∫ 192x−48x2+ex∕16(48x−16x2)+(48x+ex∕16(13x+x2)) log(−48+12x+ex∕16(−12+4x))+(−96+24x+ex∕16(−24+8x)) log2(−48+12x+ex∕16(−12+4x))________________________________________________________________________________________________________

Optimal. Leaf size=28 \[ x \left (-x+\log ^2\left (4 \left (\left (4+e^{x/16}\right ) (-3+x)-x\right )\right )\right ) \]

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Rubi [F] time = 6.88, 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 {192 x-48 x^2+e^{x/16} \left (48 x-16 x^2\right )+\left (48 x+e^{x/16} \left (13 x+x^2\right )\right ) \log \left (-48+12 x+e^{x/16} (-12+4 x)\right )+\left (-96+24 x+e^{x/16} (-24+8 x)\right ) \log ^2\left (-48+12 x+e^{x/16} (-12+4 x)\right )}{-96+24 x+e^{x/16} (-24+8 x)} \, dx \end {gather*}

Int[(192*x - 48*x^2 + E^(x/16)*(48*x - 16*x^2) + (48*x + E^(x/16)*(13*x + x^2))*Log[-48 + 12*x + E^(x/16)*(-12

+ 4*x)] + (-96 + 24*x + E^(x/16)*(-24 + 8*x))*Log[-48 + 12*x + E^(x/16)*(-12 + 4*x)]^2)/(-96 + 24*x + E^(x/16

(-35*x)/16 - (35*x^2)/32 - x^3/768 + 2*x*Log[-4*E^(x/16)*(3 - x) - 12*(4 - x)] + (x^2*Log[-4*E^(x/16)*(3 - x)

- 12*(4 - x)])/16 - (105*Log[3 - x])/16 - (105*Defer[Int][(-12 - 3*E^(x/16) + 3*x + E^(x/16)*x)^(-1), x])/16 +

6*Log[-4*E^(x/16)*(3 - x) - 12*(4 - x)]*Defer[Int][(-12 - 3*E^(x/16) + 3*x + E^(x/16)*x)^(-1), x] - (315*Defe

r[Int][1/((-3 + x)*(-12 - 3*E^(x/16) + 3*x + E^(x/16)*x)), x])/16 + 18*Log[-4*E^(x/16)*(3 - x) - 12*(4 - x)]*D

efer[Int][1/((-3 + x)*(-12 - 3*E^(x/16) + 3*x + E^(x/16)*x)), x] - (27*Defer[Int][x/(-12 - 3*E^(x/16) + 3*x +

E^(x/16)*x), x])/16 + (3*Log[-4*E^(x/16)*(3 - x) - 12*(4 - x)]*Defer[Int][x/(-12 - 3*E^(x/16) + 3*x + E^(x/16)

*x), x])/2 + (21*Defer[Int][x^2/(-12 - 3*E^(x/16) + 3*x + E^(x/16)*x), x])/64 - (3*Log[-4*E^(x/16)*(3 - x) - 1

2*(4 - x)]*Defer[Int][x^2/(-12 - 3*E^(x/16) + 3*x + E^(x/16)*x), x])/8 + (3*Defer[Int][x^3/(-12 - 3*E^(x/16) +

3*x + E^(x/16)*x), x])/256 + 6*Defer[Int][Log[12*(-4 + x) + 4*E^(x/16)*(-3 + x)]/(-3 + x), x] + Defer[Int][Lo

g[12*(-4 + x) + 4*E^(x/16)*(-3 + x)]^2, x] - (3*Defer[Int][Defer[Int][(3*(-4 + x) + E^(x/16)*(-3 + x))^(-1), x

], x])/8 - 6*Defer[Int][Defer[Int][(3*(-4 + x) + E^(x/16)*(-3 + x))^(-1), x]/(-3 + x), x] - (9*Defer[Int][Defe

r[Int][(3*(-4 + x) + E^(x/16)*(-3 + x))^(-1), x]/(-12 - 3*E^(x/16) + 3*x + E^(x/16)*x), x])/2 - 18*Defer[Int][

Defer[Int][(3*(-4 + x) + E^(x/16)*(-3 + x))^(-1), x]/((-3 + x)*(-12 - 3*E^(x/16) + 3*x + E^(x/16)*x)), x] + (9

