Integrand size = 95, antiderivative size = 30 \[ \int \frac {-28-88 x+13 x^2+16 x^3+2 x^4+e^x \left (-16+32 x-8 x^2-8 x^3-x^4\right ) \log (16)+\left (16-64 x+72 x^2-8 x^3-15 x^4-2 x^5\right ) \log (16)}{16-32 x+8 x^2+8 x^3+x^4} \, dx=2 x+\frac {3}{x-\frac {4}{4+x}}-\left (e^x+(-1+x) x\right ) \log (16) \]
Time = 0.90 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.30 \[ \int \frac {-28-88 x+13 x^2+16 x^3+2 x^4+e^x \left (-16+32 x-8 x^2-8 x^3-x^4\right ) \log (16)+\left (16-64 x+72 x^2-8 x^3-15 x^4-2 x^5\right ) \log (16)}{16-32 x+8 x^2+8 x^3+x^4} \, dx=\frac {3 (4+x)}{-4+4 x+x^2}-x (-2-\log (16))-e^x \log (16)-x^2 \log (16) \]
Integrate[(-28 - 88*x + 13*x^2 + 16*x^3 + 2*x^4 + E^x*(-16 + 32*x - 8*x^2 - 8*x^3 - x^4)*Log[16] + (16 - 64*x + 72*x^2 - 8*x^3 - 15*x^4 - 2*x^5)*Log [16])/(16 - 32*x + 8*x^2 + 8*x^3 + x^4),x]
Leaf count is larger than twice the leaf count of optimal. \(1452\) vs. \(2(30)=60\).
Time = 3.44 (sec) , antiderivative size = 1452, normalized size of antiderivative = 48.40, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.021, Rules used = {2463, 2009}
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {2 x^4+16 x^3+13 x^2+e^x \left (-x^4-8 x^3-8 x^2+32 x-16\right ) \log (16)+\left (-2 x^5-15 x^4-8 x^3+72 x^2-64 x+16\right ) \log (16)-88 x-28}{x^4+8 x^3+8 x^2-32 x+16} \, dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \int \left (\frac {2 x^4+16 x^3+13 x^2+e^x \left (-x^4-8 x^3-8 x^2+32 x-16\right ) \log (16)+\left (-2 x^5-15 x^4-8 x^3+72 x^2-64 x+16\right ) \log (16)-88 x-28}{32 \sqrt {2} \left (-2 x+4 \sqrt {2}-4\right )}+\frac {2 x^4+16 x^3+13 x^2+e^x \left (-x^4-8 x^3-8 x^2+32 x-16\right ) \log (16)+\left (-2 x^5-15 x^4-8 x^3+72 x^2-64 x+16\right ) \log (16)-88 x-28}{32 \sqrt {2} \left (2 x+4 \sqrt {2}+4\right )}+\frac {2 x^4+16 x^3+13 x^2+e^x \left (-x^4-8 x^3-8 x^2+32 x-16\right ) \log (16)+\left (-2 x^5-15 x^4-8 x^3+72 x^2-64 x+16\right ) \log (16)-88 x-28}{8 \left (-2 x+4 \sqrt {2}-4\right )^2}+\frac {2 x^4+16 x^3+13 x^2+e^x \left (-x^4-8 x^3-8 x^2+32 x-16\right ) \log (16)+\left (-2 x^5-15 x^4-8 x^3+72 x^2-64 x+16\right ) \log (16)-88 x-28}{8 \left (2 x+4 \sqrt {2}+4\right )^2}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {1}{512} \left (8+11 \sqrt {2}\right ) \log (16) x^4+\frac {1}{512} \left (8-11 \sqrt {2}\right ) \log (16) x^4-\frac {1}{32} \log (16) x^4-\frac {1}{96} \left (7+8 \sqrt {2}\right ) \log (16) x^3+\frac {1}{192} \left (14+\sqrt {2}\right ) \log (16) x^3+\frac {1}{192} \left (14-\sqrt {2}\right ) \log (16) x^3-\frac {1}{96} \left (7-8 \sqrt {2}\right ) \log (16) x^3-\frac {1}{96} \left (2+\sqrt {2}\right ) x^3-\frac {1}{96} \left (2-\sqrt {2}\right ) x^3+\frac {x^3}{24}-\frac {1}{64} \left (12+5 \sqrt {2}\right ) \log (16) x^2-\frac {1}{16} \left (5+3 \sqrt {2}\right ) \log (16) x^2-\frac {1}{16} \left (5-3 \sqrt {2}\right ) \log (16) x^2-\frac {1}{64} \left (12-5 \sqrt {2}\right ) \log (16) x^2+\frac {1}{32} \left (4+3 \sqrt {2}\right ) x^2-\frac {1}{8} \left (2+\sqrt {2}\right ) x^2-\frac {1}{8} \left (1+\sqrt {2}\right ) x^2-\frac {1}{8} \left (2-\sqrt {2}\right ) x^2-\frac {1}{8} \left (1-\sqrt {2}\right ) x^2+\frac {1}{32} \left (4-3 \sqrt {2}\right ) x^2+\frac {x^2}{2}+\frac {1}{8} \left (3+2 \sqrt {2}\right ) \log (16) x+\frac {1}{16} \left (2+\sqrt {2}\right ) \log (16) x+\frac {1}{16} \left (2-\sqrt {2}\right ) \log (16) x+\frac {1}{8} \left (3-2 \sqrt {2}\right ) \log (16) x-\frac {1}{8} \left (10+7 \sqrt {2}\right ) x+\frac {1}{2} \left (4+3 \sqrt {2}\right ) x+\frac {3}{4} \left (3+2 \sqrt {2}\right ) x-\frac {13}{64} \left (2+\sqrt {2}\right ) x-2 \left (1+\sqrt {2}\right ) x-\frac {13}{64} \left (2-\sqrt {2}\right ) x-2 \left (1-\sqrt {2}\right ) x+\frac {3}{4} \left (3-2 \sqrt {2}\right ) x+\frac {1}{2} \left (4-3 \sqrt {2}\right ) x-\frac {1}{8} \left (10-7 \sqrt {2}\right ) x+\frac {13 x}{16}+\frac {11}{8} \left (2-\sqrt {2}\right ) \log \left (x+2 \left (1-\sqrt {2}\right )\right )-\frac {13}{8} \left (1-\sqrt {2}\right ) \log \left (x+2 \left (1-\sqrt {2}\right )\right )+6 \left (3-2 \sqrt {2}\right ) \log \left (x+2 \left (1-\sqrt {2}\right )\right )+\frac {13}{32} \left (4-3 \sqrt {2}\right ) \log \left (x+2 \left (1-\sqrt {2}\right )\right )-2 \left (7-5 \sqrt {2}\right ) \log \left (x+2 \left (1-\sqrt {2}\right )\right )-\left (10-7 \sqrt {2}\right ) \log \left (x+2 \left (1-\sqrt {2}\right )\right )+\frac {1}{4} \left (24-17 \sqrt {2}\right ) \log \left (x+2 \left (1-\sqrt {2}\right )\right )+\frac {7 \log \left (x+2 \left (1-\sqrt {2}\right )\right )}{16 \sqrt {2}}-\frac {11}{4} \log \left (x+2 \left (1-\sqrt {2}\right )\right )+\frac {1}{4} \left (24+17 \sqrt {2}\right ) \log \left (x+2 \left (1+\sqrt {2}\right )\right )-\left (10+7 \sqrt {2}\right ) \log \left (x+2 \left (1+\sqrt {2}\right )\right )-2 \left (7+5 \sqrt {2}\right ) \log \left (x+2 \left (1+\sqrt {2}\right )\right )+\frac {13}{32} \left (4+3 \sqrt {2}\right ) \log \left (x+2 \left (1+\sqrt {2}\right )\right )+6 \left (3+2 \sqrt {2}\right ) \log \left (x+2 \left (1+\sqrt {2}\right )\right )+\frac {11}{8} \left (2+\sqrt {2}\right ) \log \left (x+2 \left (1+\sqrt {2}\right )\right )-\frac {13}{8} \left (1+\sqrt {2}\right ) \log \left (x+2 \left (1+\sqrt {2}\right )\right )-\frac {7 \log \left (x+2 \left (1+\sqrt {2}\right )\right )}{16 \sqrt {2}}-\frac {11}{4} \log \left (x+2 \left (1+\sqrt {2}\right )\right )-\frac {11 \left (1-\sqrt {2}\right )}{2 \left (x+2 \left (1-\sqrt {2}\right )\right )}-\frac {13 \left (3-2 \sqrt {2}\right )}{8 \left (x+2 \left (1-\sqrt {2}\right )\right )}+\frac {4 \left (7-5 \sqrt {2}\right )}{x+2 \left (1-\sqrt {2}\right )}-\frac {17-12 \sqrt {2}}{x+2 \left (1-\sqrt {2}\right )}+\frac {7}{8 \left (x+2 \left (1-\sqrt {2}\right )\right )}-\frac {17+12 \sqrt {2}}{x+2 \left (1+\sqrt {2}\right )}+\frac {4 \left (7+5 \sqrt {2}\right )}{x+2 \left (1+\sqrt {2}\right )}-\frac {13 \left (3+2 \sqrt {2}\right )}{8 \left (x+2 \left (1+\sqrt {2}\right )\right )}-\frac {11 \left (1+\sqrt {2}\right )}{2 \left (x+2 \left (1+\sqrt {2}\right )\right )}+\frac {7}{8 \left (x+2 \left (1+\sqrt {2}\right )\right )}-\frac {3}{8} e^x \log (16)-\frac {e^x \left (x+2 \left (1-\sqrt {2}\right )\right )^3 \log (16)}{64 \sqrt {2}}+\frac {e^x \left (x+2 \left (1+\sqrt {2}\right )\right )^3 \log (16)}{64 \sqrt {2}}+\frac {3 e^x \left (x+2 \left (1-\sqrt {2}\right )\right )^2 \log (16)}{64 \sqrt {2}}-\frac {3}{32} e^x \left (x+2 \left (1-\sqrt {2}\right )\right )^2 \log (16)-\frac {3 e^x \left (x+2 \left (1+\sqrt {2}\right )\right )^2 \log (16)}{64 \sqrt {2}}-\frac {3}{32} e^x \left (x+2 \left (1+\sqrt {2}\right )\right )^2 \log (16)-\frac {3 e^x \left (x+2 \left (1-\sqrt {2}\right )\right ) \log (16)}{32 \sqrt {2}}+\frac {3}{16} e^x \left (x+2 \left (1-\sqrt {2}\right )\right ) \log (16)+\frac {3 e^x \left (x+2 \left (1+\sqrt {2}\right )\right ) \log (16)}{32 \sqrt {2}}+\frac {3}{16} e^x \left (x+2 \left (1+\sqrt {2}\right )\right ) \log (16)\) |
Int[(-28 - 88*x + 13*x^2 + 16*x^3 + 2*x^4 + E^x*(-16 + 32*x - 8*x^2 - 8*x^ 3 - x^4)*Log[16] + (16 - 64*x + 72*x^2 - 8*x^3 - 15*x^4 - 2*x^5)*Log[16])/ (16 - 32*x + 8*x^2 + 8*x^3 + x^4),x]
