\(\int \frac {e^{\frac {256-\log (x^3)}{-5+x}} (25 x-10 x^2+x^3+(-30-757 x-252 x^2-x^3) \log (6+2 x)+(3 x+x^2) \log (x^3) \log (6+2 x))}{75 x^2-5 x^3-7 x^4+x^5} \, dx\) [5069]

Optimal result

Integrand size = 90, antiderivative size = 26 \[ \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \left (25 x-10 x^2+x^3+\left (-30-757 x-252 x^2-x^3\right ) \log (6+2 x)+\left (3 x+x^2\right ) \log \left (x^3\right ) \log (6+2 x)\right )}{75 x^2-5 x^3-7 x^4+x^5} \, dx=\frac {e^{\frac {-256+\log \left (x^3\right )}{5-x}} \log (2 (3+x))}{x} \]

[Out]

exp((ln(x^3)-256)/(5-x))/x*ln(2*x+6)

Rubi [F]

\[ \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \left (25 x-10 x^2+x^3+\left (-30-757 x-252 x^2-x^3\right ) \log (6+2 x)+\left (3 x+x^2\right ) \log \left (x^3\right ) \log (6+2 x)\right )}{75 x^2-5 x^3-7 x^4+x^5} \, dx=\int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \left (25 x-10 x^2+x^3+\left (-30-757 x-252 x^2-x^3\right ) \log (6+2 x)+\left (3 x+x^2\right ) \log \left (x^3\right ) \log (6+2 x)\right )}{75 x^2-5 x^3-7 x^4+x^5} \, dx \]

[In]

Int[(E^((256 - Log[x^3])/(-5 + x))*(25*x - 10*x^2 + x^3 + (-30 - 757*x - 252*x^2 - x^3)*Log[6 + 2*x] + (3*x +
x^2)*Log[x^3]*Log[6 + 2*x]))/(75*x^2 - 5*x^3 - 7*x^4 + x^5),x]

[Out]

Defer[Int][E^((256 - Log[x^3])/(-5 + x))/x, x]/3 - Defer[Int][E^((256 - Log[x^3])/(-5 + x))/(3 + x), x]/3 - (2
*Defer[Int][(E^((256 - Log[x^3])/(-5 + x))*Log[6 + 2*x])/(5 - x)^2, x])/5 - (254*Defer[Int][(E^((256 - Log[x^3
])/(-5 + x))*Log[6 + 2*x])/(-5 + x)^2, x])/5 + (253*Defer[Int][(E^((256 - Log[x^3])/(-5 + x))*Log[6 + 2*x])/(-
5 + x), x])/25 - (2*Defer[Int][(E^((256 - Log[x^3])/(-5 + x))*Log[6 + 2*x])/x^2, x])/5 - (253*Defer[Int][(E^((
256 - Log[x^3])/(-5 + x))*Log[6 + 2*x])/x, x])/25 + Defer[Int][(E^((256 - Log[x^3])/(-5 + x))*Log[x^3]*Log[6 +
2*x])/(5 - x)^2, x]/5 + (2*Defer[Int][(E^((256 - Log[x^3])/(-5 + x))*Log[x^3]*Log[6 + 2*x])/(5 - x), x])/25 +
Defer[Int][(E^((256 - Log[x^3])/(-5 + x))*Log[x^3]*Log[6 + 2*x])/(-5 + x), x]/25 + Defer[Int][(E^((256 - Log[
x^3])/(-5 + x))*Log[x^3]*Log[6 + 2*x])/x, x]/25

