\right )} e^{\left (-\frac {5}{x - 1} - 6\right )}}{x} - \frac {1}{5} \, e^{\left (-\frac {5}{x - 1} - 6\right )} + \int \frac {{\left (7 \, x {\left (40 \, e + 1\right )} - 40 \, e - 1\right )} e^{\left (-\frac {5}{x - 1}\right )}}{x^{4} e^{6} - 2 \, x^{3} e^{6} + x^{2} e^{6}}\,{d x} + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.55, size = 81, normalized size = 2.31 \begin {gather*} -\frac {16\,{\mathrm {e}}^{\frac {1}{x-1}-\frac {6\,x}{x-1}+2}}{x}-{\mathrm {e}}^{\frac {1}{x-1}-\frac {6\,x}{x-1}}\,\left (x-8\,\mathrm {e}-8\,x^2\,\mathrm {e}-{\mathrm {e}}^{\frac {6\,x}{x-1}-\frac {1}{x-1}}\,\ln \relax (x)+2\,x^3+x^5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.34, size = 49, normalized size = 1.40 \begin {gather*} \log {\relax (x )} + \frac {\left (- x^{6} - 2 x^{4} + 8 e x^{3} - x^{2} + 8 e x - 16 e^{2}\right ) e^{- \frac {4 x + 1}{x - 1}}}{x e^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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