(13*x)/16 - ((10 - 7*Sqrt[2])*x)/8 + ((4 - 3*Sqrt[2])*x)/2 + (3*(3 - 2*Sqr t[2])*x)/4 - 2*(1 - Sqrt[2])*x - (13*(2 - Sqrt[2])*x)/64 - 2*(1 + Sqrt[2]) *x - (13*(2 + Sqrt[2])*x)/64 + (3*(3 + 2*Sqrt[2])*x)/4 + ((4 + 3*Sqrt[2])* x)/2 - ((10 + 7*Sqrt[2])*x)/8 + x^2/2 + ((4 - 3*Sqrt[2])*x^2)/32 - ((1 - S qrt[2])*x^2)/8 - ((2 - Sqrt[2])*x^2)/8 - ((1 + Sqrt[2])*x^2)/8 - ((2 + Sqr t[2])*x^2)/8 + ((4 + 3*Sqrt[2])*x^2)/32 + x^3/24 - ((2 - Sqrt[2])*x^3)/96 - ((2 + Sqrt[2])*x^3)/96 + 7/(8*(2*(1 - Sqrt[2]) + x)) - (17 - 12*Sqrt[2]) /(2*(1 - Sqrt[2]) + x) + (4*(7 - 5*Sqrt[2]))/(2*(1 - Sqrt[2]) + x) - (13*( 3 - 2*Sqrt[2]))/(8*(2*(1 - Sqrt[2]) + x)) - (11*(1 - Sqrt[2]))/(2*(2*(1 - Sqrt[2]) + x)) + 7/(8*(2*(1 + Sqrt[2]) + x)) - (11*(1 + Sqrt[2]))/(2*(2*(1 + Sqrt[2]) + x)) - (13*(3 + 2*Sqrt[2]))/(8*(2*(1 + Sqrt[2]) + x)) + (4*(7 + 5*Sqrt[2]))/(2*(1 + Sqrt[2]) + x) - (17 + 12*Sqrt[2])/(2*(1 + Sqrt[2]) + x) - (3*E^x*Log[16])/8 + ((3 - 2*Sqrt[2])*x*Log[16])/8 + ((2 - Sqrt[2])* x*Log[16])/16 + ((2 + Sqrt[2])*x*Log[16])/16 + ((3 + 2*Sqrt[2])*x*Log[16]) /8 - ((12 - 5*Sqrt[2])*x^2*Log[16])/64 - ((5 - 3*Sqrt[2])*x^2*Log[16])/16 - ((5 + 3*Sqrt[2])*x^2*Log[16])/16 - ((12 + 5*Sqrt[2])*x^2*Log[16])/64 - ( (7 - 8*Sqrt[2])*x^3*Log[16])/96 + ((14 - Sqrt[2])*x^3*Log[16])/192 + ((14 + Sqrt[2])*x^3*Log[16])/192 - ((7 + 8*Sqrt[2])*x^3*Log[16])/96 - (x^4*Log[ 16])/32 + ((8 - 11*Sqrt[2])*x^4*Log[16])/512 + ((8 + 11*Sqrt[2])*x^4*Log[1 6])/512 + (3*E^x*(2*(1 - Sqrt[2]) + x)*Log[16])/16 - (3*E^x*(2*(1 - Sqr...
3.21.42.3.1 Defintions of rubi rules used
Int[(u_.)*(Px_)^(p_), x_Symbol] :> With[{Qx = Factor[Px]}, Int[ExpandIntegr and[u, Qx^p, x], x] /; !SumQ[NonfreeFactors[Qx, x]]] /; PolyQ[Px, x] && Gt Q[Expon[Px, x], 2] && !BinomialQ[Px, x] && !TrinomialQ[Px, x] && ILtQ[p, 0]
Time = 0.20 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.30
| method | result | size |
| risch | \(-4 x^{2} \ln \left (2\right )+4 x \ln \left (2\right )+2 x +\frac {3 x +12}{x^{2}+4 x -4}-4 \,{\mathrm e}^{x} \ln \left (2\right )\) | \(39\) |
| parts | \(-4 x^{2} \ln \left (2\right )+4 x \ln \left (2\right )+2 x -\frac {3 \left (-4-x \right )}{x^{2}+4 x -4}-4 \,{\mathrm e}^{x} \ln \left (2\right )\) | \(40\) |
