3.35.85 \(\int \frac {192 x+e^{\frac {x}{\log (8)}} (8+384 x) \log (8)+(96 x+192 e^{\frac {x}{\log (8)}} x \log (8)) \log (x)+(12 x+24 e^{\frac {x}{\log (8)}} x \log (8)) \log ^2(x)}{-48 x \log (8)+e^{\frac {x}{\log (8)}} (-8 x+96 x^2) \log (8)+(-24 x \log (8)+e^{\frac {x}{\log (8)}} (-2 x+48 x^2) \log (8)) \log (x)+(-3 x \log (8)+6 e^{\frac {x}{\log (8)}} x^2 \log (8)) \log ^2(x)} \, dx\)

Optimal. Leaf size=28 \[ 4 \log \left (2 e^{-\frac {x}{\log (8)}}-4 x+\frac {4}{3 (4+\log (x))}\right ) \]

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Rubi [F]  time = 7.90, 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+e^{\frac {x}{\log (8)}} (8+384 x) \log (8)+\left (96 x+192 e^{\frac {x}{\log (8)}} x \log (8)\right ) \log (x)+\left (12 x+24 e^{\frac {x}{\log (8)}} x \log (8)\right ) \log ^2(x)}{-48 x \log (8)+e^{\frac {x}{\log (8)}} \left (-8 x+96 x^2\right ) \log (8)+\left (-24 x \log (8)+e^{\frac {x}{\log (8)}} \left (-2 x+48 x^2\right ) \log (8)\right ) \log (x)+\left (-3 x \log (8)+6 e^{\frac {x}{\log (8)}} x^2 \log (8)\right ) \log ^2(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(192*x + E^(x/Log[8])*(8 + 384*x)*Log[8] + (96*x + 192*E^(x/Log[8])*x*Log[8])*Log[x] + (12*x + 24*E^(x/Log
[8])*x*Log[8])*Log[x]^2)/(-48*x*Log[8] + E^(x/Log[8])*(-8*x + 96*x^2)*Log[8] + (-24*x*Log[8] + E^(x/Log[8])*(-
2*x + 48*x^2)*Log[8])*Log[x] + (-3*x*Log[8] + 6*E^(x/Log[8])*x^2*Log[8])*Log[x]^2),x]

[Out]

