3.60.71 \(\int \frac {4-128 x-8 x^2+386 x^3-60 x^4-258 x^5+190 x^6+64 x^7+e^x (-128+256 x^2+64 x^3-128 x^4-64 x^5+192 x^6)+(4 x^2-128 x^3-4 x^4+254 x^5+64 x^6+e^x (-128 x^2+128 x^4+192 x^5)) \log (\frac {1}{256} (x^2+1024 e^{2 x} x^2-64 x^3+1024 x^4+e^x (-64 x^2+2048 x^3)))}{-x^5+32 e^x x^5+32 x^6} \, dx\)

Optimal. Leaf size=25 \[ \left (-1+\frac {1}{x^2}+x+\log \left (\left (\frac {x}{16}-2 x \left (e^x+x\right )\right )^2\right )\right )^2 \]

________________________________________________________________________________________

Rubi [F]  time = 5.42, 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 {4-128 x-8 x^2+386 x^3-60 x^4-258 x^5+190 x^6+64 x^7+e^x \left (-128+256 x^2+64 x^3-128 x^4-64 x^5+192 x^6\right )+\left (4 x^2-128 x^3-4 x^4+254 x^5+64 x^6+e^x \left (-128 x^2+128 x^4+192 x^5\right )\right ) \log \left (\frac {1}{256} \left (x^2+1024 e^{2 x} x^2-64 x^3+1024 x^4+e^x \left (-64 x^2+2048 x^3\right )\right )\right )}{-x^5+32 e^x x^5+32 x^6} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(4 - 128*x - 8*x^2 + 386*x^3 - 60*x^4 - 258*x^5 + 190*x^6 + 64*x^7 + E^x*(-128 + 256*x^2 + 64*x^3 - 128*x^
4 - 64*x^5 + 192*x^6) + (4*x^2 - 128*x^3 - 4*x^4 + 254*x^5 + 64*x^6 + E^x*(-128*x^2 + 128*x^4 + 192*x^5))*Log[
(x^2 + 1024*E^(2*x)*x^2 - 64*x^3 + 1024*x^4 + E^x*(-64*x^2 + 2048*x^3))/256])/(-x^5 + 32*E^x*x^5 + 32*x^6),x]

[Out]

