3.83.33 \(\int \frac {-12 x-6 e^x x+3 x^2+(e^x (24-6 x)-6 x) \log (x)+(24-6 x) \log ^2(x)+(12-3 x+e^x (12 x-3 x^2)) \log (e^{\log ^2(x)} (48-24 x+3 x^2))}{-4 x^3+x^4+(e^x (8 x^2-2 x^3)+(8 x^2-2 x^3) \log (x)) \log (e^{\log ^2(x)} (48-24 x+3 x^2))+(e^{2 x} (-4 x+x^2)+e^x (-8 x+2 x^2) \log (x)+(-4 x+x^2) \log ^2(x)) \log ^2(e^{\log ^2(x)} (48-24 x+3 x^2))} \, dx\)

Optimal. Leaf size=29 \[ \frac {3}{-x+\log \left (3 e^{\log ^2(x)} (-4+x)^2\right ) \left (e^x+\log (x)\right )} \]

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Rubi [F]  time = 76.74, 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 {-12 x-6 e^x x+3 x^2+\left (e^x (24-6 x)-6 x\right ) \log (x)+(24-6 x) \log ^2(x)+\left (12-3 x+e^x \left (12 x-3 x^2\right )\right ) \log \left (e^{\log ^2(x)} \left (48-24 x+3 x^2\right )\right )}{-4 x^3+x^4+\left (e^x \left (8 x^2-2 x^3\right )+\left (8 x^2-2 x^3\right ) \log (x)\right ) \log \left (e^{\log ^2(x)} \left (48-24 x+3 x^2\right )\right )+\left (e^{2 x} \left (-4 x+x^2\right )+e^x \left (-8 x+2 x^2\right ) \log (x)+\left (-4 x+x^2\right ) \log ^2(x)\right ) \log ^2\left (e^{\log ^2(x)} \left (48-24 x+3 x^2\right )\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-12*x - 6*E^x*x + 3*x^2 + (E^x*(24 - 6*x) - 6*x)*Log[x] + (24 - 6*x)*Log[x]^2 + (12 - 3*x + E^x*(12*x - 3
*x^2))*Log[E^Log[x]^2*(48 - 24*x + 3*x^2)])/(-4*x^3 + x^4 + (E^x*(8*x^2 - 2*x^3) + (8*x^2 - 2*x^3)*Log[x])*Log
[E^Log[x]^2*(48 - 24*x + 3*x^2)] + (E^(2*x)*(-4*x + x^2) + E^x*(-8*x + 2*x^2)*Log[x] + (-4*x + x^2)*Log[x]^2)*
Log[E^Log[x]^2*(48 - 24*x + 3*x^2)]^2),x]

[Out]