4*Log[x] - 4*Log[4 + Log[x]] + 12*Defer[Int][(-1 + 12*x + 3*x*Log[x])^(-1), x] + 4*Defer[Int][1/(x*(-1 + 12*x
+ 3*x*Log[x])), x] - (48*(1 - 12*Log[8])*Defer[Int][1/((-1 + 12*x + 3*x*Log[x])*(-12 - 2*E^(x/Log[8]) + 24*E^(
x/Log[8])*x - 3*Log[x] + 6*E^(x/Log[8])*x*Log[x])), x])/Log[8] + 12*Defer[Int][1/(x*(-1 + 12*x + 3*x*Log[x])*(
-12 - 2*E^(x/Log[8]) + 24*E^(x/Log[8])*x - 3*Log[x] + 6*E^(x/Log[8])*x*Log[x])), x] + (576*Defer[Int][x/((-1 +
12*x + 3*x*Log[x])*(-12 - 2*E^(x/Log[8]) + 24*E^(x/Log[8])*x - 3*Log[x] + 6*E^(x/Log[8])*x*Log[x])), x])/Log[
8] - (12*(1 - 24*Log[8])*Defer[Int][Log[x]/((-1 + 12*x + 3*x*Log[x])*(-12 - 2*E^(x/Log[8]) + 24*E^(x/Log[8])*x
- 3*Log[x] + 6*E^(x/Log[8])*x*Log[x])), x])/Log[8] + (288*Defer[Int][(x*Log[x])/((-1 + 12*x + 3*x*Log[x])*(-1
2 - 2*E^(x/Log[8]) + 24*E^(x/Log[8])*x - 3*Log[x] + 6*E^(x/Log[8])*x*Log[x])), x])/Log[8] + 36*Defer[Int][Log[
x]^2/((-1 + 12*x + 3*x*Log[x])*(-12 - 2*E^(x/Log[8]) + 24*E^(x/Log[8])*x - 3*Log[x] + 6*E^(x/Log[8])*x*Log[x])
), x] + (36*Defer[Int][(x*Log[x]^2)/((-1 + 12*x + 3*x*Log[x])*(-12 - 2*E^(x/Log[8]) + 24*E^(x/Log[8])*x - 3*Lo
g[x] + 6*E^(x/Log[8])*x*Log[x])), x])/Log[8]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-192 x-e^{\frac {x}{\log (8)}} (8+384 x) \log (8)-\left (96 x+192 e^{\frac {x}{\log (8)}} x \log (8)\right ) \log (x)-\left (12 x+24 e^{\frac {x}{\log (8)}} x \log (8)\right ) \log ^2(x)}{x \log (8) (4+\log (x)) \left (12+2 e^{\frac {x}{\log (8)}}-24 e^{\frac {x}{\log (8)}} x+3 \log (x)-6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx\\ &=\frac {\int \frac {-192 x-e^{\frac {x}{\log (8)}} (8+384 x) \log (8)-\left (96 x+192 e^{\frac {x}{\log (8)}} x \log (8)\right ) \log (x)-\left (12 x+24 e^{\frac {x}{\log (8)}} x \log (8)\right ) \log ^2(x)}{x (4+\log (x)) \left (12+2 e^{\frac {x}{\log (8)}}-24 e^{\frac {x}{\log (8)}} x+3 \log (x)-6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx}{\log (8)}\\ &=\frac {\int \left (\frac {4 \log (8) \left (1+48 x+24 x \log (x)+3 x \log ^2(x)\right )}{x (4+\log (x)) (-1+12 x+3 x \log (x))}+\frac {12 \left (48 x^2-4 x (1-12 \log (8))+\log (8)+24 x^2 \log (x)-x (1-24 \log (8)) \log (x)+3 x^2 \log ^2(x)+3 x \log (8) \log ^2(x)\right )}{x (1-12 x-3 x \log (x)) \left (12+2 e^{\frac {x}{\log (8)}}-24 e^{\frac {x}{\log (8)}} x+3 \log (x)-6 e^{\frac {x}{\log (8)}} x \log (x)\right )}\right ) \, dx}{\log (8)}\\ &=4 \int \frac {1+48 x+24 x \log (x)+3 x \log ^2(x)}{x (4+\log (x)) (-1+12 x+3 x \log (x))} \, dx+\frac {12 \int \frac {48 x^2-4 x (1-12 \log (8))+\log (8)+24 x^2 \log (x)-x (1-24 \log (8)) \log (x)+3 x^2 \log ^2(x)+3 x \log (8) \log ^2(x)}{x (1-12 x-3 x \log (x)) \left (12+2 e^{\frac {x}{\log (8)}}-24 e^{\frac {x}{\log (8)}} x+3 \log (x)-6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx}{\log (8)}\\ &=4 \int \left (\frac {1}{x}-\frac {1}{x (4+\log (x))}+\frac {1+3 x}{x (-1+12 x+3 x \log (x))}\right ) \, dx+\frac {12 \int \left (\frac {48 x}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )}+\frac {\log (8)}{x (-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )}+\frac {4 (-1+12 \log (8))}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )}+\frac {24 x \log (x)}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )}+\frac {(-1+24 \log (8)) \log (x)}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )}+\frac {3 x \log ^2(x)}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )}+\frac {3 \log (8) \log ^2(x)}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )}\right ) \, dx}{\log (8)}\\ &=4 \log (x)-4 \int \frac {1}{x (4+\log (x))} \, dx+4 \int \frac {1+3 x}{x (-1+12 x+3 x \log (x))} \, dx+12 \int \frac {1}{x (-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx+36 \int \frac {\log ^2(x)}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx+\frac {36 \int \frac {x \log ^2(x)}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx}{\log (8)}+\frac {288 \int \frac {x \log (x)}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx}{\log (8)}+\frac {576 \int \frac {x}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx}{\log (8)}-\frac {(48 (1-12 \log (8))) \int \frac {1}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx}{\log (8)}+\frac {(12 (-1+24 \log (8))) \int \frac {\log (x)}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx}{\log (8)}\\ &=4 \log (x)+4 \int \left (\frac {3}{-1+12 x+3 x \log (x)}+\frac {1}{x (-1+12 x+3 x \log (x))}\right ) \, dx-4 \operatorname {Subst}\left (\int \frac {1}{x} \, dx,x,4+\log (x)\right )+12 \int \frac {1}{x (-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx+36 \int \frac {\log ^2(x)}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx+\frac {36 \int \frac {x \log ^2(x)}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx}{\log (8)}+\frac {288 \int \frac {x \log (x)}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx}{\log (8)}+\frac {576 \int \frac {x}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx}{\log (8)}-\frac {(48 (1-12 \log (8))) \int \frac {1}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx}{\log (8)}+\frac {(12 (-1+24 \log (8))) \int \frac {\log (x)}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx}{\log (8)}\\ &=4 \log (x)-4 \log (4+\log (x))+4 \int \frac {1}{x (-1+12 x+3 x \log (x))} \, dx+12 \int \frac {1}{-1+12 x+3 x \log (x)} \, dx+12 \int \frac {1}{x (-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx+36 \int \frac {\log ^2(x)}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx+\frac {36 \int \frac {x \log ^2(x)}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx}{\log (8)}+\frac {288 \int \frac {x \log (x)}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx}{\log (8)}+\frac {576 \int \frac {x}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx}{\log (8)}-\frac {(48 (1-12 \log (8))) \int \frac {1}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx}{\log (8)}+\frac {(12 (-1+24 \log (8))) \int \frac {\log (x)}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx}{\log (8)}\\ \end {aligned} \end {gather*}