x^(-4) - 4/x^2 - 2/x - 2*x + 3*x^2 - 6*(1 + x)^2 + (2*(1 + x)^2)/x^2 - 4*Log[x] + (2*Log[((1 - 32*E^x - 32*x)^
2*x^2)/256])/x^2 + 6*x*Log[((1 - 32*E^x - 32*x)^2*x^2)/256] - 132*Defer[Int][(-1 + 32*E^x + 32*x)^(-1), x] + 1
32*Log[((1 - 32*E^x - 32*x)^2*x^2)/256]*Defer[Int][(-1 + 32*E^x + 32*x)^(-1), x] - 136*Defer[Int][x/(-1 + 32*E
^x + 32*x), x] - 128*Log[((1 - 32*E^x - 32*x)^2*x^2)/256]*Defer[Int][x/(-1 + 32*E^x + 32*x), x] + 256*Defer[In
t][x^2/(-1 + 32*E^x + 32*x), x] + 4*Defer[Int][Log[(x^2*(-1 + 32*E^x + 32*x)^2)/256]/x, x] - 264*Defer[Int][De
fer[Int][(-1 + 32*E^x + 32*x)^(-1), x], x] - 264*Defer[Int][Defer[Int][(-1 + 32*E^x + 32*x)^(-1), x]/x, x] - 8
712*Defer[Int][Defer[Int][(-1 + 32*E^x + 32*x)^(-1), x]/(-1 + 32*E^x + 32*x), x] + 8448*Defer[Int][(x*Defer[In
t][(-1 + 32*E^x + 32*x)^(-1), x])/(-1 + 32*E^x + 32*x), x] + 256*Defer[Int][Defer[Int][x/(-1 + 32*E^x + 32*x),
x], x] + 256*Defer[Int][Defer[Int][x/(-1 + 32*E^x + 32*x), x]/x, x] + 8448*Defer[Int][Defer[Int][x/(-1 + 32*E
^x + 32*x), x]/(-1 + 32*E^x + 32*x), x] - 8192*Defer[Int][(x*Defer[Int][x/(-1 + 32*E^x + 32*x), x])/(-1 + 32*E
^x + 32*x), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 \left (2-64 x-2 x^2+127 x^3+32 x^4+32 e^x \left (-2+2 x^2+3 x^3\right )\right ) \left (-1+x^2-x^3-x^2 \log \left (\frac {1}{256} x^2 \left (-1+32 e^x+32 x\right )^2\right )\right )}{\left (1-32 e^x-32 x\right ) x^5} \, dx\\ &=2 \int \frac {\left (2-64 x-2 x^2+127 x^3+32 x^4+32 e^x \left (-2+2 x^2+3 x^3\right )\right ) \left (-1+x^2-x^3-x^2 \log \left (\frac {1}{256} x^2 \left (-1+32 e^x+32 x\right )^2\right )\right )}{\left (1-32 e^x-32 x\right ) x^5} \, dx\\ &=2 \int \left (-\frac {2 (-33+32 x) \left (1-x^2+x^3+x^2 \log \left (\frac {1}{256} x^2 \left (-1+32 e^x+32 x\right )^2\right )\right )}{x^2 \left (-1+32 e^x+32 x\right )}+\frac {\left (-2+2 x^2+3 x^3\right ) \left (1-x^2+x^3+x^2 \log \left (\frac {1}{256} x^2 \left (-1+32 e^x+32 x\right )^2\right )\right )}{x^5}\right ) \, dx\\ &=2 \int \frac {\left (-2+2 x^2+3 x^3\right ) \left (1-x^2+x^3+x^2 \log \left (\frac {1}{256} x^2 \left (-1+32 e^x+32 x\right )^2\right )\right )}{x^5} \, dx-4 \int \frac {(-33+32 x) \left (1-x^2+x^3+x^2 \log \left (\frac {1}{256} x^2 \left (-1+32 e^x+32 x\right )^2\right )\right )}{x^2 \left (-1+32 e^x+32 x\right )} \, dx\\ &=2 \int \left (\frac {\left (1-x^2+x^3\right ) \left (-2+2 x^2+3 x^3\right )}{x^5}+\frac {\left (-2+2 x^2+3 x^3\right ) \log \left (\frac {1}{256} x^2 \left (-1+32 e^x+32 x\right )^2\right )}{x^3}\right ) \, dx-4 \int \left (-\frac {33 \left (1-x^2+x^3+x^2 \log \left (\frac {1}{256} x^2 \left (-1+32 e^x+32 x\right )^2\right )\right )}{x^2 \left (-1+32 e^x+32 x\right )}+\frac {32 \left (1-x^2+x^3+x^2 \log \left (\frac {1}{256} x^2 \left (-1+32 e^x+32 x\right )^2\right )\right )}{x \left (-1+32 e^x+32 x\right )}\right ) \, dx\\ &=2 \int \frac {\left (1-x^2+x^3\right ) \left (-2+2 x^2+3 x^3\right )}{x^5} \, dx+2 \int \frac {\left (-2+2 x^2+3 x^3\right ) \log \left (\frac {1}{256} x^2 \left (-1+32 e^x+32 x\right )^2\right )}{x^3} \, dx-128 \int \frac {1-x^2+x^3+x^2 \log \left (\frac {1}{256} x^2 \left (-1+32 e^x+32 x\right )^2\right )}{x \left (-1+32 e^x+32 x\right )} \, dx+132 \int \frac {1-x^2+x^3+x^2 \log \left (\frac {1}{256} x^2 \left (-1+32 e^x+32 x\right )^2\right )}{x^2 \left (-1+32 e^x+32 x\right )} \, dx\\ &=2 \int \left (-1-\frac {2}{x^5}+\frac {4}{x^3}+\frac {1}{x^2}-\frac {2}{x}+3 x\right ) \, dx+2 \int \left (3 \log \left (\frac {1}{256} x^2 \left (-1+32 e^x+32 x\right )^2\right )-\frac {2 \log \left (\frac {1}{256} x^2 \left (-1+32 e^x+32 x\right )^2\right )}{x^3}+\frac {2 \log \left (\frac {1}{256} x^2 \left (-1+32 e^x+32 x\right )^2\right )}{x}\right ) \, dx-128 \int \left (\frac {1}{x \left (-1+32 e^x+32 x\right )}-\frac {x}{-1+32 e^x+32 x}+\frac {x^2}{-1+32 e^x+32 x}+\frac {x \log \left (\frac {1}{256} x^2 \left (-1+32 e^x+32 x\right )^2\right )}{-1+32 e^x+32 x}\right ) \, dx+132 \int \left (-\frac {1}{-1+32 e^x+32 x}+\frac {1}{x^2 \left (-1+32 e^x+32 x\right )}+\frac {x}{-1+32 e^x+32 x}+\frac {\log \left (\frac {1}{256} x^2 \left (-1+32 e^x+32 x\right )^2\right )}{-1+32 e^x+32 x}\right ) \, dx\\ &=\frac {1}{x^4}-\frac {4}{x^2}-\frac {2}{x}-2 x+3 x^2-4 \log (x)-4 \int \frac {\log \left (\frac {1}{256} x^2 \left (-1+32 e^x+32 x\right )^2\right )}{x^3} \, dx+4 \int \frac {\log \left (\frac {1}{256} x^2 \left (-1+32 e^x+32 x\right )^2\right )}{x} \, dx+6 \int \log \left (\frac {1}{256} x^2 \left (-1+32 e^x+32 x\right )^2\right ) \, dx-128 \int \frac {1}{x \left (-1+32 e^x+32 x\right )} \, dx+128 \int \frac {x}{-1+32 e^x+32 x} \, dx-128 \int \frac {x^2}{-1+32 e^x+32 x} \, dx-128 \int \frac {x \log \left (\frac {1}{256} x^2 \left (-1+32 e^x+32 x\right )^2\right )}{-1+32 e^x+32 x} \, dx-132 \int \frac {1}{-1+32 e^x+32 x} \, dx+132 \int \frac {1}{x^2 \left (-1+32 e^x+32 x\right )} \, dx+132 \int \frac {x}{-1+32 e^x+32 x} \, dx+132 \int \frac {\log \left (\frac {1}{256} x^2 \left (-1+32 e^x+32 x\right )^2\right )}{-1+32 e^x+32 x} \, dx\\ &=\frac {1}{x^4}-\frac {4}{x^2}-\frac {2}{x}-2 x+3 x^2-4 \log (x)+\frac {2 \log \left (\frac {1}{256} \left (1-32 e^x-32 x\right )^2 x^2\right )}{x^2}+6 x \log \left (\frac {1}{256} \left (1-32 e^x-32 x\right )^2 x^2\right )-2 \int \frac {2-128 x-64 e^x (1+x)}{\left (1-32 e^x-32 x\right ) x^3} \, dx+4 \int \frac {\log \left (\frac {1}{256} x^2 \left (-1+32 e^x+32 x\right )^2\right )}{x} \, dx-6 \int \frac {2-128 x-64 e^x (1+x)}{1-32 e^x-32 x} \, dx-128 \int \frac {1}{x \left (-1+32 e^x+32 x\right )} \, dx+128 \int \frac {x}{-1+32 e^x+32 x} \, dx-128 \int \frac {x^2}{-1+32 e^x+32 x} \, dx+128 \int \frac {2 \left (1-64 x-32 e^x (1+x)\right ) \int \frac {x}{-1+32 e^x+32 x} \, dx}{\left (1-32 e^x-32 x\right ) x} \, dx-132 \int \frac {1}{-1+32 e^x+32 x} \, dx+132 \int \frac {1}{x^2 \left (-1+32 e^x+32 x\right )} \, dx+132 \int \frac {x}{-1+32 e^x+32 x} \, dx-132 \int \frac {2 \left (1-64 x-32 e^x (1+x)\right ) \int \frac {1}{-1+32 e^x+32 x} \, dx}{\left (1-32 e^x-32 x\right ) x} \, dx-\left (128 \log \left (\frac {1}{256} x^2 \left (-1+32 e^x+32 x\right )^2\right )\right ) \int \frac {x}{-1+32 e^x+32 x} \, dx+\left (132 \log \left (\frac {1}{256} x^2 \left (-1+32 e^x+32 x\right )^2\right )\right ) \int \frac {1}{-1+32 e^x+32 x} \, dx\\ &=\frac {1}{x^4}-\frac {4}{x^2}-\frac {2}{x}-2 x+3 x^2-4 \log (x)+\frac {2 \log \left (\frac {1}{256} \left (1-32 e^x-32 x\right )^2 x^2\right )}{x^2}+6 x \log \left (\frac {1}{256} \left (1-32 e^x-32 x\right )^2 x^2\right )-2 \int \left (\frac {2 (1+x)}{x^3}-\frac {2 (-33+32 x)}{x^2 \left (-1+32 e^x+32 x\right )}\right ) \, dx+4 \int \frac {\log \left (\frac {1}{256} x^2 \left (-1+32 e^x+32 x\right )^2\right )}{x} \, dx-6 \int \left (2 (1+x)-\frac {2 x (-33+32 x)}{-1+32 e^x+32 x}\right ) \, dx-128 \int \frac {1}{x \left (-1+32 e^x+32 x\right )} \, dx+128 \int \frac {x}{-1+32 e^x+32 x} \, dx-128 \int \frac {x^2}{-1+32 e^x+32 x} \, dx-132 \int \frac {1}{-1+32 e^x+32 x} \, dx+132 \int \frac {1}{x^2 \left (-1+32 e^x+32 x\right )} \, dx+132 \int \frac {x}{-1+32 e^x+32 x} \, dx+256 \int \frac {\left (1-64 x-32 e^x (1+x)\right ) \int \frac {x}{-1+32 e^x+32 x} \, dx}{\left (1-32 e^x-32 x\right ) x} \, dx-264 \int \frac {\left (1-64 x-32 e^x (1+x)\right ) \int \frac {1}{-1+32 e^x+32 x} \, dx}{\left (1-32 e^x-32 x\right ) x} \, dx-\left (128 \log \left (\frac {1}{256} x^2 \left (-1+32 e^x+32 x\right )^2\right )\right ) \int \frac {x}{-1+32 e^x+32 x} \, dx+\left (132 \log \left (\frac {1}{256} x^2 \left (-1+32 e^x+32 x\right )^2\right )\right ) \int \frac {1}{-1+32 e^x+32 x} \, dx\\ &=\frac {1}{x^4}-\frac {4}{x^2}-\frac {2}{x}-2 x+3 x^2-6 (1+x)^2-4 \log (x)+\frac {2 \log \left (\frac {1}{256} \left (1-32 e^x-32 x\right )^2 x^2\right )}{x^2}+6 x \log \left (\frac {1}{256} \left (1-32 e^x-32 x\right )^2 x^2\right )-4 \int \frac {1+x}{x^3} \, dx+4 \int \frac {-33+32 x}{x^2 \left (-1+32 e^x+32 x\right )} \, dx+4 \int \frac {\log \left (\frac {1}{256} x^2 \left (-1+32 e^x+32 x\right )^2\right )}{x} \, dx+12 \int \frac {x (-33+32 x)}{-1+32 e^x+32 x} \, dx-128 \int \frac {1}{x \left (-1+32 e^x+32 x\right )} \, dx+128 \int \frac {x}{-1+32 e^x+32 x} \, dx-128 \int \frac {x^2}{-1+32 e^x+32 x} \, dx-132 \int \frac {1}{-1+32 e^x+32 x} \, dx+132 \int \frac {1}{x^2 \left (-1+32 e^x+32 x\right )} \, dx+132 \int \frac {x}{-1+32 e^x+32 x} \, dx+256 \int \left (\frac {(1+x) \int \frac {x}{-1+32 e^x+32 x} \, dx}{x}-\frac {(-33+32 x) \int \frac {x}{-1+32 e^x+32 x} \, dx}{-1+32 e^x+32 x}\right ) \, dx-264 \int \left (\frac {(1+x) \int \frac {1}{-1+32 e^x+32 x} \, dx}{x}-\frac {(-33+32 x) \int \frac {1}{-1+32 e^x+32 x} \, dx}{-1+32 e^x+32 x}\right ) \, dx-\left (128 \log \left (\frac {1}{256} x^2 \left (-1+32 e^x+32 x\right )^2\right )\right ) \int \frac {x}{-1+32 e^x+32 x} \, dx+\left (132 \log \left (\frac {1}{256} x^2 \left (-1+32 e^x+32 x\right )^2\right )\right ) \int \frac {1}{-1+32 e^x+32 x} \, dx\\ &=\frac {1}{x^4}-\frac {4}{x^2}-\frac {2}{x}-2 x+3 x^2-6 (1+x)^2+\frac {2 (1+x)^2}{x^2}-4 \log (x)+\frac {2 \log \left (\frac {1}{256} \left (1-32 e^x-32 x\right )^2 x^2\right )}{x^2}+6 x \log \left (\frac {1}{256} \left (1-32 e^x-32 x\right )^2 x^2\right )+4 \int \left (-\frac {33}{x^2 \left (-1+32 e^x+32 x\right )}+\frac {32}{x \left (-1+32 e^x+32 x\right )}\right ) \, dx+4 \int \frac {\log \left (\frac {1}{256} x^2 \left (-1+32 e^x+32 x\right )^2\right )}{x} \, dx+12 \int \left (-\frac {33 x}{-1+32 e^x+32 x}+\frac {32 x^2}{-1+32 e^x+32 x}\right ) \, dx-128 \int \frac {1}{x \left (-1+32 e^x+32 x\right )} \, dx+128 \int \frac {x}{-1+32 e^x+32 x} \, dx-128 \int \frac {x^2}{-1+32 e^x+32 x} \, dx-132 \int \frac {1}{-1+32 e^x+32 x} \, dx+132 \int \frac {1}{x^2 \left (-1+32 e^x+32 x\right )} \, dx+132 \int \frac {x}{-1+32 e^x+32 x} \, dx+256 \int \frac {(1+x) \int \frac {x}{-1+32 e^x+32 x} \, dx}{x} \, dx-256 \int \frac {(-33+32 x) \int \frac {x}{-1+32 e^x+32 x} \, dx}{-1+32 e^x+32 x} \, dx-264 \int \frac {(1+x) \int \frac {1}{-1+32 e^x+32 x} \, dx}{x} \, dx+264 \int \frac {(-33+32 x) \int \frac {1}{-1+32 e^x+32 x} \, dx}{-1+32 e^x+32 x} \, dx-\left (128 \log \left (\frac {1}{256} x^2 \left (-1+32 e^x+32 x\right )^2\right )\right ) \int \frac {x}{-1+32 e^x+32 x} \, dx+\left (132 \log \left (\frac {1}{256} x^2 \left (-1+32 e^x+32 x\right )^2\right )\right ) \int \frac {1}{-1+32 e^x+32 x} \, dx\\ &=\frac {1}{x^4}-\frac {4}{x^2}-\frac {2}{x}-2 x+3 x^2-6 (1+x)^2+\frac {2 (1+x)^2}{x^2}-4 \log (x)+\frac {2 \log \left (\frac {1}{256} \left (1-32 e^x-32 x\right )^2 x^2\right )}{x^2}+6 x \log \left (\frac {1}{256} \left (1-32 e^x-32 x\right )^2 x^2\right )+4 \int \frac {\log \left (\frac {1}{256} x^2 \left (-1+32 e^x+32 x\right )^2\right )}{x} \, dx+128 \int \frac {x}{-1+32 e^x+32 x} \, dx-128 \int \frac {x^2}{-1+32 e^x+32 x} \, dx-132 \int \frac {1}{-1+32 e^x+32 x} \, dx+132 \int \frac {x}{-1+32 e^x+32 x} \, dx+256 \int \left (\int \frac {x}{-1+32 e^x+32 x} \, dx+\frac {\int \frac {x}{-1+32 e^x+32 x} \, dx}{x}\right ) \, dx-256 \int \left (-\frac {33 \int \frac {x}{-1+32 e^x+32 x} \, dx}{-1+32 e^x+32 x}+\frac {32 x \int \frac {x}{-1+32 e^x+32 x} \, dx}{-1+32 e^x+32 x}\right ) \, dx-264 \int \left (\int \frac {1}{-1+32 e^x+32 x} \, dx+\frac {\int \frac {1}{-1+32 e^x+32 x} \, dx}{x}\right ) \, dx+264 \int \left (-\frac {33 \int \frac {1}{-1+32 e^x+32 x} \, dx}{-1+32 e^x+32 x}+\frac {32 x \int \frac {1}{-1+32 e^x+32 x} \, dx}{-1+32 e^x+32 x}\right ) \, dx+384 \int \frac {x^2}{-1+32 e^x+32 x} \, dx-396 \int \frac {x}{-1+32 e^x+32 x} \, dx-\left (128 \log \left (\frac {1}{256} x^2 \left (-1+32 e^x+32 x\right )^2\right )\right ) \int \frac {x}{-1+32 e^x+32 x} \, dx+\left (132 \log \left (\frac {1}{256} x^2 \left (-1+32 e^x+32 x\right )^2\right )\right ) \int \frac {1}{-1+32 e^x+32 x} \, dx\\ &=\frac {1}{x^4}-\frac {4}{x^2}-\frac {2}{x}-2 x+3 x^2-6 (1+x)^2+\frac {2 (1+x)^2}{x^2}-4 \log (x)+\frac {2 \log \left (\frac {1}{256} \left (1-32 e^x-32 x\right )^2 x^2\right )}{x^2}+6 x \log \left (\frac {1}{256} \left (1-32 e^x-32 x\right )^2 x^2\right )+4 \int \frac {\log \left (\frac {1}{256} x^2 \left (-1+32 e^x+32 x\right )^2\right )}{x} \, dx+128 \int \frac {x}{-1+32 e^x+32 x} \, dx-128 \int \frac {x^2}{-1+32 e^x+32 x} \, dx-132 \int \frac {1}{-1+32 e^x+32 x} \, dx+132 \int \frac {x}{-1+32 e^x+32 x} \, dx+256 \int \left (\int \frac {x}{-1+32 e^x+32 x} \, dx\right ) \, dx+256 \int \frac {\int \frac {x}{-1+32 e^x+32 x} \, dx}{x} \, dx-264 \int \left (\int \frac {1}{-1+32 e^x+32 x} \, dx\right ) \, dx-264 \int \frac {\int \frac {1}{-1+32 e^x+32 x} \, dx}{x} \, dx+384 \int \frac {x^2}{-1+32 e^x+32 x} \, dx-396 \int \frac {x}{-1+32 e^x+32 x} \, dx-8192 \int \frac {x \int \frac {x}{-1+32 e^x+32 x} \, dx}{-1+32 e^x+32 x} \, dx+8448 \int \frac {x \int \frac {1}{-1+32 e^x+32 x} \, dx}{-1+32 e^x+32 x} \, dx+8448 \int \frac {\int \frac {x}{-1+32 e^x+32 x} \, dx}{-1+32 e^x+32 x} \, dx-8712 \int \frac {\int \frac {1}{-1+32 e^x+32 x} \, dx}{-1+32 e^x+32 x} \, dx-\left (128 \log \left (\frac {1}{256} x^2 \left (-1+32 e^x+32 x\right )^2\right )\right ) \int \frac {x}{-1+32 e^x+32 x} \, dx+\left (132 \log \left (\frac {1}{256} x^2 \left (-1+32 e^x+32 x\right )^2\right )\right ) \int \frac {1}{-1+32 e^x+32 x} \, dx\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [B]  time = 0.10, size = 89, normalized size = 3.56 \begin {gather*} \frac {1}{x^4}-\frac {2}{x^2}+\frac {2}{x}-2 x+x^2-4 \log \left (1-32 e^x-32 x\right )-4 \log (x)+\frac {2 \left (1+x^3\right ) \log \left (\frac {1}{256} x^2 \left (-1+32 e^x+32 x\right )^2\right )}{x^2}+\log ^2\left (\frac {1}{256} x^2 \left (-1+32 e^x+32 x\right )^2\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(4 - 128*x - 8*x^2 + 386*x^3 - 60*x^4 - 258*x^5 + 190*x^6 + 64*x^7 + E^x*(-128 + 256*x^2 + 64*x^3 -
128*x^4 - 64*x^5 + 192*x^6) + (4*x^2 - 128*x^3 - 4*x^4 + 254*x^5 + 64*x^6 + E^x*(-128*x^2 + 128*x^4 + 192*x^5)
)*Log[(x^2 + 1024*E^(2*x)*x^2 - 64*x^3 + 1024*x^4 + E^x*(-64*x^2 + 2048*x^3))/256])/(-x^5 + 32*E^x*x^5 + 32*x^
6),x]