3*Defer[Int][(x - Log[3*E^Log[x]^2*(-4 + x)^2]*(E^x + Log[x]))^(-2), x] - 3*Defer[Int][x/(x - Log[3*E^Log[x]^2
*(-4 + x)^2]*(E^x + Log[x]))^2, x] - 6*Defer[Int][1/(Log[3*E^Log[x]^2*(-4 + x)^2]*(x - Log[3*E^Log[x]^2*(-4 +
x)^2]*(E^x + Log[x]))^2), x] - 24*Defer[Int][1/((-4 + x)*Log[3*E^Log[x]^2*(-4 + x)^2]*(x - Log[3*E^Log[x]^2*(-
4 + x)^2]*(E^x + Log[x]))^2), x] - 3*Defer[Int][Log[3*E^Log[x]^2*(-4 + x)^2]/(x*(x - Log[3*E^Log[x]^2*(-4 + x)
^2]*(E^x + Log[x]))^2), x] - 6*Defer[Int][Log[x]/(Log[3*E^Log[x]^2*(-4 + x)^2]*(x - Log[3*E^Log[x]^2*(-4 + x)^
2]*(E^x + Log[x]))^2), x] + 3*Defer[Int][(Log[3*E^Log[x]^2*(-4 + x)^2]*Log[x])/(x - Log[3*E^Log[x]^2*(-4 + x)^
2]*(E^x + Log[x]))^2, x] + 3*Defer[Int][(x - Log[3*E^Log[x]^2*(-4 + x)^2]*(E^x + Log[x]))^(-1), x] + 6*Defer[I
nt][1/((-4 + x)*Log[3*E^Log[x]^2*(-4 + x)^2]*(x - Log[3*E^Log[x]^2*(-4 + x)^2]*(E^x + Log[x]))), x] + 6*Defer[
Int][Log[x]/(x*Log[3*E^Log[x]^2*(-4 + x)^2]*(x - Log[3*E^Log[x]^2*(-4 + x)^2]*(E^x + Log[x]))), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {3 \left (-x \left (-4-2 e^x+x\right )+(-4+x) \left (1+e^x x\right ) \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )+2 \left (e^x (-4+x)+x\right ) \log (x)+2 (-4+x) \log ^2(x)\right )}{(4-x) x \left (x-\log \left (3 e^{\log ^2(x)} (-4+x)^2\right ) \left (e^x+\log (x)\right )\right )^2} \, dx\\ &=3 \int \frac {-x \left (-4-2 e^x+x\right )+(-4+x) \left (1+e^x x\right ) \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )+2 \left (e^x (-4+x)+x\right ) \log (x)+2 (-4+x) \log ^2(x)}{(4-x) x \left (x-\log \left (3 e^{\log ^2(x)} (-4+x)^2\right ) \left (e^x+\log (x)\right )\right )^2} \, dx\\ &=3 \int \left (\frac {2 x-4 x \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )+x^2 \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )-8 \log (x)+2 x \log (x)}{(-4+x) x \log \left (3 e^{\log ^2(x)} (-4+x)^2\right ) \left (x-e^x \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )-\log \left (3 e^{\log ^2(x)} (-4+x)^2\right ) \log (x)\right )}-\frac {2 x^2+4 x \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )-5 x^2 \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )+x^3 \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )-4 \log ^2\left (3 e^{\log ^2(x)} (-4+x)^2\right )+x \log ^2\left (3 e^{\log ^2(x)} (-4+x)^2\right )-8 x \log (x)+2 x^2 \log (x)+4 x \log ^2\left (3 e^{\log ^2(x)} (-4+x)^2\right ) \log (x)-x^2 \log ^2\left (3 e^{\log ^2(x)} (-4+x)^2\right ) \log (x)}{(-4+x) x \log \left (3 e^{\log ^2(x)} (-4+x)^2\right ) \left (x-e^x \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )-\log \left (3 e^{\log ^2(x)} (-4+x)^2\right ) \log (x)\right )^2}\right ) \, dx\\ &=3 \int \frac {2 x-4 x \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )+x^2 \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )-8 \log (x)+2 x \log (x)}{(-4+x) x \log \left (3 e^{\log ^2(x)} (-4+x)^2\right ) \left (x-e^x \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )-\log \left (3 e^{\log ^2(x)} (-4+x)^2\right ) \log (x)\right )} \, dx-3 \int \frac {2 x^2+4 x \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )-5 x^2 \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )+x^3 \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )-4 \log ^2\left (3 e^{\log ^2(x)} (-4+x)^2\right )+x \log ^2\left (3 e^{\log ^2(x)} (-4+x)^2\right )-8 x \log (x)+2 x^2 \log (x)+4 x \log ^2\left (3 e^{\log ^2(x)} (-4+x)^2\right ) \log (x)-x^2 \log ^2\left (3 e^{\log ^2(x)} (-4+x)^2\right ) \log (x)}{(-4+x) x \log \left (3 e^{\log ^2(x)} (-4+x)^2\right ) \left (x-e^x \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )-\log \left (3 e^{\log ^2(x)} (-4+x)^2\right ) \log (x)\right )^2} \, dx\\ &=3 \int \frac {-\left ((-4+x) x \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )\right )-2 (x+(-4+x) \log (x))}{(4-x) x \log \left (3 e^{\log ^2(x)} (-4+x)^2\right ) \left (x-\log \left (3 e^{\log ^2(x)} (-4+x)^2\right ) \left (e^x+\log (x)\right )\right )} \, dx-3 \int \frac {-x \left (4-5 x+x^2\right ) \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )-2 x (x+(-4+x) \log (x))+(-4+x) \log ^2\left (3 e^{\log ^2(x)} (-4+x)^2\right ) (-1+x \log (x))}{(4-x) x \log \left (3 e^{\log ^2(x)} (-4+x)^2\right ) \left (x-\log \left (3 e^{\log ^2(x)} (-4+x)^2\right ) \left (e^x+\log (x)\right )\right )^2} \, dx\\ &=3 \int \left (\frac {2 x-4 x \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )+x^2 \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )-8 \log (x)+2 x \log (x)}{4 (-4+x) \log \left (3 e^{\log ^2(x)} (-4+x)^2\right ) \left (x-e^x \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )-\log \left (3 e^{\log ^2(x)} (-4+x)^2\right ) \log (x)\right )}-\frac {2 x-4 x \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )+x^2 \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )-8 \log (x)+2 x \log (x)}{4 x \log \left (3 e^{\log ^2(x)} (-4+x)^2\right ) \left (x-e^x \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )-\log \left (3 e^{\log ^2(x)} (-4+x)^2\right ) \log (x)\right )}\right ) \, dx-3 \int \left (\frac {2 x^2+4 x \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )-5 x^2 \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )+x^3 \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )-4 \log ^2\left (3 e^{\log ^2(x)} (-4+x)^2\right )+x \log ^2\left (3 e^{\log ^2(x)} (-4+x)^2\right )-8 x \log (x)+2 x^2 \log (x)+4 x \log ^2\left (3 e^{\log ^2(x)} (-4+x)^2\right ) \log (x)-x^2 \log ^2\left (3 e^{\log ^2(x)} (-4+x)^2\right ) \log (x)}{4 (-4+x) \log \left (3 e^{\log ^2(x)} (-4+x)^2\right ) \left (x-e^x \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )-\log \left (3 e^{\log ^2(x)} (-4+x)^2\right ) \log (x)\right )^2}-\frac {2 x^2+4 x \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )-5 x^2 \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )+x^3 \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )-4 \log ^2\left (3 e^{\log ^2(x)} (-4+x)^2\right )+x \log ^2\left (3 e^{\log ^2(x)} (-4+x)^2\right )-8 x \log (x)+2 x^2 \log (x)+4 x \log ^2\left (3 e^{\log ^2(x)} (-4+x)^2\right ) \log (x)-x^2 \log ^2\left (3 e^{\log ^2(x)} (-4+x)^2\right ) \log (x)}{4 x \log \left (3 e^{\log ^2(x)} (-4+x)^2\right ) \left (x-e^x \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )-\log \left (3 e^{\log ^2(x)} (-4+x)^2\right ) \log (x)\right )^2}\right ) \, dx\\ &=\frac {3}{4} \int \frac {2 x-4 x \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )+x^2 \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )-8 \log (x)+2 x \log (x)}{(-4+x) \log \left (3 e^{\log ^2(x)} (-4+x)^2\right ) \left (x-e^x \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )-\log \left (3 e^{\log ^2(x)} (-4+x)^2\right ) \log (x)\right )} \, dx-\frac {3}{4} \int \frac {2 x-4 x \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )+x^2 \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )-8 \log (x)+2 x \log (x)}{x \log \left (3 e^{\log ^2(x)} (-4+x)^2\right ) \left (x-e^x \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )-\log \left (3 e^{\log ^2(x)} (-4+x)^2\right ) \log (x)\right )} \, dx-\frac {3}{4} \int \frac {2 x^2+4 x \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )-5 x^2 \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )+x^3 \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )-4 \log ^2\left (3 e^{\log ^2(x)} (-4+x)^2\right )+x \log ^2\left (3 e^{\log ^2(x)} (-4+x)^2\right )-8 x \log (x)+2 x^2 \log (x)+4 x \log ^2\left (3 e^{\log ^2(x)} (-4+x)^2\right ) \log (x)-x^2 \log ^2\left (3 e^{\log ^2(x)} (-4+x)^2\right ) \log (x)}{(-4+x) \log \left (3 e^{\log ^2(x)} (-4+x)^2\right ) \left (x-e^x \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )-\log \left (3 e^{\log ^2(x)} (-4+x)^2\right ) \log (x)\right )^2} \, dx+\frac {3}{4} \int \frac {2 x^2+4 x \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )-5 x^2 \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )+x^3 \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )-4 \log ^2\left (3 e^{\log ^2(x)} (-4+x)^2\right )+x \log ^2\left (3 e^{\log ^2(x)} (-4+x)^2\right )-8 x \log (x)+2 x^2 \log (x)+4 x \log ^2\left (3 e^{\log ^2(x)} (-4+x)^2\right ) \log (x)-x^2 \log ^2\left (3 e^{\log ^2(x)} (-4+x)^2\right ) \log (x)}{x \log \left (3 e^{\log ^2(x)} (-4+x)^2\right ) \left (x-e^x \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )-\log \left (3 e^{\log ^2(x)} (-4+x)^2\right ) \log (x)\right )^2} \, dx\\ &=\frac {3}{4} \int \frac {-\left ((-4+x) x \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )\right )-2 (x+(-4+x) \log (x))}{(4-x) \log \left (3 e^{\log ^2(x)} (-4+x)^2\right ) \left (x-\log \left (3 e^{\log ^2(x)} (-4+x)^2\right ) \left (e^x+\log (x)\right )\right )} \, dx-\frac {3}{4} \int \frac {(-4+x) x \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )+2 (x+(-4+x) \log (x))}{x \log \left (3 e^{\log ^2(x)} (-4+x)^2\right ) \left (x-\log \left (3 e^{\log ^2(x)} (-4+x)^2\right ) \left (e^x+\log (x)\right )\right )} \, dx+\frac {3}{4} \int \frac {x \left (4-5 x+x^2\right ) \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )+2 x (x+(-4+x) \log (x))-(-4+x) \log ^2\left (3 e^{\log ^2(x)} (-4+x)^2\right ) (-1+x \log (x))}{x \log \left (3 e^{\log ^2(x)} (-4+x)^2\right ) \left (x-\log \left (3 e^{\log ^2(x)} (-4+x)^2\right ) \left (e^x+\log (x)\right )\right )^2} \, dx-\frac {3}{4} \int \frac {-x \left (4-5 x+x^2\right ) \log \left (3 e^{\log ^2(x)} (-4+x)^2\right )-2 x (x+(-4+x) \log (x))+(-4+x) \log ^2\left (3 e^{\log ^2(x)} (-4+x)^2\right ) (-1+x \log (x))}{(4-x) \log \left (3 e^{\log ^2(x)} (-4+x)^2\right ) \left (x-\log \left (3 e^{\log ^2(x)} (-4+x)^2\right ) \left (e^x+\log (x)\right )\right )^2} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 1.71, size = 28, normalized size = 0.97 \begin {gather*} -\frac {3}{x-\log \left (3 e^{\log ^2(x)} (-4+x)^2\right ) \left (e^x+\log (x)\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-12*x - 6*E^x*x + 3*x^2 + (E^x*(24 - 6*x) - 6*x)*Log[x] + (24 - 6*x)*Log[x]^2 + (12 - 3*x + E^x*(12
*x - 3*x^2))*Log[E^Log[x]^2*(48 - 24*x + 3*x^2)])/(-4*x^3 + x^4 + (E^x*(8*x^2 - 2*x^3) + (8*x^2 - 2*x^3)*Log[x
])*Log[E^Log[x]^2*(48 - 24*x + 3*x^2)] + (E^(2*x)*(-4*x + x^2) + E^x*(-8*x + 2*x^2)*Log[x] + (-4*x + x^2)*Log[
x]^2)*Log[E^Log[x]^2*(48 - 24*x + 3*x^2)]^2),x]