*Defer[Int][(x*Defer[Int][(3*(-4 + x) + E^(x/16)*(-3 + x))^(-1), x])/(-12 - 3*E^(x/16) + 3*x + E^(x/16)*x), x]

)/8 - (9*Defer[Int][Defer[Int][1/((3*(-4 + x) + E^(x/16)*(-3 + x))*(-3 + x)), x], x])/8 - 18*Defer[Int][Defer[

Int][1/((3*(-4 + x) + E^(x/16)*(-3 + x))*(-3 + x)), x]/(-3 + x), x] - (27*Defer[Int][Defer[Int][1/((3*(-4 + x)

+ E^(x/16)*(-3 + x))*(-3 + x)), x]/(-12 - 3*E^(x/16) + 3*x + E^(x/16)*x), x])/2 - 54*Defer[Int][Defer[Int][1/

((3*(-4 + x) + E^(x/16)*(-3 + x))*(-3 + x)), x]/((-3 + x)*(-12 - 3*E^(x/16) + 3*x + E^(x/16)*x)), x] + (27*Def

er[Int][(x*Defer[Int][1/((3*(-4 + x) + E^(x/16)*(-3 + x))*(-3 + x)), x])/(-12 - 3*E^(x/16) + 3*x + E^(x/16)*x)

, x])/8 - (3*Defer[Int][Defer[Int][x/(3*(-4 + x) + E^(x/16)*(-3 + x)), x], x])/32 - (3*Defer[Int][Defer[Int][x

/(3*(-4 + x) + E^(x/16)*(-3 + x)), x]/(-3 + x), x])/2 - (9*Defer[Int][Defer[Int][x/(3*(-4 + x) + E^(x/16)*(-3

+ x)), x]/(-12 - 3*E^(x/16) + 3*x + E^(x/16)*x), x])/8 - (9*Defer[Int][Defer[Int][x/(3*(-4 + x) + E^(x/16)*(-3

+ x)), x]/((-3 + x)*(-12 - 3*E^(x/16) + 3*x + E^(x/16)*x)), x])/2 + (9*Defer[Int][(x*Defer[Int][x/(3*(-4 + x)

+ E^(x/16)*(-3 + x)), x])/(-12 - 3*E^(x/16) + 3*x + E^(x/16)*x), x])/32 + (3*Defer[Int][Defer[Int][x^2/(3*(-4

+ x) + E^(x/16)*(-3 + x)), x], x])/128 + (3*Defer[Int][Defer[Int][x^2/(3*(-4 + x) + E^(x/16)*(-3 + x)), x]/(-

3 + x), x])/8 + (9*Defer[Int][Defer[Int][x^2/(3*(-4 + x) + E^(x/16)*(-3 + x)), x]/(-12 - 3*E^(x/16) + 3*x + E^

(x/16)*x), x])/32 + (9*Defer[Int][Defer[Int][x^2/(3*(-4 + x) + E^(x/16)*(-3 + x)), x]/((-3 + x)*(-12 - 3*E^(x/

16) + 3*x + E^(x/16)*x)), x])/8 - (9*Defer[Int][(x*Defer[Int][x^2/(3*(-4 + x) + E^(x/16)*(-3 + x)), x])/(-12 -