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Mathematica [F]  time = 0.78, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {192 x+e^{\frac {x}{\log (8)}} (8+384 x) \log (8)+\left (96 x+192 e^{\frac {x}{\log (8)}} x \log (8)\right ) \log (x)+\left (12 x+24 e^{\frac {x}{\log (8)}} x \log (8)\right ) \log ^2(x)}{-48 x \log (8)+e^{\frac {x}{\log (8)}} \left (-8 x+96 x^2\right ) \log (8)+\left (-24 x \log (8)+e^{\frac {x}{\log (8)}} \left (-2 x+48 x^2\right ) \log (8)\right ) \log (x)+\left (-3 x \log (8)+6 e^{\frac {x}{\log (8)}} x^2 \log (8)\right ) \log ^2(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(192*x + E^(x/Log[8])*(8 + 384*x)*Log[8] + (96*x + 192*E^(x/Log[8])*x*Log[8])*Log[x] + (12*x + 24*E^
(x/Log[8])*x*Log[8])*Log[x]^2)/(-48*x*Log[8] + E^(x/Log[8])*(-8*x + 96*x^2)*Log[8] + (-24*x*Log[8] + E^(x/Log[
8])*(-2*x + 48*x^2)*Log[8])*Log[x] + (-3*x*Log[8] + 6*E^(x/Log[8])*x^2*Log[8])*Log[x]^2),x]

[Out]