[Out]

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

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fricas [A]  time = 0.68, size = 30, normalized size = 1.03 \begin {gather*} \frac {3}{{\left (e^{x} + \log \relax (x)\right )} \log \left (3 \, {\left (x^{2} - 8 \, x + 16\right )} e^{\left (\log \relax (x)^{2}\right )}\right ) - x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-3*x^2+12*x)*exp(x)-3*x+12)*log((3*x^2-24*x+48)*exp(log(x)^2))+(-6*x+24)*log(x)^2+((-6*x+24)*exp(
x)-6*x)*log(x)-6*exp(x)*x+3*x^2-12*x)/(((x^2-4*x)*log(x)^2+(2*x^2-8*x)*exp(x)*log(x)+(x^2-4*x)*exp(x)^2)*log((
3*x^2-24*x+48)*exp(log(x)^2))^2+((-2*x^3+8*x^2)*log(x)+(-2*x^3+8*x^2)*exp(x))*log((3*x^2-24*x+48)*exp(log(x)^2
))+x^4-4*x^3),x, algorithm="fricas")

[Out]

3/((e^x + log(x))*log(3*(x^2 - 8*x + 16)*e^(log(x)^2)) - x)

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giac [A]  time = 4.78, size = 47, normalized size = 1.62 \begin {gather*} \frac {3}{e^{x} \log \relax (x)^{2} + \log \relax (x)^{3} + e^{x} \log \left (3 \, x^{2} - 24 \, x + 48\right ) + \log \left (3 \, x^{2} - 24 \, x + 48\right ) \log \relax (x) - x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-3*x^2+12*x)*exp(x)-3*x+12)*log((3*x^2-24*x+48)*exp(log(x)^2))+(-6*x+24)*log(x)^2+((-6*x+24)*exp(
x)-6*x)*log(x)-6*exp(x)*x+3*x^2-12*x)/(((x^2-4*x)*log(x)^2+(2*x^2-8*x)*exp(x)*log(x)+(x^2-4*x)*exp(x)^2)*log((
3*x^2-24*x+48)*exp(log(x)^2))^2+((-2*x^3+8*x^2)*log(x)+(-2*x^3+8*x^2)*exp(x))*log((3*x^2-24*x+48)*exp(log(x)^2
))+x^4-4*x^3),x, algorithm="giac")

[Out]

3/(e^x*log(x)^2 + log(x)^3 + e^x*log(3*x^2 - 24*x + 48) + log(3*x^2 - 24*x + 48)*log(x) - x)

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maple [C]  time = 4.11, size = 417, normalized size = 14.38