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-2 x+\frac {x \left (48+e^{x/16} (13+x)\right ) \log \left (12 (-4+x)+4 e^{x/16} (-3+x)\right )}{8 \left (3 (-4+x)+e^{x/16} (-3+x)\right )}+\log ^2\left (12 (-4+x)+4 e^{x/16} (-3+x)\right )\right ) \, dx\\ &=-x^2+\frac {1}{8} \int \frac {x \left (48+e^{x/16} (13+x)\right ) \log \left (12 (-4+x)+4 e^{x/16} (-3+x)\right )}{3 (-4+x)+e^{x/16} (-3+x)} \, dx+\int \log ^2\left (12 (-4+x)+4 e^{x/16} (-3+x)\right ) \, dx\\ &=-x^2+\frac {1}{8} \int \left (\frac {x (13+x) \log \left (12 (-4+x)+4 e^{x/16} (-3+x)\right )}{-3+x}-\frac {3 x \left (-4-7 x+x^2\right ) \log \left (12 (-4+x)+4 e^{x/16} (-3+x)\right )}{(-3+x) \left (-12-3 e^{x/16}+3 x+e^{x/16} x\right )}\right ) \, dx+\int \log ^2\left (12 (-4+x)+4 e^{x/16} (-3+x)\right ) \, dx\\ &=-x^2+\frac {1}{8} \int \frac {x (13+x) \log \left (12 (-4+x)+4 e^{x/16} (-3+x)\right )}{-3+x} \, dx-\frac {3}{8} \int \frac {x \left (-4-7 x+x^2\right ) \log \left (12 (-4+x)+4 e^{x/16} (-3+x)\right )}{(-3+x) \left (-12-3 e^{x/16}+3 x+e^{x/16} x\right )} \, dx+\int \log ^2\left (12 (-4+x)+4 e^{x/16} (-3+x)\right ) \, dx\\ &=-x^2+\frac {1}{8} \int \left (16 \log \left (12 (-4+x)+4 e^{x/16} (-3+x)\right )+\frac {48 \log \left (12 (-4+x)+4 e^{x/16} (-3+x)\right )}{-3+x}+x \log \left (12 (-4+x)+4 e^{x/16} (-3+x)\right )\right ) \, dx+\frac {3}{8} \int \frac {\left (48+e^{x/16} (13+x)\right ) \left (-16 \int \frac {1}{3 (-4+x)+e^{x/16} (-3+x)} \, dx-48 \int \frac {1}{\left (3 (-4+x)+e^{x/16} (-3+x)\right ) (-3+x)} \, dx-4 \int \frac {x}{3 (-4+x)+e^{x/16} (-3+x)} \, dx+\int \frac {x^2}{3 (-4+x)+e^{x/16} (-3+x)} \, dx\right )}{16 \left (3 (-4+x)+e^{x/16} (-3+x)\right )} \, dx-\frac {1}{8} \left (3 \log \left (12 (-4+x)+4 e^{x/16} (-3+x)\right )\right ) \int \frac {x^2}{-12-3 e^{x/16}+3 x+e^{x/16} x} \, dx+\frac {1}{2} \left (3 \log \left (12 (-4+x)+4 e^{x/16} (-3+x)\right )\right ) \int \frac {x}{-12-3 e^{x/16}+3 x+e^{x/16} x} \, dx+\left (6 \log \left (12 (-4+x)+4 e^{x/16} (-3+x)\right )\right ) \int \frac {1}{-12-3 e^{x/16}+3 x+e^{x/16} x} \, dx+\left (18 \log \left (12 (-4+x)+4 e^{x/16} (-3+x)\right )\right ) \int \frac {1}{(-3+x) \left (-12-3 e^{x/16}+3 x+e^{x/16} x\right )} \, dx+\int \log ^2\left (12 (-4+x)+4 e^{x/16} (-3+x)\right ) \, dx\\ &=-x^2+\frac {3}{128} \int \frac {\left (48+e^{x/16} (13+x)\right ) \left (-16 \int \frac {1}{3 (-4+x)+e^{x/16} (-3+x)} \, dx-48 \int \frac {1}{\left (3 (-4+x)+e^{x/16} (-3+x)\right ) (-3+x)} \, dx-4 \int \frac {x}{3 (-4+x)+e^{x/16} (-3+x)} \, dx+\int \frac {x^2}{3 (-4+x)+e^{x/16} (-3+x)} \, dx\right )}{3 (-4+x)+e^{x/16} (-3+x)} \, dx+\frac {1}{8} \int x \log \left (12 (-4+x)+4 e^{x/16} (-3+x)\right ) \, dx+2 \int \log \left (12 (-4+x)+4 e^{x/16} (-3+x)\right ) \, dx+6 \int \frac {\log \left (12 (-4+x)+4 e^{x/16} (-3+x)\right )}{-3+x} \, dx-\frac {1}{8} \left (3 \log \left (12 (-4+x)+4 e^{x/16} (-3+x)\right )\right ) \int \frac {x^2}{-12-3 e^{x/16}+3 x+e^{x/16} x} \, dx+\frac {1}{2} \left (3 \log \left (12 (-4+x)+4 e^{x/16} (-3+x)\right )\right ) \int \frac {x}{-12-3 e^{x/16}+3 x+e^{x/16} x} \, dx+\left (6 \log \left (12 (-4+x)+4 e^{x/16} (-3+x)\right )\right ) \int \frac {1}{-12-3 e^{x/16}+3 x+e^{x/16} x} \, dx+\left (18 \log \left (12 (-4+x)+4 e^{x/16} (-3+x)\right )\right ) \int \frac {1}{(-3+x) \left (-12-3 e^{x/16}+3 x+e^{x/16} x\right )} \, dx+\int \log ^2\left (12 (-4+x)+4 e^{x/16} (-3+x)\right ) \, dx\\ &=-x^2+2 x \log \left (-4 e^{x/16} (3-x)-12 (4-x)\right )+\frac {1}{16} x^2 \log \left (-4 e^{x/16} (3-x)-12 (4-x)\right )+\frac {3}{128} \int \left (-\frac {(13+x) \left (16 \int \frac {1}{3 (-4+x)+e^{x/16} (-3+x)} \, dx+48 \int \frac {1}{\left (3 (-4+x)+e^{x/16} (-3+x)\right ) (-3+x)} \, dx+4 \int \frac {x}{3 (-4+x)+e^{x/16} (-3+x)} \, dx-\int \frac {x^2}{3 (-4+x)+e^{x/16} (-3+x)} \, dx\right )}{-3+x}+\frac {3 \left (-4-7 x+x^2\right ) \left (16 \int \frac {1}{3 (-4+x)+e^{x/16} (-3+x)} \, dx+48 \int \frac {1}{\left (3 (-4+x)+e^{x/16} (-3+x)\right ) (-3+x)} \, dx+4 \int \frac {x}{3 (-4+x)+e^{x/16} (-3+x)} \, dx-\int \frac {x^2}{3 (-4+x)+e^{x/16} (-3+x)} \, dx\right )}{(-3+x) \left (-12-3 e^{x/16}+3 x+e^{x/16} x\right )}\right ) \, dx-\frac {1}{16} \int \frac {x^2 \left (48+e^{x/16} (13+x)\right )}{16 \left (3 (-4+x)+e^{x/16} (-3+x)\right )} \, dx-2 \int \frac {x \left (48+e^{x/16} (13+x)\right )}{16 \left (3 (-4+x)+e^{x/16} (-3+x)\right )} \, dx+6 \int \frac {\log \left (12 (-4+x)+4 e^{x/16} (-3+x)\right )}{-3+x} \, dx-\frac {1}{8} \left (3 \log \left (12 (-4+x)+4 e^{x/16} (-3+x)\right )\right ) \int \frac {x^2}{-12-3 e^{x/16}+3 x+e^{x/16} x} \, dx+\frac {1}{2} \left (3 \log \left (12 (-4+x)+4 e^{x/16} (-3+x)\right )\right ) \int \frac {x}{-12-3 e^{x/16}+3 x+e^{x/16} x} \, dx+\left (6 \log \left (12 (-4+x)+4 e^{x/16} (-3+x)\right )\right ) \int \frac {1}{-12-3 e^{x/16}+3 x+e^{x/16} x} \, dx+\left (18 \log \left (12 (-4+x)+4 e^{x/16} (-3+x)\right )\right ) \int \frac {1}{(-3+x) \left (-12-3 e^{x/16}+3 x+e^{x/16} x\right )} \, dx+\int \log ^2\left (12 (-4+x)+4 e^{x/16} (-3+x)\right ) \, dx\\ &=-x^2+2 x \log \left (-4 e^{x/16} (3-x)-12 (4-x)\right )+\frac {1}{16} x^2 \log \left (-4 e^{x/16} (3-x)-12 (4-x)\right )-\frac {1}{256} \int \frac {x^2 \left (48+e^{x/16} (13+x)\right )}{3 (-4+x)+e^{x/16} (-3+x)} \, dx-\frac {3}{128} \int \frac {(13+x) \left (16 \int \frac {1}{3 (-4+x)+e^{x/16} (-3+x)} \, dx+48 \int \frac {1}{\left (3 (-4+x)+e^{x/16} (-3+x)\right ) (-3+x)} \, dx+4 \int \frac {x}{3 (-4+x)+e^{x/16} (-3+x)} \, dx-\int \frac {x^2}{3 (-4+x)+e^{x/16} (-3+x)} \, dx\right )}{-3+x} \, dx+\frac {9}{128} \int \frac {\left (-4-7 x+x^2\right ) \left (16 \int \frac {1}{3 (-4+x)+e^{x/16} (-3+x)} \, dx+48 \int \frac {1}{\left (3 (-4+x)+e^{x/16} (-3+x)\right ) (-3+x)} \, dx+4 \int \frac {x}{3 (-4+x)+e^{x/16} (-3+x)} \, dx-\int \frac {x^2}{3 (-4+x)+e^{x/16} (-3+x)} \, dx\right )}{(-3+x) \left (-12-3 e^{x/16}+3 x+e^{x/16} x\right )} \, dx-\frac {1}{8} \int \frac {x \left (48+e^{x/16} (13+x)\right )}{3 (-4+x)+e^{x/16} (-3+x)} \, dx+6 \int \frac {\log \left (12 (-4+x)+4 e^{x/16} (-3+x)\right )}{-3+x} \, dx-\frac {1}{8} \left (3 \log \left (12 (-4+x)+4 e^{x/16} (-3+x)\right )\right ) \int \frac {x^2}{-12-3 e^{x/16}+3 x+e^{x/16} x} \, dx+\frac {1}{2} \left (3 \log \left (12 (-4+x)+4 e^{x/16} (-3+x)\right )\right ) \int \frac {x}{-12-3 e^{x/16}+3 x+e^{x/16} x} \, dx+\left (6 \log \left (12 (-4+x)+4 e^{x/16} (-3+x)\right )\right ) \int \frac {1}{-12-3 e^{x/16}+3 x+e^{x/16} x} \, dx+\left (18 \log \left (12 (-4+x)+4 e^{x/16} (-3+x)\right )\right ) \int \frac {1}{(-3+x) \left (-12-3 e^{x/16}+3 x+e^{x/16} x\right )} \, dx+\int \log ^2\left (12 (-4+x)+4 e^{x/16} (-3+x)\right ) \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [F] time = 1.17, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {192 x-48 x^2+e^{x/16} \left (48 x-16 x^2\right )+\left (48 x+e^{x/16} \left (13 x+x^2\right )\right ) \log \left (-48+12 x+e^{x/16} (-12+4 x)\right )+\left (-96+24 x+e^{x/16} (-24+8 x)\right ) \log ^2\left (-48+12 x+e^{x/16} (-12+4 x)\right )}{-96+24 x+e^{x/16} (-24+8 x)} \, dx \end {gather*}