[Out]

x^(-4) - 2/x^2 + 2/x - 2*x + x^2 - 4*Log[1 - 32*E^x - 32*x] - 4*Log[x] + (2*(1 + x^3)*Log[(x^2*(-1 + 32*E^x +
32*x)^2)/256])/x^2 + Log[(x^2*(-1 + 32*E^x + 32*x)^2)/256]^2

________________________________________________________________________________________

fricas [B]  time = 0.77, size = 126, normalized size = 5.04 \begin {gather*} \frac {x^{6} + x^{4} \log \left (4 \, x^{4} - \frac {1}{4} \, x^{3} + 4 \, x^{2} e^{\left (2 \, x\right )} + \frac {1}{256} \, x^{2} + \frac {1}{4} \, {\left (32 \, x^{3} - x^{2}\right )} e^{x}\right )^{2} - 2 \, x^{5} + 2 \, x^{3} - 2 \, x^{2} + 2 \, {\left (x^{5} - x^{4} + x^{2}\right )} \log \left (4 \, x^{4} - \frac {1}{4} \, x^{3} + 4 \, x^{2} e^{\left (2 \, x\right )} + \frac {1}{256} \, x^{2} + \frac {1}{4} \, {\left (32 \, x^{3} - x^{2}\right )} e^{x}\right ) + 1}{x^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((192*x^5+128*x^4-128*x^2)*exp(x)+64*x^6+254*x^5-4*x^4-128*x^3+4*x^2)*log(4*exp(x)^2*x^2+1/256*(204
8*x^3-64*x^2)*exp(x)+4*x^4-1/4*x^3+1/256*x^2)+(192*x^6-64*x^5-128*x^4+64*x^3+256*x^2-128)*exp(x)+64*x^7+190*x^
6-258*x^5-60*x^4+386*x^3-8*x^2-128*x+4)/(32*x^5*exp(x)+32*x^6-x^5),x, algorithm="fricas")

[Out]

(x^6 + x^4*log(4*x^4 - 1/4*x^3 + 4*x^2*e^(2*x) + 1/256*x^2 + 1/4*(32*x^3 - x^2)*e^x)^2 - 2*x^5 + 2*x^3 - 2*x^2
+ 2*(x^5 - x^4 + x^2)*log(4*x^4 - 1/4*x^3 + 4*x^2*e^(2*x) + 1/256*x^2 + 1/4*(32*x^3 - x^2)*e^x) + 1)/x^4

________________________________________________________________________________________

giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {2 \, {\left (32 \, x^{7} + 95 \, x^{6} - 129 \, x^{5} - 30 \, x^{4} + 193 \, x^{3} - 4 \, x^{2} + 32 \, {\left (3 \, x^{6} - x^{5} - 2 \, x^{4} + x^{3} + 4 \, x^{2} - 2\right )} e^{x} + {\left (32 \, x^{6} + 127 \, x^{5} - 2 \, x^{4} - 64 \, x^{3} + 2 \, x^{2} + 32 \, {\left (3 \, x^{5} + 2 \, x^{4} - 2 \, x^{2}\right )} e^{x}\right )} \log \left (4 \, x^{4} - \frac {1}{4} \, x^{3} + 4 \, x^{2} e^{\left (2 \, x\right )} + \frac {1}{256} \, x^{2} + \frac {1}{4} \, {\left (32 \, x^{3} - x^{2}\right )} e^{x}\right ) - 64 \, x + 2\right )}}{32 \, x^{6} + 32 \, x^{5} e^{x} - x^{5}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((192*x^5+128*x^4-128*x^2)*exp(x)+64*x^6+254*x^5-4*x^4-128*x^3+4*x^2)*log(4*exp(x)^2*x^2+1/256*(204
8*x^3-64*x^2)*exp(x)+4*x^4-1/4*x^3+1/256*x^2)+(192*x^6-64*x^5-128*x^4+64*x^3+256*x^2-128)*exp(x)+64*x^7+190*x^
6-258*x^5-60*x^4+386*x^3-8*x^2-128*x+4)/(32*x^5*exp(x)+32*x^6-x^5),x, algorithm="giac")

[Out]

integrate(2*(32*x^7 + 95*x^6 - 129*x^5 - 30*x^4 + 193*x^3 - 4*x^2 + 32*(3*x^6 - x^5 - 2*x^4 + x^3 + 4*x^2 - 2)
*e^x + (32*x^6 + 127*x^5 - 2*x^4 - 64*x^3 + 2*x^2 + 32*(3*x^5 + 2*x^4 - 2*x^2)*e^x)*log(4*x^4 - 1/4*x^3 + 4*x^
2*e^(2*x) + 1/256*x^2 + 1/4*(32*x^3 - x^2)*e^x) - 64*x + 2)/(32*x^6 + 32*x^5*e^x - x^5), x)