method	result	size
risch	\(\frac {6 i}{\pi \mathrm {csgn}\left (i {\mathrm e}^{\ln \relax (x )^{2}} \left (x -4\right )^{2}\right )^{3} \ln \relax (x )+\pi \mathrm {csgn}\left (i \left (x -4\right )\right )^{2} \mathrm {csgn}\left (i \left (x -4\right )^{2}\right ) {\mathrm e}^{x}+\pi \mathrm {csgn}\left (i \left (x -4\right )\right )^{2} \mathrm {csgn}\left (i \left (x -4\right )^{2}\right ) \ln \relax (x )-2 \pi \,\mathrm {csgn}\left (i \left (x -4\right )\right ) \mathrm {csgn}\left (i \left (x -4\right )^{2}\right )^{2} {\mathrm e}^{x}-2 \pi \,\mathrm {csgn}\left (i \left (x -4\right )\right ) \mathrm {csgn}\left (i \left (x -4\right )^{2}\right )^{2} \ln \relax (x )-\pi \mathrm {csgn}\left (i {\mathrm e}^{\ln \relax (x )^{2}} \left (x -4\right )^{2}\right )^{2} \mathrm {csgn}\left (i {\mathrm e}^{\ln \relax (x )^{2}}\right ) {\mathrm e}^{x}-\pi \mathrm {csgn}\left (i {\mathrm e}^{\ln \relax (x )^{2}} \left (x -4\right )^{2}\right )^{2} \mathrm {csgn}\left (i {\mathrm e}^{\ln \relax (x )^{2}}\right ) \ln \relax (x )-\pi \mathrm {csgn}\left (i {\mathrm e}^{\ln \relax (x )^{2}} \left (x -4\right )^{2}\right )^{2} \mathrm {csgn}\left (i \left (x -4\right )^{2}\right ) {\mathrm e}^{x}-\pi \mathrm {csgn}\left (i {\mathrm e}^{\ln \relax (x )^{2}} \left (x -4\right )^{2}\right )^{2} \mathrm {csgn}\left (i \left (x -4\right )^{2}\right ) \ln \relax (x )+\pi \mathrm {csgn}\left (i {\mathrm e}^{\ln \relax (x )^{2}} \left (x -4\right )^{2}\right )^{3} {\mathrm e}^{x}+2 i {\mathrm e}^{x} \ln \left ({\mathrm e}^{\ln \relax (x )^{2}}\right )+2 i \ln \relax (x ) \ln \left ({\mathrm e}^{\ln \relax (x )^{2}}\right )+2 i \ln \relax (3) \ln \relax (x )+4 i \ln \relax (x ) \ln \left (x -4\right )+4 i {\mathrm e}^{x} \ln \left (x -4\right )+2 i \ln \relax (3) {\mathrm e}^{x}-2 i x +\pi \,\mathrm {csgn}\left (i {\mathrm e}^{\ln \relax (x )^{2}} \left (x -4\right )^{2}\right ) \mathrm {csgn}\left (i {\mathrm e}^{\ln \relax (x )^{2}}\right ) \mathrm {csgn}\left (i \left (x -4\right )^{2}\right ) {\mathrm e}^{x}+\pi \,\mathrm {csgn}\left (i {\mathrm e}^{\ln \relax (x )^{2}} \left (x -4\right )^{2}\right ) \mathrm {csgn}\left (i {\mathrm e}^{\ln \relax (x )^{2}}\right ) \mathrm {csgn}\left (i \left (x -4\right )^{2}\right ) \ln \relax (x )+\pi \mathrm {csgn}\left (i \left (x -4\right )^{2}\right )^{3} \ln \relax (x )+\pi \mathrm {csgn}\left (i \left (x -4\right )^{2}\right )^{3} {\mathrm e}^{x}}\)	\(417\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-3*x^2+12*x)*exp(x)-3*x+12)*ln((3*x^2-24*x+48)*exp(ln(x)^2))+(-6*x+24)*ln(x)^2+((-6*x+24)*exp(x)-6*x)*l
n(x)-6*exp(x)*x+3*x^2-12*x)/(((x^2-4*x)*ln(x)^2+(2*x^2-8*x)*exp(x)*ln(x)+(x^2-4*x)*exp(x)^2)*ln((3*x^2-24*x+48
)*exp(ln(x)^2))^2+((-2*x^3+8*x^2)*ln(x)+(-2*x^3+8*x^2)*exp(x))*ln((3*x^2-24*x+48)*exp(ln(x)^2))+x^4-4*x^3),x,m
ethod=_RETURNVERBOSE)

[Out]

6*I/(Pi*csgn(I*exp(ln(x)^2)*(x-4)^2)^3*ln(x)+Pi*csgn(I*(x-4))^2*csgn(I*(x-4)^2)*exp(x)+Pi*csgn(I*(x-4))^2*csgn
(I*(x-4)^2)*ln(x)-2*Pi*csgn(I*(x-4))*csgn(I*(x-4)^2)^2*exp(x)-2*Pi*csgn(I*(x-4))*csgn(I*(x-4)^2)^2*ln(x)-Pi*cs
gn(I*exp(ln(x)^2)*(x-4)^2)^2*csgn(I*exp(ln(x)^2))*exp(x)-Pi*csgn(I*exp(ln(x)^2)*(x-4)^2)^2*csgn(I*exp(ln(x)^2)
)*ln(x)-Pi*csgn(I*exp(ln(x)^2)*(x-4)^2)^2*csgn(I*(x-4)^2)*exp(x)-Pi*csgn(I*exp(ln(x)^2)*(x-4)^2)^2*csgn(I*(x-4
)^2)*ln(x)+Pi*csgn(I*exp(ln(x)^2)*(x-4)^2)^3*exp(x)+2*I*exp(x)*ln(exp(ln(x)^2))+2*I*ln(x)*ln(exp(ln(x)^2))+2*I
*ln(3)*ln(x)+4*I*ln(x)*ln(x-4)+4*I*exp(x)*ln(x-4)+2*I*ln(3)*exp(x)-2*I*x+Pi*csgn(I*exp(ln(x)^2)*(x-4)^2)*csgn(
I*exp(ln(x)^2))*csgn(I*(x-4)^2)*exp(x)+Pi*csgn(I*exp(ln(x)^2)*(x-4)^2)*csgn(I*exp(ln(x)^2))*csgn(I*(x-4)^2)*ln
(x)+Pi*csgn(I*(x-4)^2)^3*ln(x)+Pi*csgn(I*(x-4)^2)^3*exp(x))