Integrate[(192*x - 48*x^2 + E^(x/16)*(48*x - 16*x^2) + (48*x + E^(x/16)*(13*x + x^2))*Log[-48 + 12*x + E^(x/16

)*(-12 + 4*x)] + (-96 + 24*x + E^(x/16)*(-24 + 8*x))*Log[-48 + 12*x + E^(x/16)*(-12 + 4*x)]^2)/(-96 + 24*x + E

Integrate[(192*x - 48*x^2 + E^(x/16)*(48*x - 16*x^2) + (48*x + E^(x/16)*(13*x + x^2))*Log[-48 + 12*x + E^(x/16

)*(-12 + 4*x)] + (-96 + 24*x + E^(x/16)*(-24 + 8*x))*Log[-48 + 12*x + E^(x/16)*(-12 + 4*x)]^2)/(-96 + 24*x + E

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fricas [A] time = 0.62, size = 25, normalized size = 0.89 \begin {gather*} x \log \left (4 \, {\left (x - 3\right )} e^{\left (\frac {1}{16} \, x\right )} + 12 \, x - 48\right )^{2} - x^{2} \end {gather*}

integrate((((8*x-24)*exp(1/16*x)+24*x-96)*log((4*x-12)*exp(1/16*x)+12*x-48)^2+((x^2+13*x)*exp(1/16*x)+48*x)*lo

g((4*x-12)*exp(1/16*x)+12*x-48)+(-16*x^2+48*x)*exp(1/16*x)-48*x^2+192*x)/((8*x-24)*exp(1/16*x)+24*x-96),x, alg

x*log(4*(x - 3)*e^(1/16*x) + 12*x - 48)^2 - x^2

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giac [A] time = 1.26, size = 29, normalized size = 1.04 \begin {gather*} x \log \left (4 \, x e^{\left (\frac {1}{16} \, x\right )} + 12 \, x - 12 \, e^{\left (\frac {1}{16} \, x\right )} - 48\right )^{2} - x^{2} \end {gather*}

integrate((((8*x-24)*exp(1/16*x)+24*x-96)*log((4*x-12)*exp(1/16*x)+12*x-48)^2+((x^2+13*x)*exp(1/16*x)+48*x)*lo