Rubi steps \begin{align*} \text {integral}& = \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \left (25 x-10 x^2+x^3+\left (-30-757 x-252 x^2-x^3\right ) \log (6+2 x)+\left (3 x+x^2\right ) \log \left (x^3\right ) \log (6+2 x)\right )}{(5-x)^2 x^2 (3+x)} \, dx \\ & = \int \left (-\frac {10 e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{(-5+x)^2 (3+x)}+\frac {25 e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{(-5+x)^2 x (3+x)}+\frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} x}{(-5+x)^2 (3+x)}+\frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \left (-10-249 x-x^2+x \log \left (x^3\right )\right ) \log (6+2 x)}{(5-x)^2 x^2}\right ) \, dx \\ & = -\left (10 \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{(-5+x)^2 (3+x)} \, dx\right )+25 \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{(-5+x)^2 x (3+x)} \, dx+\int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} x}{(-5+x)^2 (3+x)} \, dx+\int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \left (-10-249 x-x^2+x \log \left (x^3\right )\right ) \log (6+2 x)}{(5-x)^2 x^2} \, dx \\ & = -\left (10 \int \left (\frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{8 (-5+x)^2}-\frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{64 (-5+x)}+\frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{64 (3+x)}\right ) \, dx\right )+25 \int \left (\frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{40 (-5+x)^2}-\frac {13 e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{1600 (-5+x)}+\frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{75 x}-\frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{192 (3+x)}\right ) \, dx+\int \left (\frac {5 e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{8 (-5+x)^2}+\frac {3 e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{64 (-5+x)}-\frac {3 e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{64 (3+x)}\right ) \, dx+\int \left (\frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \left (-10-249 x-x^2+x \log \left (x^3\right )\right ) \log (6+2 x)}{25 (5-x)^2}+\frac {2 e^{\frac {256-\log \left (x^3\right )}{-5+x}} \left (-10-249 x-x^2+x \log \left (x^3\right )\right ) \log (6+2 x)}{125 (5-x)}+\frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \left (-10-249 x-x^2+x \log \left (x^3\right )\right ) \log (6+2 x)}{25 x^2}+\frac {2 e^{\frac {256-\log \left (x^3\right )}{-5+x}} \left (-10-249 x-x^2+x \log \left (x^3\right )\right ) \log (6+2 x)}{125 x}\right ) \, dx \\ & = \frac {2}{125} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \left (-10-249 x-x^2+x \log \left (x^3\right )\right ) \log (6+2 x)}{5-x} \, dx+\frac {2}{125} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \left (-10-249 x-x^2+x \log \left (x^3\right )\right ) \log (6+2 x)}{x} \, dx+\frac {1}{25} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \left (-10-249 x-x^2+x \log \left (x^3\right )\right ) \log (6+2 x)}{(5-x)^2} \, dx+\frac {1}{25} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \left (-10-249 x-x^2+x \log \left (x^3\right )\right ) \log (6+2 x)}{x^2} \, dx+\frac {3}{64} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{-5+x} \, dx-\frac {3}{64} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{3+x} \, dx-\frac {25}{192} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{3+x} \, dx+\frac {5}{32} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{-5+x} \, dx-\frac {5}{32} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{3+x} \, dx-\frac {13}{64} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{-5+x} \, dx+\frac {1}{3} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{x} \, dx+2 \left (\frac {5}{8} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{(-5+x)^2} \, dx\right )-\frac {5}{4} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{(-5+x)^2} \, dx \\ & = \frac {2}{125} \int \left (-249 e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log (6+2 x)-\frac {10 e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log (6+2 x)}{x}-e^{\frac {256-\log \left (x^3\right )}{-5+x}} x \log (6+2 x)+e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log \left (x^3\right ) \log (6+2 x)\right ) \, dx+\frac {2}{125} \int \left (\frac {10 e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log (6+2 x)}{-5+x}+\frac {249 e^{\frac {256-\log \left (x^3\right )}{-5+x}} x \log (6+2 x)}{-5+x}+\frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} x^2 \log (6+2 x)}{-5+x}+\frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} x \log \left (x^3\right ) \log (6+2 x)}{5-x}\right ) \, dx+\frac {1}{25} \int \left (-e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log (6+2 x)-\frac {10 e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log (6+2 x)}{x^2}-\frac {249 e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log (6+2 x)}{x}+\frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log \left (x^3\right ) \log (6+2 x)}{x}\right ) \, dx+\frac {1}{25} \int \left (-\frac {10 e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log (6+2 x)}{(5-x)^2}-\frac {249 e^{\frac {256-\log \left (x^3\right )}{-5+x}} x \log (6+2 x)}{(5-x)^2}-\frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} x^2 \log (6+2 x)}{(5-x)^2}+\frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} x \log \left (x^3\right ) \log (6+2 x)}{(5-x)^2}\right ) \, dx+\frac {3}{64} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{-5+x} \, dx-\frac {3}{64} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{3+x} \, dx-\frac {25}{192} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{3+x} \, dx+\frac {5}{32} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{-5+x} \, dx-\frac {5}{32} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{3+x} \, dx-\frac {13}{64} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{-5+x} \, dx+\frac {1}{3} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{x} \, dx+2 \left (\frac {5}{8} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{(-5+x)^2} \, dx\right )-\frac {5}{4} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{(-5+x)^2} \, dx \\ & = -\left (\frac {2}{125} \int e^{\frac {256-\log \left (x^3\right )}{-5+x}} x \log (6+2 x) \, dx\right )+\frac {2}{125} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} x^2 \log (6+2 x)}{-5+x} \, dx+\frac {2}{125} \int e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log \left (x^3\right ) \log (6+2 x) \, dx+\frac {2}{125} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} x \log \left (x^3\right ) \log (6+2 x)}{5-x} \, dx-\frac {1}{25} \int e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log (6+2 x) \, dx-\frac {1}{25} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} x^2 \log (6+2 x)}{(5-x)^2} \, dx+\frac {1}{25} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log \left (x^3\right ) \log (6+2 x)}{x} \, dx+\frac {1}{25} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} x \log \left (x^3\right ) \log (6+2 x)}{(5-x)^2} \, dx+\frac {3}{64} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{-5+x} \, dx-\frac {3}{64} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{3+x} \, dx-\frac {25}{192} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{3+x} \, dx+\frac {5}{32} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{-5+x} \, dx-\frac {5}{32} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{3+x} \, dx+\frac {4}{25} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log (6+2 x)}{-5+x} \, dx-\frac {4}{25} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log (6+2 x)}{x} \, dx-\frac {13}{64} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{-5+x} \, dx+\frac {1}{3} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{x} \, dx-\frac {2}{5} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log (6+2 x)}{(5-x)^2} \, dx-\frac {2}{5} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log (6+2 x)}{x^2} \, dx+2 \left (\frac {5}{8} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{(-5+x)^2} \, dx\right )-\frac {5}{4} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{(-5+x)^2} \, dx-\frac {498}{125} \int e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log (6+2 x) \, dx+\frac {498}{125} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} x \log (6+2 x)}{-5+x} \, dx-\frac {249}{25} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log (6+2 x)}{x} \, dx-\frac {249}{25} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} x \log (6+2 x)}{(5-x)^2} \, dx \\ & = -\left (\frac {2}{125} \int e^{\frac {256-\log \left (x^3\right )}{-5+x}} x \log (6+2 x) \, dx\right )+\frac {2}{125} \int e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log \left (x^3\right ) \log (6+2 x) \, dx+\frac {2}{125} \int \left (5 e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log (6+2 x)+\frac {25 e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log (6+2 x)}{-5+x}+e^{\frac {256-\log \left (x^3\right )}{-5+x}} x \log (6+2 x)\right ) \, dx+\frac {2}{125} \int \left (-e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log \left (x^3\right ) \log (6+2 x)+\frac {5 e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log \left (x^3\right ) \log (6+2 x)}{5-x}\right ) \, dx-\frac {1}{25} \int e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log (6+2 x) \, dx+\frac {1}{25} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log \left (x^3\right ) \log (6+2 x)}{x} \, dx-\frac {1}{25} \int \left (e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log (6+2 x)+\frac {25 e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log (6+2 x)}{(-5+x)^2}+\frac {10 e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log (6+2 x)}{-5+x}\right ) \, dx+\frac {1}{25} \int \left (\frac {5 e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log \left (x^3\right ) \log (6+2 x)}{(5-x)^2}+\frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log \left (x^3\right ) \log (6+2 x)}{-5+x}\right ) \, dx+\frac {3}{64} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{-5+x} \, dx-\frac {3}{64} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{3+x} \, dx-\frac {25}{192} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{3+x} \, dx+\frac {5}{32} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{-5+x} \, dx-\frac {5}{32} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{3+x} \, dx+\frac {4}{25} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log (6+2 x)}{-5+x} \, dx-\frac {4}{25} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log (6+2 x)}{x} \, dx-\frac {13}{64} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{-5+x} \, dx+\frac {1}{3} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{x} \, dx-\frac {2}{5} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log (6+2 x)}{(5-x)^2} \, dx-\frac {2}{5} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log (6+2 x)}{x^2} \, dx+2 \left (\frac {5}{8} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{(-5+x)^2} \, dx\right )-\frac {5}{4} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{(-5+x)^2} \, dx-\frac {498}{125} \int e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log (6+2 x) \, dx+\frac {498}{125} \int \left (e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log (6+2 x)+\frac {5 e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log (6+2 x)}{-5+x}\right ) \, dx-\frac {249}{25} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log (6+2 x)}{x} \, dx-\frac {249}{25} \int \left (\frac {5 e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log (6+2 x)}{(-5+x)^2}+\frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log (6+2 x)}{-5+x}\right ) \, dx \\ & = -2 \left (\frac {1}{25} \int e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log (6+2 x) \, dx\right )+\frac {1}{25} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log \left (x^3\right ) \log (6+2 x)}{-5+x} \, dx+\frac {1}{25} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log \left (x^3\right ) \log (6+2 x)}{x} \, dx+\frac {3}{64} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{-5+x} \, dx-\frac {3}{64} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{3+x} \, dx+\frac {2}{25} \int e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log (6+2 x) \, dx+\frac {2}{25} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log \left (x^3\right ) \log (6+2 x)}{5-x} \, dx-\frac {25}{192} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{3+x} \, dx+\frac {5}{32} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{-5+x} \, dx-\frac {5}{32} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{3+x} \, dx+\frac {4}{25} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log (6+2 x)}{-5+x} \, dx-\frac {4}{25} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log (6+2 x)}{x} \, dx+\frac {1}{5} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log \left (x^3\right ) \log (6+2 x)}{(5-x)^2} \, dx-\frac {13}{64} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{-5+x} \, dx+\frac {1}{3} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{x} \, dx-\frac {2}{5} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log (6+2 x)}{(5-x)^2} \, dx-\frac {2}{5} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log (6+2 x)}{x^2} \, dx+2 \left (\frac {5}{8} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{(-5+x)^2} \, dx\right )-\frac {5}{4} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}}}{(-5+x)^2} \, dx-\frac {249}{25} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log (6+2 x)}{-5+x} \, dx-\frac {249}{25} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log (6+2 x)}{x} \, dx+\frac {498}{25} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log (6+2 x)}{-5+x} \, dx-\frac {249}{5} \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log (6+2 x)}{(-5+x)^2} \, dx-\int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \log (6+2 x)}{(-5+x)^2} \, dx \\ \end{align*}

