3.95.40 \(\int \frac {-32 x+8 x^3+16 x^4+12 x^5+(-32+16 x^2+32 x^3+24 x^4) \log (x)+(8 x+16 x^2+12 x^3) \log ^2(x)+(-16-32 x-8 x^4-12 x^5+(-16-16 x^3-24 x^4) \log (x)+(-8 x^2-12 x^3) \log ^2(x)) \log (\frac {8-2 x^2-4 x^3-3 x^4+(-2 x-4 x^2-3 x^3) \log (x)}{x^2+x \log (x)})+(8 x-2 x^3-4 x^4-3 x^5+(8-4 x^2-8 x^3-6 x^4) \log (x)+(-2 x-4 x^2-3 x^3) \log ^2(x)) \log ^2(\frac {8-2 x^2-4 x^3-3 x^4+(-2 x-4 x^2-3 x^3) \log (x)}{x^2+x \log (x)})}{-8 x+2 x^3+4 x^4+3 x^5+(-8+4 x^2+8 x^3+6 x^4) \log (x)+(2 x+4 x^2+3 x^3) \log ^2(x)} \, dx\) [9440]

Optimal. Leaf size=31 \[ x \left (4-\log ^2\left (-2+x-x (5+3 x)+\frac {8}{x (x+\log (x))}\right )\right ) \]

[Out]

(4-ln(x-2-x*(5+3*x)+8/(x+ln(x))/x)^2)*x

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Rubi [F]
time = 41.57, 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 {-32 x+8 x^3+16 x^4+12 x^5+\left (-32+16 x^2+32 x^3+24 x^4\right ) \log (x)+\left (8 x+16 x^2+12 x^3\right ) \log ^2(x)+\left (-16-32 x-8 x^4-12 x^5+\left (-16-16 x^3-24 x^4\right ) \log (x)+\left (-8 x^2-12 x^3\right ) \log ^2(x)\right ) \log \left (\frac {8-2 x^2-4 x^3-3 x^4+\left (-2 x-4 x^2-3 x^3\right ) \log (x)}{x^2+x \log (x)}\right )+\left (8 x-2 x^3-4 x^4-3 x^5+\left (8-4 x^2-8 x^3-6 x^4\right ) \log (x)+\left (-2 x-4 x^2-3 x^3\right ) \log ^2(x)\right ) \log ^2\left (\frac {8-2 x^2-4 x^3-3 x^4+\left (-2 x-4 x^2-3 x^3\right ) \log (x)}{x^2+x \log (x)}\right )}{-8 x+2 x^3+4 x^4+3 x^5+\left (-8+4 x^2+8 x^3+6 x^4\right ) \log (x)+\left (2 x+4 x^2+3 x^3\right ) \log ^2(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-32*x + 8*x^3 + 16*x^4 + 12*x^5 + (-32 + 16*x^2 + 32*x^3 + 24*x^4)*Log[x] + (8*x + 16*x^2 + 12*x^3)*Log[x
]^2 + (-16 - 32*x - 8*x^4 - 12*x^5 + (-16 - 16*x^3 - 24*x^4)*Log[x] + (-8*x^2 - 12*x^3)*Log[x]^2)*Log[(8 - 2*x
^2 - 4*x^3 - 3*x^4 + (-2*x - 4*x^2 - 3*x^3)*Log[x])/(x^2 + x*Log[x])] + (8*x - 2*x^3 - 4*x^4 - 3*x^5 + (8 - 4*
x^2 - 8*x^3 - 6*x^4)*Log[x] + (-2*x - 4*x^2 - 3*x^3)*Log[x]^2)*Log[(8 - 2*x^2 - 4*x^3 - 3*x^4 + (-2*x - 4*x^2
- 3*x^3)*Log[x])/(x^2 + x*Log[x])]^2)/(-8*x + 2*x^3 + 4*x^4 + 3*x^5 + (-8 + 4*x^2 + 8*x^3 + 6*x^4)*Log[x] + (2
*x + 4*x^2 + 3*x^3)*Log[x]^2),x]

[Out]