________________________________________________________________________________________

maple [C]  time = 0.46, size = 1264, normalized size = 50.56

method	result	size
risch	\(4 \ln \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )^{2}+\frac {4 \left (x^{3}+2 x^{2} \ln \relax (x )+1\right ) \ln \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )}{x^{2}}+\frac {1+4 x^{2} \ln \relax (x )+2 x^{3}-2 x^{2}+x^{6}-2 x^{5}+4 x^{5} \ln \relax (x )+4 x^{4} \ln \relax (x )^{2}-16 x^{5} \ln \relax (2)-4 x^{4} \ln \relax (x )-16 x^{2} \ln \relax (2)+4 i \pi \ln \left (x +{\mathrm e}^{x}-\frac {1}{32}\right ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2} x^{4}-2 i \pi \ln \left (x +{\mathrm e}^{x}-\frac {1}{32}\right ) \mathrm {csgn}\left (i \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )\right )^{2} \mathrm {csgn}\left (i \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )^{2}\right ) x^{4}+4 i \pi \ln \left (x +{\mathrm e}^{x}-\frac {1}{32}\right ) \mathrm {csgn}\left (i \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )\right ) \mathrm {csgn}\left (i \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )^{2}\right )^{2} x^{4}-i \pi \,x^{2} \mathrm {csgn}\left (i \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )^{2}\right ) \mathrm {csgn}\left (i x^{2} \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )^{2}\right ) \mathrm {csgn}\left (i x^{2}\right )-i \pi \,x^{5} \mathrm {csgn}\left (i \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )^{2}\right ) \mathrm {csgn}\left (i x^{2} \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )^{2}\right ) \mathrm {csgn}\left (i x^{2}\right )-4 \ln \left (x +{\mathrm e}^{x}-\frac {1}{32}\right ) x^{4}-32 \ln \relax (x ) \ln \relax (2) x^{4}-32 \ln \relax (2) \ln \left (x +{\mathrm e}^{x}-\frac {1}{32}\right ) x^{4}-i \pi \,x^{2} \mathrm {csgn}\left (i x^{2} \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )^{2}\right )^{3}+4 i \pi \ln \relax (x ) \mathrm {csgn}\left (i \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )\right ) \mathrm {csgn}\left (i \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )^{2}\right )^{2} x^{4}+2 i \pi \ln \relax (x ) \mathrm {csgn}\left (i \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )^{2}\right ) \mathrm {csgn}\left (i x^{2} \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )^{2}\right )^{2} x^{4}+2 i \pi \ln \relax (x ) \mathrm {csgn}\left (i x^{2} \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )^{2}\right )^{2} \mathrm {csgn}\left (i x^{2}\right ) x^{4}-2 i \pi \ln \relax (x ) \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right ) x^{4}+4 i \pi \ln \relax (x ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2} x^{4}+2 i \pi \ln \left (x +{\mathrm e}^{x}-\frac {1}{32}\right ) \mathrm {csgn}\left (i \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )^{2}\right ) \mathrm {csgn}\left (i x^{2} \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )^{2}\right )^{2} x^{4}+2 i \pi \ln \left (x +{\mathrm e}^{x}-\frac {1}{32}\right ) \mathrm {csgn}\left (i x^{2} \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )^{2}\right )^{2} \mathrm {csgn}\left (i x^{2}\right ) x^{4}-2 i \pi \ln \left (x +{\mathrm e}^{x}-\frac {1}{32}\right ) \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right ) x^{4}+2 i \pi \,x^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-i \pi \,x^{5} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+2 i \pi \,x^{5} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-i \pi \,x^{2} \mathrm {csgn}\left (i \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )\right )^{2} \mathrm {csgn}\left (i \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )^{2}\right )+2 i \pi \,x^{2} \mathrm {csgn}\left (i \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )\right ) \mathrm {csgn}\left (i \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )^{2}\right )^{2}-i \pi \,x^{5} \mathrm {csgn}\left (i \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )\right )^{2} \mathrm {csgn}\left (i \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )^{2}\right )+2 i \pi \,x^{5} \mathrm {csgn}\left (i \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )\right ) \mathrm {csgn}\left (i \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )^{2}\right )^{2}-2 i \pi \ln \left (x +{\mathrm e}^{x}-\frac {1}{32}\right ) \mathrm {csgn}\left (i \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )^{2}\right )^{3} x^{4}-2 i \pi \ln \left (x +{\mathrm e}^{x}-\frac {1}{32}\right ) \mathrm {csgn}\left (i x^{2} \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )^{2}\right )^{3} x^{4}-2 i \pi \ln \left (x +{\mathrm e}^{x}-\frac {1}{32}\right ) \mathrm {csgn}\left (i x^{2}\right )^{3} x^{4}+i \pi \,x^{2} \mathrm {csgn}\left (i \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )^{2}\right ) \mathrm {csgn}\left (i x^{2} \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )^{2}\right )^{2}+i \pi \,x^{5} \mathrm {csgn}\left (i \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )^{2}\right ) \mathrm {csgn}\left (i x^{2} \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )^{2}\right )^{2}+i \pi \,x^{5} \mathrm {csgn}\left (i x^{2} \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )^{2}\right )^{2} \mathrm {csgn}\left (i x^{2}\right )-2 i \pi \ln \relax (x ) \mathrm {csgn}\left (i \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )^{2}\right ) \mathrm {csgn}\left (i x^{2} \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )^{2}\right ) \mathrm {csgn}\left (i x^{2}\right ) x^{4}-2 i \pi \ln \left (x +{\mathrm e}^{x}-\frac {1}{32}\right ) \mathrm {csgn}\left (i \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )^{2}\right ) \mathrm {csgn}\left (i x^{2} \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )^{2}\right ) \mathrm {csgn}\left (i x^{2}\right ) x^{4}-i \pi \,x^{5} \mathrm {csgn}\left (i x^{2} \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )^{2}\right )^{3}-i \pi \,x^{5} \mathrm {csgn}\left (i x^{2}\right )^{3}-i \pi \,x^{2} \mathrm {csgn}\left (i \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )^{2}\right )^{3}-2 i \pi \ln \relax (x ) \mathrm {csgn}\left (i \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )\right )^{2} \mathrm {csgn}\left (i \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )^{2}\right ) x^{4}+i \pi \,x^{2} \mathrm {csgn}\left (i x^{2} \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )^{2}\right )^{2} \mathrm {csgn}\left (i x^{2}\right )-2 i \pi \ln \relax (x ) \mathrm {csgn}\left (i \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )^{2}\right )^{3} x^{4}-2 i \pi \ln \relax (x ) \mathrm {csgn}\left (i x^{2} \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )^{2}\right )^{3} x^{4}-2 i \pi \ln \relax (x ) \mathrm {csgn}\left (i x^{2}\right )^{3} x^{4}-i \pi \,x^{2} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-i \pi \,x^{2} \mathrm {csgn}\left (i x^{2}\right )^{3}-i \pi \,x^{5} \mathrm {csgn}\left (i \left (x +{\mathrm e}^{x}-\frac {1}{32}\right )^{2}\right )^{3}}{x^{4}}\)	\(1264\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((192*x^5+128*x^4-128*x^2)*exp(x)+64*x^6+254*x^5-4*x^4-128*x^3+4*x^2)*ln(4*exp(x)^2*x^2+1/256*(2048*x^3-6
4*x^2)*exp(x)+4*x^4-1/4*x^3+1/256*x^2)+(192*x^6-64*x^5-128*x^4+64*x^3+256*x^2-128)*exp(x)+64*x^7+190*x^6-258*x
^5-60*x^4+386*x^3-8*x^2-128*x+4)/(32*x^5*exp(x)+32*x^6-x^5),x,method=_RETURNVERBOSE)