| norman | \(\frac {\left (2-12 \ln \left (2\right )\right ) x^{3}+\left (-37-144 \ln \left (2\right )\right ) x -4 x^{4} \ln \left (2\right )+16 \,{\mathrm e}^{x} \ln \left (2\right )-16 x \ln \left (2\right ) {\mathrm e}^{x}-4 x^{2} \ln \left (2\right ) {\mathrm e}^{x}+44+128 \ln \left (2\right )}{x^{2}+4 x -4}\) | \(65\) |
| parallelrisch | \(-\frac {4 x^{4} \ln \left (2\right )+12 x^{3} \ln \left (2\right )+4 x^{2} \ln \left (2\right ) {\mathrm e}^{x}+16 x \ln \left (2\right ) {\mathrm e}^{x}-2 x^{3}-44+144 x \ln \left (2\right )-16 \,{\mathrm e}^{x} \ln \left (2\right )-128 \ln \left (2\right )+37 x}{x^{2}+4 x -4}\) | \(68\) |
| default | \(\text {Expression too large to display}\) | \(946\) |
int((4*(-x^4-8*x^3-8*x^2+32*x-16)*ln(2)*exp(x)+4*(-2*x^5-15*x^4-8*x^3+72*x ^2-64*x+16)*ln(2)+2*x^4+16*x^3+13*x^2-88*x-28)/(x^4+8*x^3+8*x^2-32*x+16),x ,method=_RETURNVERBOSE)
Leaf count of result is larger than twice the leaf count of optimal. 61 vs. \(2 (29) = 58\).
Time = 0.26 (sec) , antiderivative size = 61, normalized size of antiderivative = 2.03 \[ \int \frac {-28-88 x+13 x^2+16 x^3+2 x^4+e^x \left (-16+32 x-8 x^2-8 x^3-x^4\right ) \log (16)+\left (16-64 x+72 x^2-8 x^3-15 x^4-2 x^5\right ) \log (16)}{16-32 x+8 x^2+8 x^3+x^4} \, dx=\frac {2 \, x^{3} - 4 \, {\left (x^{2} + 4 \, x - 4\right )} e^{x} \log \left (2\right ) + 8 \, x^{2} - 4 \, {\left (x^{4} + 3 \, x^{3} - 8 \, x^{2} + 4 \, x\right )} \log \left (2\right ) - 5 \, x + 12}{x^{2} + 4 \, x - 4} \]
integrate((4*(-x^4-8*x^3-8*x^2+32*x-16)*log(2)*exp(x)+4*(-2*x^5-15*x^4-8*x ^3+72*x^2-64*x+16)*log(2)+2*x^4+16*x^3+13*x^2-88*x-28)/(x^4+8*x^3+8*x^2-32 *x+16),x, algorithm=\
(2*x^3 - 4*(x^2 + 4*x - 4)*e^x*log(2) + 8*x^2 - 4*(x^4 + 3*x^3 - 8*x^2 + 4 *x)*log(2) - 5*x + 12)/(x^2 + 4*x - 4)
Time = 0.15 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.40 \[ \int \frac {-28-88 x+13 x^2+16 x^3+2 x^4+e^x \left (-16+32 x-8 x^2-8 x^3-x^4\right ) \log (16)+\left (16-64 x+72 x^2-8 x^3-15 x^4-2 x^5\right ) \log (16)}{16-32 x+8 x^2+8 x^3+x^4} \, dx=- 4 x^{2} \log {\left (2 \right )} - x \left (- 4 \log {\left (2 \right )} - 2\right ) - \frac {- 3 x - 12}{x^{2} + 4 x - 4} - 4 e^{x} \log {\left (2 \right )} \]
integrate((4*(-x**4-8*x**3-8*x**2+32*x-16)*ln(2)*exp(x)+4*(-2*x**5-15*x**4 -8*x**3+72*x**2-64*x+16)*ln(2)+2*x**4+16*x**3+13*x**2-88*x-28)/(x**4+8*x** 3+8*x**2-32*x+16),x)
Leaf count of result is larger than twice the leaf count of optimal. 410 vs. \(2 (29) = 58\).