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \frac {3 \, {\left (x - 4\right )}}{e^{x} \log \relax (3) + 2 \, {\left (e^{x} + \log \relax (x)\right )} \log \left (x - 4\right ) + \log \relax (3) \log \relax (x) + {\left (e^{x} + \log \relax (x)\right )} \log \left (e^{\left (\log \relax (x)^{2}\right )}\right ) - x} - 3 \, \int \frac {1}{e^{x} \log \relax (3) + 2 \, {\left (e^{x} + \log \relax (x)\right )} \log \left (x - 4\right ) + \log \relax (3) \log \relax (x) + {\left (e^{x} + \log \relax (x)\right )} \log \left (e^{\left (\log \relax (x)^{2}\right )}\right ) - x}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-3*x^2+12*x)*exp(x)-3*x+12)*log((3*x^2-24*x+48)*exp(log(x)^2))+(-6*x+24)*log(x)^2+((-6*x+24)*exp(
x)-6*x)*log(x)-6*exp(x)*x+3*x^2-12*x)/(((x^2-4*x)*log(x)^2+(2*x^2-8*x)*exp(x)*log(x)+(x^2-4*x)*exp(x)^2)*log((
3*x^2-24*x+48)*exp(log(x)^2))^2+((-2*x^3+8*x^2)*log(x)+(-2*x^3+8*x^2)*exp(x))*log((3*x^2-24*x+48)*exp(log(x)^2
))+x^4-4*x^3),x, algorithm="maxima")

[Out]

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

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mupad [B]  time = 5.21, size = 30, normalized size = 1.03 \begin {gather*} -\frac {3}{x-\ln \left ({\mathrm {e}}^{{\ln \relax (x)}^2}\,\left (3\,x^2-24\,x+48\right )\right )\,\left ({\mathrm {e}}^x+\ln \relax (x)\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((12*x - log(exp(log(x)^2)*(3*x^2 - 24*x + 48))*(exp(x)*(12*x - 3*x^2) - 3*x + 12) + 6*x*exp(x) - 3*x^2 + l
og(x)^2*(6*x - 24) + log(x)*(6*x + exp(x)*(6*x - 24)))/(log(exp(log(x)^2)*(3*x^2 - 24*x + 48))^2*(exp(2*x)*(4*
x - x^2) + log(x)^2*(4*x - x^2) + exp(x)*log(x)*(8*x - 2*x^2)) - log(exp(log(x)^2)*(3*x^2 - 24*x + 48))*(exp(x
)*(8*x^2 - 2*x^3) + log(x)*(8*x^2 - 2*x^3)) + 4*x^3 - x^4),x)

[Out]

-3/(x - log(exp(log(x)^2)*(3*x^2 - 24*x + 48))*(exp(x) + log(x)))

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sympy [A]  time = 0.88, size = 27, normalized size = 0.93 \begin {gather*} \frac {3}{- x + \left (e^{x} + \log {\relax (x )}\right ) \log {\left (\left (3 x^{2} - 24 x + 48\right ) e^{\log {\relax (x )}^{2}} \right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-3*x**2+12*x)*exp(x)-3*x+12)*ln((3*x**2-24*x+48)*exp(ln(x)**2))+(-6*x+24)*ln(x)**2+((-6*x+24)*exp
(x)-6*x)*ln(x)-6*exp(x)*x+3*x**2-12*x)/(((x**2-4*x)*ln(x)**2+(2*x**2-8*x)*exp(x)*ln(x)+(x**2-4*x)*exp(x)**2)*l
n((3*x**2-24*x+48)*exp(ln(x)**2))**2+((-2*x**3+8*x**2)*ln(x)+(-2*x**3+8*x**2)*exp(x))*ln((3*x**2-24*x+48)*exp(
ln(x)**2))+x**4-4*x**3),x)

[Out]

3/(-x + (exp(x) + log(x))*log((3*x**2 - 24*x + 48)*exp(log(x)**2)))

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