[Out]

4*ln(x+exp(x)-1/32)^2+4*(x^3+2*x^2*ln(x)+1)/x^2*ln(x+exp(x)-1/32)+(1+4*x^2*ln(x)+2*x^3-2*x^2+x^6-2*x^5+4*x^5*l
n(x)+4*x^4*ln(x)^2-16*x^5*ln(2)-4*x^4*ln(x)-16*x^2*ln(2)-I*Pi*x^2*csgn(I*x^2)^3-I*Pi*x^5*csgn(I*(x+exp(x)-1/32
)^2)^3-4*ln(x+exp(x)-1/32)*x^4-32*ln(x)*ln(2)*x^4-32*ln(2)*ln(x+exp(x)-1/32)*x^4-2*I*Pi*ln(x)*csgn(I*(x+exp(x)
-1/32)^2)*csgn(I*x^2*(x+exp(x)-1/32)^2)*csgn(I*x^2)*x^4-2*I*Pi*ln(x+exp(x)-1/32)*csgn(I*(x+exp(x)-1/32)^2)*csg
n(I*x^2*(x+exp(x)-1/32)^2)*csgn(I*x^2)*x^4-I*Pi*x^5*csgn(I*x^2*(x+exp(x)-1/32)^2)^3-I*Pi*x^5*csgn(I*x^2)^3-I*P
i*x^2*csgn(I*(x+exp(x)-1/32)^2)^3-I*Pi*x^2*csgn(I*x^2*(x+exp(x)-1/32)^2)^3+4*I*Pi*ln(x)*csgn(I*(x+exp(x)-1/32)
)*csgn(I*(x+exp(x)-1/32)^2)^2*x^4+2*I*Pi*ln(x)*csgn(I*(x+exp(x)-1/32)^2)*csgn(I*x^2*(x+exp(x)-1/32)^2)^2*x^4+2
*I*Pi*ln(x)*csgn(I*x^2*(x+exp(x)-1/32)^2)^2*csgn(I*x^2)*x^4-2*I*Pi*ln(x)*csgn(I*x)^2*csgn(I*x^2)*x^4+4*I*Pi*ln
(x)*csgn(I*x)*csgn(I*x^2)^2*x^4+2*I*Pi*ln(x+exp(x)-1/32)*csgn(I*(x+exp(x)-1/32)^2)*csgn(I*x^2*(x+exp(x)-1/32)^
2)^2*x^4+2*I*Pi*ln(x+exp(x)-1/32)*csgn(I*x^2*(x+exp(x)-1/32)^2)^2*csgn(I*x^2)*x^4-2*I*Pi*ln(x+exp(x)-1/32)*csg
n(I*x)^2*csgn(I*x^2)*x^4+4*I*Pi*ln(x+exp(x)-1/32)*csgn(I*x)*csgn(I*x^2)^2*x^4-2*I*Pi*ln(x+exp(x)-1/32)*csgn(I*
(x+exp(x)-1/32))^2*csgn(I*(x+exp(x)-1/32)^2)*x^4+4*I*Pi*ln(x+exp(x)-1/32)*csgn(I*(x+exp(x)-1/32))*csgn(I*(x+ex
p(x)-1/32)^2)^2*x^4-I*Pi*x^2*csgn(I*(x+exp(x)-1/32)^2)*csgn(I*x^2*(x+exp(x)-1/32)^2)*csgn(I*x^2)-I*Pi*x^5*csgn
(I*(x+exp(x)-1/32)^2)*csgn(I*x^2*(x+exp(x)-1/32)^2)*csgn(I*x^2)+I*Pi*x^2*csgn(I*x^2*(x+exp(x)-1/32)^2)^2*csgn(
I*x^2)-2*I*Pi*ln(x)*csgn(I*(x+exp(x)-1/32)^2)^3*x^4-2*I*Pi*ln(x)*csgn(I*x^2*(x+exp(x)-1/32)^2)^3*x^4-2*I*Pi*ln
(x)*csgn(I*x^2)^3*x^4-I*Pi*x^2*csgn(I*x)^2*csgn(I*x^2)+2*I*Pi*x^2*csgn(I*x)*csgn(I*x^2)^2-I*Pi*x^5*csgn(I*x)^2
*csgn(I*x^2)+2*I*Pi*x^5*csgn(I*x)*csgn(I*x^2)^2-I*Pi*x^2*csgn(I*(x+exp(x)-1/32))^2*csgn(I*(x+exp(x)-1/32)^2)+2
*I*Pi*x^2*csgn(I*(x+exp(x)-1/32))*csgn(I*(x+exp(x)-1/32)^2)^2-2*I*Pi*ln(x)*csgn(I*(x+exp(x)-1/32))^2*csgn(I*(x
+exp(x)-1/32)^2)*x^4-I*Pi*x^5*csgn(I*(x+exp(x)-1/32))^2*csgn(I*(x+exp(x)-1/32)^2)+2*I*Pi*x^5*csgn(I*(x+exp(x)-
1/32))*csgn(I*(x+exp(x)-1/32)^2)^2-2*I*Pi*ln(x+exp(x)-1/32)*csgn(I*(x+exp(x)-1/32)^2)^3*x^4-2*I*Pi*ln(x+exp(x)
-1/32)*csgn(I*x^2*(x+exp(x)-1/32)^2)^3*x^4-2*I*Pi*ln(x+exp(x)-1/32)*csgn(I*x^2)^3*x^4+I*Pi*x^2*csgn(I*(x+exp(x
)-1/32)^2)*csgn(I*x^2*(x+exp(x)-1/32)^2)^2+I*Pi*x^5*csgn(I*(x+exp(x)-1/32)^2)*csgn(I*x^2*(x+exp(x)-1/32)^2)^2+
I*Pi*x^5*csgn(I*x^2*(x+exp(x)-1/32)^2)^2*csgn(I*x^2))/x^4