Time = 0.29 (sec) , antiderivative size = 410, normalized size of antiderivative = 13.67 \[ \int \frac {-28-88 x+13 x^2+16 x^3+2 x^4+e^x \left (-16+32 x-8 x^2-8 x^3-x^4\right ) \log (16)+\left (16-64 x+72 x^2-8 x^3-15 x^4-2 x^5\right ) \log (16)}{16-32 x+8 x^2+8 x^3+x^4} \, dx=-2 \, {\left (2 \, x^{2} - 79 \, \sqrt {2} \log \left (\frac {x - 2 \, \sqrt {2} + 2}{x + 2 \, \sqrt {2} + 2}\right ) - 32 \, x + \frac {8 \, {\left (41 \, x - 34\right )}}{x^{2} + 4 \, x - 4} + 112 \, \log \left (x^{2} + 4 \, x - 4\right )\right )} \log \left (2\right ) - \frac {15}{2} \, {\left (23 \, \sqrt {2} \log \left (\frac {x - 2 \, \sqrt {2} + 2}{x + 2 \, \sqrt {2} + 2}\right ) + 8 \, x - \frac {8 \, {\left (17 \, x - 14\right )}}{x^{2} + 4 \, x - 4} - 32 \, \log \left (x^{2} + 4 \, x - 4\right )\right )} \log \left (2\right ) + 2 \, {\left (5 \, \sqrt {2} \log \left (\frac {x - 2 \, \sqrt {2} + 2}{x + 2 \, \sqrt {2} + 2}\right ) - \frac {8 \, {\left (7 \, x - 6\right )}}{x^{2} + 4 \, x - 4} - 8 \, \log \left (x^{2} + 4 \, x - 4\right )\right )} \log \left (2\right ) + 9 \, {\left (\sqrt {2} \log \left (\frac {x - 2 \, \sqrt {2} + 2}{x + 2 \, \sqrt {2} + 2}\right ) - \frac {8 \, {\left (3 \, x - 2\right )}}{x^{2} + 4 \, x - 4}\right )} \log \left (2\right ) - \frac {1}{2} \, {\left (\sqrt {2} \log \left (\frac {x - 2 \, \sqrt {2} + 2}{x + 2 \, \sqrt {2} + 2}\right ) + \frac {8 \, {\left (x + 2\right )}}{x^{2} + 4 \, x - 4}\right )} \log \left (2\right ) - 4 \, {\left (\sqrt {2} \log \left (\frac {x - 2 \, \sqrt {2} + 2}{x + 2 \, \sqrt {2} + 2}\right ) + \frac {8 \, {\left (x - 2\right )}}{x^{2} + 4 \, x - 4}\right )} \log \left (2\right ) - 4 \, e^{x} \log \left (2\right ) + 2 \, x - \frac {2 \, {\left (17 \, x - 14\right )}}{x^{2} + 4 \, x - 4} + \frac {8 \, {\left (7 \, x - 6\right )}}{x^{2} + 4 \, x - 4} - \frac {13 \, {\left (3 \, x - 2\right )}}{4 \, {\left (x^{2} + 4 \, x - 4\right )}} + \frac {7 \, {\left (x + 2\right )}}{4 \, {\left (x^{2} + 4 \, x - 4\right )}} - \frac {11 \, {\left (x - 2\right )}}{x^{2} + 4 \, x - 4} \]
integrate((4*(-x^4-8*x^3-8*x^2+32*x-16)*log(2)*exp(x)+4*(-2*x^5-15*x^4-8*x ^3+72*x^2-64*x+16)*log(2)+2*x^4+16*x^3+13*x^2-88*x-28)/(x^4+8*x^3+8*x^2-32 *x+16),x, algorithm=\