Integrate[(192*x + E^(x/Log[8])*(8 + 384*x)*Log[8] + (96*x + 192*E^(x/Log[8])*x*Log[8])*Log[x] + (12*x + 24*E^
(x/Log[8])*x*Log[8])*Log[x]^2)/(-48*x*Log[8] + E^(x/Log[8])*(-8*x + 96*x^2)*Log[8] + (-24*x*Log[8] + E^(x/Log[
8])*(-2*x + 48*x^2)*Log[8])*Log[x] + (-3*x*Log[8] + 6*E^(x/Log[8])*x^2*Log[8])*Log[x]^2), x]

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fricas [B]  time = 0.70, size = 102, normalized size = 3.64 \begin {gather*} \frac {4 \, {\left (3 \, \log \relax (2) \log \relax (x) + 3 \, \log \relax (2) \log \left (\frac {2 \, {\left (12 \, x - 1\right )} e^{\left (\frac {x}{3 \, \log \relax (2)}\right )} + 3 \, {\left (2 \, x e^{\left (\frac {x}{3 \, \log \relax (2)}\right )} - 1\right )} \log \relax (x) - 12}{2 \, x e^{\left (\frac {x}{3 \, \log \relax (2)}\right )} - 1}\right ) + 3 \, \log \relax (2) \log \left (\frac {2 \, x e^{\left (\frac {x}{3 \, \log \relax (2)}\right )} - 1}{x}\right ) - 3 \, \log \relax (2) \log \left (\log \relax (x) + 4\right ) - x\right )}}{3 \, \log \relax (2)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((72*x*log(2)*exp(1/3*x/log(2))+12*x)*log(x)^2+(576*x*log(2)*exp(1/3*x/log(2))+96*x)*log(x)+3*(384*x
+8)*log(2)*exp(1/3*x/log(2))+192*x)/((18*x^2*log(2)*exp(1/3*x/log(2))-9*x*log(2))*log(x)^2+(3*(48*x^2-2*x)*log
(2)*exp(1/3*x/log(2))-72*x*log(2))*log(x)+3*(96*x^2-8*x)*log(2)*exp(1/3*x/log(2))-144*x*log(2)),x, algorithm="
fricas")

[Out]

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

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giac [B]  time = 2.63, size = 94, normalized size = 3.36 \begin {gather*} \frac {4 \, {\left (3 \, \log \relax (2) \log \left (6 \, x e^{\left (\frac {x}{3 \, \log \relax (2)}\right )} \log \relax (x) + 24 \, x e^{\left (\frac {x}{3 \, \log \relax (2)}\right )} - 2 \, e^{\left (\frac {x}{3 \, \log \relax (2)}\right )} - 3 \, \log \relax (x) - 12\right ) + 3 \, \log \relax (2) \log \left (3 \, x \log \relax (x) + 12 \, x - 1\right ) - 3 \, \log \relax (2) \log \left (-3 \, x \log \relax (x) - 12 \, x + 1\right ) - 3 \, \log \relax (2) \log \left (\log \relax (x) + 4\right ) - x\right )}}{3 \, \log \relax (2)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((72*x*log(2)*exp(1/3*x/log(2))+12*x)*log(x)^2+(576*x*log(2)*exp(1/3*x/log(2))+96*x)*log(x)+3*(384*x
+8)*log(2)*exp(1/3*x/log(2))+192*x)/((18*x^2*log(2)*exp(1/3*x/log(2))-9*x*log(2))*log(x)^2+(3*(48*x^2-2*x)*log
(2)*exp(1/3*x/log(2))-72*x*log(2))*log(x)+3*(96*x^2-8*x)*log(2)*exp(1/3*x/log(2))-144*x*log(2)),x, algorithm="
giac")

[Out]

4/3*(3*log(2)*log(6*x*e^(1/3*x/log(2))*log(x) + 24*x*e^(1/3*x/log(2)) - 2*e^(1/3*x/log(2)) - 3*log(x) - 12) +
3*log(2)*log(3*x*log(x) + 12*x - 1) - 3*log(2)*log(-3*x*log(x) - 12*x + 1) - 3*log(2)*log(log(x) + 4) - x)/log
(2)