________________________________________________________________________________________

maxima [B]  time = 0.48, size = 121, normalized size = 4.84 \begin {gather*} \frac {x^{6} - 2 \, x^{5} {\left (8 \, \log \relax (2) + 1\right )} + 4 \, x^{4} \log \left (32 \, x + 32 \, e^{x} - 1\right )^{2} + 4 \, x^{4} \log \relax (x)^{2} + 2 \, x^{3} - 2 \, x^{2} {\left (8 \, \log \relax (2) + 1\right )} + 4 \, {\left (x^{5} - x^{4} {\left (8 \, \log \relax (2) + 1\right )} + 2 \, x^{4} \log \relax (x) + x^{2}\right )} \log \left (32 \, x + 32 \, e^{x} - 1\right ) + 4 \, {\left (x^{5} - x^{4} {\left (8 \, \log \relax (2) + 1\right )} + x^{2}\right )} \log \relax (x) + 1}{x^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((192*x^5+128*x^4-128*x^2)*exp(x)+64*x^6+254*x^5-4*x^4-128*x^3+4*x^2)*log(4*exp(x)^2*x^2+1/256*(204
8*x^3-64*x^2)*exp(x)+4*x^4-1/4*x^3+1/256*x^2)+(192*x^6-64*x^5-128*x^4+64*x^3+256*x^2-128)*exp(x)+64*x^7+190*x^
6-258*x^5-60*x^4+386*x^3-8*x^2-128*x+4)/(32*x^5*exp(x)+32*x^6-x^5),x, algorithm="maxima")

[Out]

(x^6 - 2*x^5*(8*log(2) + 1) + 4*x^4*log(32*x + 32*e^x - 1)^2 + 4*x^4*log(x)^2 + 2*x^3 - 2*x^2*(8*log(2) + 1) +
4*(x^5 - x^4*(8*log(2) + 1) + 2*x^4*log(x) + x^2)*log(32*x + 32*e^x - 1) + 4*(x^5 - x^4*(8*log(2) + 1) + x^2)
*log(x) + 1)/x^4

________________________________________________________________________________________

mupad [B]  time = 4.47, size = 129, normalized size = 5.16 \begin {gather*} \frac {2\,x^3-2\,x^2+1}{x^4}-2\,x+{\ln \left (4\,x^2\,{\mathrm {e}}^{2\,x}-\frac {{\mathrm {e}}^x\,\left (64\,x^2-2048\,x^3\right )}{256}+\frac {x^2}{256}-\frac {x^3}{4}+4\,x^4\right )}^2+\ln \left (4\,x^2\,{\mathrm {e}}^{2\,x}-\frac {{\mathrm {e}}^x\,\left (64\,x^2-2048\,x^3\right )}{256}+\frac {x^2}{256}-\frac {x^3}{4}+4\,x^4\right )\,\left (5\,x-\frac {32\,\left (\frac {3\,x^3}{32}+\frac {x^2}{16}-\frac {1}{16}\right )}{x^2}\right )+x^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(4*x^2*exp(2*x) - (exp(x)*(64*x^2 - 2048*x^3))/256 + x^2/256 - x^3/4 + 4*x^4)*(exp(x)*(128*x^4 - 128*x
^2 + 192*x^5) + 4*x^2 - 128*x^3 - 4*x^4 + 254*x^5 + 64*x^6) - 128*x + exp(x)*(256*x^2 + 64*x^3 - 128*x^4 - 64*
x^5 + 192*x^6 - 128) - 8*x^2 + 386*x^3 - 60*x^4 - 258*x^5 + 190*x^6 + 64*x^7 + 4)/(32*x^5*exp(x) - x^5 + 32*x^
6),x)

[Out]

(2*x^3 - 2*x^2 + 1)/x^4 - 2*x + log(4*x^2*exp(2*x) - (exp(x)*(64*x^2 - 2048*x^3))/256 + x^2/256 - x^3/4 + 4*x^
4)^2 + log(4*x^2*exp(2*x) - (exp(x)*(64*x^2 - 2048*x^3))/256 + x^2/256 - x^3/4 + 4*x^4)*(5*x - (32*(x^2/16 + (
3*x^3)/32 - 1/16))/x^2) + x^2

________________________________________________________________________________________

sympy [B]  time = 0.68, size = 131, normalized size = 5.24 \begin {gather*} x^{2} - 2 x - 4 \log {\relax (x )} - 4 \log {\left (x + e^{x} - \frac {1}{32} \right )} + \log {\left (4 x^{4} - \frac {x^{3}}{4} + 4 x^{2} e^{2 x} + \frac {x^{2}}{256} + \left (8 x^{3} - \frac {x^{2}}{4}\right ) e^{x} \right )}^{2} + \frac {\left (2 x^{3} + 2\right ) \log {\left (4 x^{4} - \frac {x^{3}}{4} + 4 x^{2} e^{2 x} + \frac {x^{2}}{256} + \left (8 x^{3} - \frac {x^{2}}{4}\right ) e^{x} \right )}}{x^{2}} + \frac {2 x^{3} - 2 x^{2} + 1}{x^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((192*x**5+128*x**4-128*x**2)*exp(x)+64*x**6+254*x**5-4*x**4-128*x**3+4*x**2)*ln(4*exp(x)**2*x**2+1
/256*(2048*x**3-64*x**2)*exp(x)+4*x**4-1/4*x**3+1/256*x**2)+(192*x**6-64*x**5-128*x**4+64*x**3+256*x**2-128)*e
xp(x)+64*x**7+190*x**6-258*x**5-60*x**4+386*x**3-8*x**2-128*x+4)/(32*x**5*exp(x)+32*x**6-x**5),x)

[Out]

x**2 - 2*x - 4*log(x) - 4*log(x + exp(x) - 1/32) + log(4*x**4 - x**3/4 + 4*x**2*exp(2*x) + x**2/256 + (8*x**3
- x**2/4)*exp(x))**2 + (2*x**3 + 2)*log(4*x**4 - x**3/4 + 4*x**2*exp(2*x) + x**2/256 + (8*x**3 - x**2/4)*exp(x
))/x**2 + (2*x**3 - 2*x**2 + 1)/x**4

________________________________________________________________________________________