Mathematica [A] (verified)

Time = 5.15 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.15 \[ \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \left (25 x-10 x^2+x^3+\left (-30-757 x-252 x^2-x^3\right ) \log (6+2 x)+\left (3 x+x^2\right ) \log \left (x^3\right ) \log (6+2 x)\right )}{75 x^2-5 x^3-7 x^4+x^5} \, dx=\frac {e^{\frac {256}{-5+x}} \left (x^3\right )^{-\frac {1}{-5+x}} \log (2 (3+x))}{x} \]

[In]

Integrate[(E^((256 - Log[x^3])/(-5 + x))*(25*x - 10*x^2 + x^3 + (-30 - 757*x - 252*x^2 - x^3)*Log[6 + 2*x] + (
3*x + x^2)*Log[x^3]*Log[6 + 2*x]))/(75*x^2 - 5*x^3 - 7*x^4 + x^5),x]

[Out]

(E^(256/(-5 + x))*Log[2*(3 + x)])/(x*(x^3)^(-5 + x)^(-1))

Maple [A] (verified)

Time = 4.46 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.96

method	result	size
parallelrisch	\(\frac {\ln \left (2 x +6\right ) {\mathrm e}^{-\frac {\ln \left (x^{3}\right )-256}{-5+x}}}{x}\)	\(25\)
risch	\(\frac {\ln \left (2 x +6\right ) x^{-\frac {3}{-5+x}} {\mathrm e}^{\frac {i \pi \operatorname {csgn}\left (i x^{2}\right )^{3}-2 i \pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )^{2}+i \pi \operatorname {csgn}\left (i x \right )^{2} \operatorname {csgn}\left (i x^{2}\right )+i \pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right ) \operatorname {csgn}\left (i x^{3}\right )-i \pi \,\operatorname {csgn}\left (i x^{2}\right ) \operatorname {csgn}\left (i x^{3}\right )^{2}-i \pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{3}\right )^{2}+i \pi \operatorname {csgn}\left (i x^{3}\right )^{3}+512}{2 x -10}}}{x}\)	\(153\)

[In]

int(((x^2+3*x)*ln(2*x+6)*ln(x^3)+(-x^3-252*x^2-757*x-30)*ln(2*x+6)+x^3-10*x^2+25*x)*exp((-ln(x^3)+256)/(-5+x))
/(x^5-7*x^4-5*x^3+75*x^2),x,method=_RETURNVERBOSE)

[Out]

1/x*ln(2*x+6)*exp(-(ln(x^3)-256)/(-5+x))

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.92 \[ \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \left (25 x-10 x^2+x^3+\left (-30-757 x-252 x^2-x^3\right ) \log (6+2 x)+\left (3 x+x^2\right ) \log \left (x^3\right ) \log (6+2 x)\right )}{75 x^2-5 x^3-7 x^4+x^5} \, dx=\frac {e^{\left (-\frac {\log \left (x^{3}\right ) - 256}{x - 5}\right )} \log \left (2 \, x + 6\right )}{x} \]

[In]

integrate(((x^2+3*x)*log(2*x+6)*log(x^3)+(-x^3-252*x^2-757*x-30)*log(2*x+6)+x^3-10*x^2+25*x)*exp((-log(x^3)+25
6)/(-5+x))/(x^5-7*x^4-5*x^3+75*x^2),x, algorithm="fricas")

[Out]

e^(-(log(x^3) - 256)/(x - 5))*log(2*x + 6)/x

Sympy [A] (verification not implemented)

Time = 0.27 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.73 \[ \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \left (25 x-10 x^2+x^3+\left (-30-757 x-252 x^2-x^3\right ) \log (6+2 x)+\left (3 x+x^2\right ) \log \left (x^3\right ) \log (6+2 x)\right )}{75 x^2-5 x^3-7 x^4+x^5} \, dx=\frac {e^{\frac {256 - \log {\left (x^{3} \right )}}{x - 5}} \log {\left (2 x + 6 \right )}}{x} \]

[In]

integrate(((x**2+3*x)*ln(2*x+6)*ln(x**3)+(-x**3-252*x**2-757*x-30)*ln(2*x+6)+x**3-10*x**2+25*x)*exp((-ln(x**3)
+256)/(-5+x))/(x**5-7*x**4-5*x**3+75*x**2),x)

[Out]

exp((256 - log(x**3))/(x - 5))*log(2*x + 6)/x

Maxima [A] (verification not implemented)

none

Time = 0.36 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.12 \[ \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \left (25 x-10 x^2+x^3+\left (-30-757 x-252 x^2-x^3\right ) \log (6+2 x)+\left (3 x+x^2\right ) \log \left (x^3\right ) \log (6+2 x)\right )}{75 x^2-5 x^3-7 x^4+x^5} \, dx=\frac {{\left (\log \left (2\right ) + \log \left (x + 3\right )\right )} e^{\left (-\frac {3 \, \log \left (x\right )}{x - 5} + \frac {256}{x - 5}\right )}}{x} \]