-2*(2*x^2 - 79*sqrt(2)*log((x - 2*sqrt(2) + 2)/(x + 2*sqrt(2) + 2)) - 32*x + 8*(41*x - 34)/(x^2 + 4*x - 4) + 112*log(x^2 + 4*x - 4))*log(2) - 15/2*( 23*sqrt(2)*log((x - 2*sqrt(2) + 2)/(x + 2*sqrt(2) + 2)) + 8*x - 8*(17*x - 14)/(x^2 + 4*x - 4) - 32*log(x^2 + 4*x - 4))*log(2) + 2*(5*sqrt(2)*log((x - 2*sqrt(2) + 2)/(x + 2*sqrt(2) + 2)) - 8*(7*x - 6)/(x^2 + 4*x - 4) - 8*lo g(x^2 + 4*x - 4))*log(2) + 9*(sqrt(2)*log((x - 2*sqrt(2) + 2)/(x + 2*sqrt( 2) + 2)) - 8*(3*x - 2)/(x^2 + 4*x - 4))*log(2) - 1/2*(sqrt(2)*log((x - 2*s qrt(2) + 2)/(x + 2*sqrt(2) + 2)) + 8*(x + 2)/(x^2 + 4*x - 4))*log(2) - 4*( sqrt(2)*log((x - 2*sqrt(2) + 2)/(x + 2*sqrt(2) + 2)) + 8*(x - 2)/(x^2 + 4* x - 4))*log(2) - 4*e^x*log(2) + 2*x - 2*(17*x - 14)/(x^2 + 4*x - 4) + 8*(7 *x - 6)/(x^2 + 4*x - 4) - 13/4*(3*x - 2)/(x^2 + 4*x - 4) + 7/4*(x + 2)/(x^ 2 + 4*x - 4) - 11*(x - 2)/(x^2 + 4*x - 4)
Leaf count of result is larger than twice the leaf count of optimal. 75 vs. \(2 (29) = 58\).
Time = 0.28 (sec) , antiderivative size = 75, normalized size of antiderivative = 2.50 \[ \int \frac {-28-88 x+13 x^2+16 x^3+2 x^4+e^x \left (-16+32 x-8 x^2-8 x^3-x^4\right ) \log (16)+\left (16-64 x+72 x^2-8 x^3-15 x^4-2 x^5\right ) \log (16)}{16-32 x+8 x^2+8 x^3+x^4} \, dx=-\frac {4 \, x^{4} \log \left (2\right ) + 12 \, x^{3} \log \left (2\right ) + 4 \, x^{2} e^{x} \log \left (2\right ) - 2 \, x^{3} - 32 \, x^{2} \log \left (2\right ) + 16 \, x e^{x} \log \left (2\right ) - 8 \, x^{2} + 16 \, x \log \left (2\right ) - 16 \, e^{x} \log \left (2\right ) + 5 \, x - 12}{x^{2} + 4 \, x - 4} \]
integrate((4*(-x^4-8*x^3-8*x^2+32*x-16)*log(2)*exp(x)+4*(-2*x^5-15*x^4-8*x ^3+72*x^2-64*x+16)*log(2)+2*x^4+16*x^3+13*x^2-88*x-28)/(x^4+8*x^3+8*x^2-32 *x+16),x, algorithm=\
-(4*x^4*log(2) + 12*x^3*log(2) + 4*x^2*e^x*log(2) - 2*x^3 - 32*x^2*log(2) + 16*x*e^x*log(2) - 8*x^2 + 16*x*log(2) - 16*e^x*log(2) + 5*x - 12)/(x^2 + 4*x - 4)
Time = 0.50 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.27 \[ \int \frac {-28-88 x+13 x^2+16 x^3+2 x^4+e^x \left (-16+32 x-8 x^2-8 x^3-x^4\right ) \log (16)+\left (16-64 x+72 x^2-8 x^3-15 x^4-2 x^5\right ) \log (16)}{16-32 x+8 x^2+8 x^3+x^4} \, dx=x\,\left (4\,\ln \left (2\right )+2\right )+\frac {3\,x+12}{x^2+4\,x-4}-4\,x^2\,\ln \left (2\right )-4\,{\mathrm {e}}^x\,\ln \left (2\right ) \]