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maple [A]  time = 0.40, size = 59, normalized size = 2.11

method	result	size
norman	\(-\frac {4 x}{3 \ln \relax (2)}-4 \ln \left (\ln \relax (x )+4\right )+4 \ln \left (6 \ln \relax (x ) {\mathrm e}^{\frac {x}{3 \ln \relax (2)}} x +24 x \,{\mathrm e}^{\frac {x}{3 \ln \relax (2)}}-2 \,{\mathrm e}^{\frac {x}{3 \ln \relax (2)}}-3 \ln \relax (x )-12\right )\)	\(59\)
risch	\(4 \ln \relax (x )+4 \ln \left ({\mathrm e}^{\frac {x}{3 \ln \relax (2)}}-\frac {1}{2 x}\right )-\frac {4 x}{3 \ln \relax (2)}+4 \ln \left (\ln \relax (x )+\frac {8 x \,{\mathrm e}^{\frac {x}{3 \ln \relax (2)}}-\frac {2 \,{\mathrm e}^{\frac {x}{3 \ln \relax (2)}}}{3}-4}{2 x \,{\mathrm e}^{\frac {x}{3 \ln \relax (2)}}-1}\right )-4 \ln \left (\ln \relax (x )+4\right )\)	\(83\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((72*x*ln(2)*exp(1/3*x/ln(2))+12*x)*ln(x)^2+(576*x*ln(2)*exp(1/3*x/ln(2))+96*x)*ln(x)+3*(384*x+8)*ln(2)*ex
p(1/3*x/ln(2))+192*x)/((18*x^2*ln(2)*exp(1/3*x/ln(2))-9*x*ln(2))*ln(x)^2+(3*(48*x^2-2*x)*ln(2)*exp(1/3*x/ln(2)
)-72*x*ln(2))*ln(x)+3*(96*x^2-8*x)*ln(2)*exp(1/3*x/ln(2))-144*x*ln(2)),x,method=_RETURNVERBOSE)

[Out]

-4/3*x/ln(2)-4*ln(ln(x)+4)+4*ln(6*ln(x)*exp(1/3*x/ln(2))*x+24*x*exp(1/3*x/ln(2))-2*exp(1/3*x/ln(2))-3*ln(x)-12
)

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maxima [B]  time = 0.76, size = 80, normalized size = 2.86 \begin {gather*} -\frac {4 \, x}{3 \, \log \relax (2)} + 4 \, \log \relax (x) + 4 \, \log \left (\frac {2 \, {\left (3 \, x \log \relax (x) + 12 \, x - 1\right )} e^{\left (\frac {x}{3 \, \log \relax (2)}\right )} - 3 \, \log \relax (x) - 12}{2 \, {\left (3 \, x \log \relax (x) + 12 \, x - 1\right )}}\right ) + 4 \, \log \left (\frac {3 \, x \log \relax (x) + 12 \, x - 1}{3 \, x}\right ) - 4 \, \log \left (\log \relax (x) + 4\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((72*x*log(2)*exp(1/3*x/log(2))+12*x)*log(x)^2+(576*x*log(2)*exp(1/3*x/log(2))+96*x)*log(x)+3*(384*x
+8)*log(2)*exp(1/3*x/log(2))+192*x)/((18*x^2*log(2)*exp(1/3*x/log(2))-9*x*log(2))*log(x)^2+(3*(48*x^2-2*x)*log
(2)*exp(1/3*x/log(2))-72*x*log(2))*log(x)+3*(96*x^2-8*x)*log(2)*exp(1/3*x/log(2))-144*x*log(2)),x, algorithm="
maxima")

[Out]