[In]

integrate(((x^2+3*x)*log(2*x+6)*log(x^3)+(-x^3-252*x^2-757*x-30)*log(2*x+6)+x^3-10*x^2+25*x)*exp((-log(x^3)+25
6)/(-5+x))/(x^5-7*x^4-5*x^3+75*x^2),x, algorithm="maxima")

[Out]

(log(2) + log(x + 3))*e^(-3*log(x)/(x - 5) + 256/(x - 5))/x

Giac [F]

\[ \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \left (25 x-10 x^2+x^3+\left (-30-757 x-252 x^2-x^3\right ) \log (6+2 x)+\left (3 x+x^2\right ) \log \left (x^3\right ) \log (6+2 x)\right )}{75 x^2-5 x^3-7 x^4+x^5} \, dx=\int { \frac {{\left (x^{3} + {\left (x^{2} + 3 \, x\right )} \log \left (x^{3}\right ) \log \left (2 \, x + 6\right ) - 10 \, x^{2} - {\left (x^{3} + 252 \, x^{2} + 757 \, x + 30\right )} \log \left (2 \, x + 6\right ) + 25 \, x\right )} e^{\left (-\frac {\log \left (x^{3}\right ) - 256}{x - 5}\right )}}{x^{5} - 7 \, x^{4} - 5 \, x^{3} + 75 \, x^{2}} \,d x } \]

[In]

integrate(((x^2+3*x)*log(2*x+6)*log(x^3)+(-x^3-252*x^2-757*x-30)*log(2*x+6)+x^3-10*x^2+25*x)*exp((-log(x^3)+25
6)/(-5+x))/(x^5-7*x^4-5*x^3+75*x^2),x, algorithm="giac")

[Out]

integrate((x^3 + (x^2 + 3*x)*log(x^3)*log(2*x + 6) - 10*x^2 - (x^3 + 252*x^2 + 757*x + 30)*log(2*x + 6) + 25*x
)*e^(-(log(x^3) - 256)/(x - 5))/(x^5 - 7*x^4 - 5*x^3 + 75*x^2), x)

Mupad [F(-1)]

Timed out. \[ \int \frac {e^{\frac {256-\log \left (x^3\right )}{-5+x}} \left (25 x-10 x^2+x^3+\left (-30-757 x-252 x^2-x^3\right ) \log (6+2 x)+\left (3 x+x^2\right ) \log \left (x^3\right ) \log (6+2 x)\right )}{75 x^2-5 x^3-7 x^4+x^5} \, dx=\int \frac {{\mathrm {e}}^{-\frac {\ln \left (x^3\right )-256}{x-5}}\,\left (25\,x-\ln \left (2\,x+6\right )\,\left (x^3+252\,x^2+757\,x+30\right )-10\,x^2+x^3+\ln \left (x^3\right )\,\ln \left (2\,x+6\right )\,\left (x^2+3\,x\right )\right )}{x^5-7\,x^4-5\,x^3+75\,x^2} \,d x \]

[In]

int((exp(-(log(x^3) - 256)/(x - 5))*(25*x - log(2*x + 6)*(757*x + 252*x^2 + x^3 + 30) - 10*x^2 + x^3 + log(x^3
)*log(2*x + 6)*(3*x + x^2)))/(75*x^2 - 5*x^3 - 7*x^4 + x^5),x)

[Out]

int((exp(-(log(x^3) - 256)/(x - 5))*(25*x - log(2*x + 6)*(757*x + 252*x^2 + x^3 + 30) - 10*x^2 + x^3 + log(x^3
)*log(2*x + 6)*(3*x + x^2)))/(75*x^2 - 5*x^3 - 7*x^4 + x^5), x)