g((4*x-12)*exp(1/16*x)+12*x-48)+(-16*x^2+48*x)*exp(1/16*x)-48*x^2+192*x)/((8*x-24)*exp(1/16*x)+24*x-96),x, alg

x*log(4*x*e^(1/16*x) + 12*x - 12*e^(1/16*x) - 48)^2 - x^2

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method	result	size

norman	\(x \ln \left (\left (4 x -12\right ) {\mathrm e}^{\frac {x}{16}}+12 x -48\right )^{2}-x^{2}\)	\(27\)
risch	\(x \ln \left (\left (4 x -12\right ) {\mathrm e}^{\frac {x}{16}}+12 x -48\right )^{2}-x^{2}\)	\(27\)

int((((8*x-24)*exp(1/16*x)+24*x-96)*ln((4*x-12)*exp(1/16*x)+12*x-48)^2+((x^2+13*x)*exp(1/16*x)+48*x)*ln((4*x-1

2)*exp(1/16*x)+12*x-48)+(-16*x^2+48*x)*exp(1/16*x)-48*x^2+192*x)/((8*x-24)*exp(1/16*x)+24*x-96),x,method=_RETU

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maxima [B] time = 0.91, size = 50, normalized size = 1.79 \begin {gather*} 4 \, x \log \relax (2)^{2} + 4 \, x \log \relax (2) \log \left ({\left (x - 3\right )} e^{\left (\frac {1}{16} \, x\right )} + 3 \, x - 12\right ) + x \log \left ({\left (x - 3\right )} e^{\left (\frac {1}{16} \, x\right )} + 3 \, x - 12\right )^{2} - x^{2} \end {gather*}

integrate((((8*x-24)*exp(1/16*x)+24*x-96)*log((4*x-12)*exp(1/16*x)+12*x-48)^2+((x^2+13*x)*exp(1/16*x)+48*x)*lo

g((4*x-12)*exp(1/16*x)+12*x-48)+(-16*x^2+48*x)*exp(1/16*x)-48*x^2+192*x)/((8*x-24)*exp(1/16*x)+24*x-96),x, alg

4*x*log(2)^2 + 4*x*log(2)*log((x - 3)*e^(1/16*x) + 3*x - 12) + x*log((x - 3)*e^(1/16*x) + 3*x - 12)^2 - x^2

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mupad [B] time = 0.67, size = 25, normalized size = 0.89 \begin {gather*} -x\,\left (x-{\ln \left (12\,x+{\mathrm {e}}^{x/16}\,\left (4\,x-12\right )-48\right )}^2\right ) \end {gather*}

int((192*x + exp(x/16)*(48*x - 16*x^2) + log(12*x + exp(x/16)*(4*x - 12) - 48)^2*(24*x + exp(x/16)*(8*x - 24)

- 96) + log(12*x + exp(x/16)*(4*x - 12) - 48)*(48*x + exp(x/16)*(13*x + x^2)) - 48*x^2)/(24*x + exp(x/16)*(8*x

-x*(x - log(12*x + exp(x/16)*(4*x - 12) - 48)^2)

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sympy [A] time = 0.45, size = 22, normalized size = 0.79 \begin {gather*} - x^{2} + x \log {\left (12 x + \left (4 x - 12\right ) e^{\frac {x}{16}} - 48 \right )}^{2} \end {gather*}

integrate((((8*x-24)*exp(1/16*x)+24*x-96)*ln((4*x-12)*exp(1/16*x)+12*x-48)**2+((x**2+13*x)*exp(1/16*x)+48*x)*l

n((4*x-12)*exp(1/16*x)+12*x-48)+(-16*x**2+48*x)*exp(1/16*x)-48*x**2+192*x)/((8*x-24)*exp(1/16*x)+24*x-96),x)

-x**2 + x*log(12*x + (4*x - 12)*exp(x/16) - 48)**2

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3.5.86 \(\int \frac {192 x-48 x^2+e^{x/16} (48 x-16 x^2)+(48 x+e^{x/16} (13 x+x^2)) \log (-48+12 x+e^{x/16} (-12+4 x))+(-96+24 x+e^{x/16} (-24+8 x)) \log ^2(-48+12 x+e^{x/16} (-12+4 x))}{-96+24 x+e^{x/16} (-24+8 x)} \, dx\)