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

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int -\frac {\left (12\,x+72\,x\,{\mathrm {e}}^{\frac {x}{3\,\ln \relax (2)}}\,\ln \relax (2)\right )\,{\ln \relax (x)}^2+\left (96\,x+576\,x\,{\mathrm {e}}^{\frac {x}{3\,\ln \relax (2)}}\,\ln \relax (2)\right )\,\ln \relax (x)+192\,x+3\,{\mathrm {e}}^{\frac {x}{3\,\ln \relax (2)}}\,\ln \relax (2)\,\left (384\,x+8\right )}{\left (9\,x\,\ln \relax (2)-18\,x^2\,{\mathrm {e}}^{\frac {x}{3\,\ln \relax (2)}}\,\ln \relax (2)\right )\,{\ln \relax (x)}^2+\left (72\,x\,\ln \relax (2)+3\,{\mathrm {e}}^{\frac {x}{3\,\ln \relax (2)}}\,\ln \relax (2)\,\left (2\,x-48\,x^2\right )\right )\,\ln \relax (x)+144\,x\,\ln \relax (2)+3\,{\mathrm {e}}^{\frac {x}{3\,\ln \relax (2)}}\,\ln \relax (2)\,\left (8\,x-96\,x^2\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(192*x + log(x)^2*(12*x + 72*x*exp(x/(3*log(2)))*log(2)) + log(x)*(96*x + 576*x*exp(x/(3*log(2)))*log(2))
+ 3*exp(x/(3*log(2)))*log(2)*(384*x + 8))/(log(x)*(72*x*log(2) + 3*exp(x/(3*log(2)))*log(2)*(2*x - 48*x^2)) +
144*x*log(2) + log(x)^2*(9*x*log(2) - 18*x^2*exp(x/(3*log(2)))*log(2)) + 3*exp(x/(3*log(2)))*log(2)*(8*x - 96
*x^2)),x)

[Out]

int(-(192*x + log(x)^2*(12*x + 72*x*exp(x/(3*log(2)))*log(2)) + log(x)*(96*x + 576*x*exp(x/(3*log(2)))*log(2))
+ 3*exp(x/(3*log(2)))*log(2)*(384*x + 8))/(log(x)*(72*x*log(2) + 3*exp(x/(3*log(2)))*log(2)*(2*x - 48*x^2)) +
144*x*log(2) + log(x)^2*(9*x*log(2) - 18*x^2*exp(x/(3*log(2)))*log(2)) + 3*exp(x/(3*log(2)))*log(2)*(8*x - 96
*x^2)), x)

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sympy [B]  time = 4.10, size = 71, normalized size = 2.54 \begin {gather*} \frac {- 4 x + 12 \log {\relax (2 )} \log {\relax (x )}}{3 \log {\relax (2 )}} + 4 \log {\left (\frac {- 3 \log {\relax (x )} - 12}{6 x \log {\relax (x )} + 24 x - 2} + e^{\frac {x}{3 \log {\relax (2 )}}} \right )} - 4 \log {\left (\log {\relax (x )} + 4 \right )} + 4 \log {\left (\log {\relax (x )} + \frac {96 x - 8}{24 x} \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((72*x*ln(2)*exp(1/3*x/ln(2))+12*x)*ln(x)**2+(576*x*ln(2)*exp(1/3*x/ln(2))+96*x)*ln(x)+3*(384*x+8)*l
n(2)*exp(1/3*x/ln(2))+192*x)/((18*x**2*ln(2)*exp(1/3*x/ln(2))-9*x*ln(2))*ln(x)**2+(3*(48*x**2-2*x)*ln(2)*exp(1
/3*x/ln(2))-72*x*ln(2))*ln(x)+3*(96*x**2-8*x)*ln(2)*exp(1/3*x/ln(2))-144*x*ln(2)),x)

[Out]

(-4*x + 12*log(2)*log(x))/(3*log(2)) + 4*log((-3*log(x) - 12)/(6*x*log(x) + 24*x - 2) + exp(x/(3*log(2)))) - 4
*log(log(x) + 4) + 4*log(log(x) + (96*x - 8)/(24*x))

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