4*x - 16*Defer[Int][Log[-((-8 + 2*x^2 + 4*x^3 + 3*x^4 + x*(2 + 4*x + 3*x^2)*Log[x])/(x*(x + Log[x])))]/((x + L
og[x])*(-8 + 2*x^2 + 4*x^3 + 3*x^4 + 2*x*Log[x] + 4*x^2*Log[x] + 3*x^3*Log[x])), x] - 32*Defer[Int][(x*Log[-((
-8 + 2*x^2 + 4*x^3 + 3*x^4 + x*(2 + 4*x + 3*x^2)*Log[x])/(x*(x + Log[x])))])/((x + Log[x])*(-8 + 2*x^2 + 4*x^3
+ 3*x^4 + 2*x*Log[x] + 4*x^2*Log[x] + 3*x^3*Log[x])), x] - 8*Defer[Int][(x^4*Log[-((-8 + 2*x^2 + 4*x^3 + 3*x^
4 + x*(2 + 4*x + 3*x^2)*Log[x])/(x*(x + Log[x])))])/((x + Log[x])*(-8 + 2*x^2 + 4*x^3 + 3*x^4 + 2*x*Log[x] + 4
*x^2*Log[x] + 3*x^3*Log[x])), x] - 12*Defer[Int][(x^5*Log[-((-8 + 2*x^2 + 4*x^3 + 3*x^4 + x*(2 + 4*x + 3*x^2)*
Log[x])/(x*(x + Log[x])))])/((x + Log[x])*(-8 + 2*x^2 + 4*x^3 + 3*x^4 + 2*x*Log[x] + 4*x^2*Log[x] + 3*x^3*Log[
x])), x] - 16*Defer[Int][(Log[x]*Log[-((-8 + 2*x^2 + 4*x^3 + 3*x^4 + x*(2 + 4*x + 3*x^2)*Log[x])/(x*(x + Log[x
])))])/((x + Log[x])*(-8 + 2*x^2 + 4*x^3 + 3*x^4 + 2*x*Log[x] + 4*x^2*Log[x] + 3*x^3*Log[x])), x] - 16*Defer[I
nt][(x^3*Log[x]*Log[-((-8 + 2*x^2 + 4*x^3 + 3*x^4 + x*(2 + 4*x + 3*x^2)*Log[x])/(x*(x + Log[x])))])/((x + Log[
x])*(-8 + 2*x^2 + 4*x^3 + 3*x^4 + 2*x*Log[x] + 4*x^2*Log[x] + 3*x^3*Log[x])), x] - 24*Defer[Int][(x^4*Log[x]*L
og[-((-8 + 2*x^2 + 4*x^3 + 3*x^4 + x*(2 + 4*x + 3*x^2)*Log[x])/(x*(x + Log[x])))])/((x + Log[x])*(-8 + 2*x^2 +
4*x^3 + 3*x^4 + 2*x*Log[x] + 4*x^2*Log[x] + 3*x^3*Log[x])), x] - 8*Defer[Int][(x^2*Log[x]^2*Log[-((-8 + 2*x^2
+ 4*x^3 + 3*x^4 + x*(2 + 4*x + 3*x^2)*Log[x])/(x*(x + Log[x])))])/((x + Log[x])*(-8 + 2*x^2 + 4*x^3 + 3*x^4 +
2*x*Log[x] + 4*x^2*Log[x] + 3*x^3*Log[x])), x] - 12*Defer[Int][(x^3*Log[x]^2*Log[-((-8 + 2*x^2 + 4*x^3 + 3*x^
4 + x*(2 + 4*x + 3*x^2)*Log[x])/(x*(x + Log[x])))])/((x + Log[x])*(-8 + 2*x^2 + 4*x^3 + 3*x^4 + 2*x*Log[x] + 4
*x^2*Log[x] + 3*x^3*Log[x])), x] - Defer[Int][Log[-((-8 + 2*x^2 + 4*x^3 + 3*x^4 + x*(2 + 4*x + 3*x^2)*Log[x])/
(x*(x + Log[x])))]^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {32 x}{(x+\log (x)) \left (-8+2 x^2+4 x^3+3 x^4+2 x \log (x)+4 x^2 \log (x)+3 x^3 \log (x)\right )}+\frac {8 x^3}{(x+\log (x)) \left (-8+2 x^2+4 x^3+3 x^4+2 x \log (x)+4 x^2 \log (x)+3 x^3 \log (x)\right )}+\frac {16 x^4}{(x+\log (x)) \left (-8+2 x^2+4 x^3+3 x^4+2 x \log (x)+4 x^2 \log (x)+3 x^3 \log (x)\right )}+\frac {12 x^5}{(x+\log (x)) \left (-8+2 x^2+4 x^3+3 x^4+2 x \log (x)+4 x^2 \log (x)+3 x^3 \log (x)\right )}+\frac {8 \left (-4+2 x^2+4 x^3+3 x^4\right ) \log (x)}{(x+\log (x)) \left (-8+2 x^2+4 x^3+3 x^4+2 x \log (x)+4 x^2 \log (x)+3 x^3 \log (x)\right )}+\frac {4 x \left (2+4 x+3 x^2\right ) \log ^2(x)}{(x+\log (x)) \left (-8+2 x^2+4 x^3+3 x^4+2 x \log (x)+4 x^2 \log (x)+3 x^3 \log (x)\right )}-\frac {4 \left (4+8 x+2 x^4+3 x^5+4 \log (x)+4 x^3 \log (x)+6 x^4 \log (x)+2 x^2 \log ^2(x)+3 x^3 \log ^2(x)\right ) \log \left (-\frac {-8+2 x^2+4 x^3+3 x^4+x \left (2+4 x+3 x^2\right ) \log (x)}{x (x+\log (x))}\right )}{(x+\log (x)) \left (-8+2 x^2+4 x^3+3 x^4+2 x \log (x)+4 x^2 \log (x)+3 x^3 \log (x)\right )}-\log ^2\left (-\frac {-8+2 x^2+4 x^3+3 x^4+x \left (2+4 x+3 x^2\right ) \log (x)}{x (x+\log (x))}\right )\right ) \, dx\\ &=4 \int \frac {x \left (2+4 x+3 x^2\right ) \log ^2(x)}{(x+\log (x)) \left (-8+2 x^2+4 x^3+3 x^4+2 x \log (x)+4 x^2 \log (x)+3 x^3 \log (x)\right )} \, dx-4 \int \frac {\left (4+8 x+2 x^4+3 x^5+4 \log (x)+4 x^3 \log (x)+6 x^4 \log (x)+2 x^2 \log ^2(x)+3 x^3 \log ^2(x)\right ) \log \left (-\frac {-8+2 x^2+4 x^3+3 x^4+x \left (2+4 x+3 x^2\right ) \log (x)}{x (x+\log (x))}\right )}{(x+\log (x)) \left (-8+2 x^2+4 x^3+3 x^4+2 x \log (x)+4 x^2 \log (x)+3 x^3 \log (x)\right )} \, dx+8 \int \frac {x^3}{(x+\log (x)) \left (-8+2 x^2+4 x^3+3 x^4+2 x \log (x)+4 x^2 \log (x)+3 x^3 \log (x)\right )} \, dx+8 \int \frac {\left (-4+2 x^2+4 x^3+3 x^4\right ) \log (x)}{(x+\log (x)) \left (-8+2 x^2+4 x^3+3 x^4+2 x \log (x)+4 x^2 \log (x)+3 x^3 \log (x)\right )} \, dx+12 \int \frac {x^5}{(x+\log (x)) \left (-8+2 x^2+4 x^3+3 x^4+2 x \log (x)+4 x^2 \log (x)+3 x^3 \log (x)\right )} \, dx+16 \int \frac {x^4}{(x+\log (x)) \left (-8+2 x^2+4 x^3+3 x^4+2 x \log (x)+4 x^2 \log (x)+3 x^3 \log (x)\right )} \, dx-32 \int \frac {x}{(x+\log (x)) \left (-8+2 x^2+4 x^3+3 x^4+2 x \log (x)+4 x^2 \log (x)+3 x^3 \log (x)\right )} \, dx-\int \log ^2\left (-\frac {-8+2 x^2+4 x^3+3 x^4+x \left (2+4 x+3 x^2\right ) \log (x)}{x (x+\log (x))}\right ) \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [F]
time = 5.41, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {-32 x+8 x^3+16 x^4+12 x^5+\left (-32+16 x^2+32 x^3+24 x^4\right ) \log (x)+\left (8 x+16 x^2+12 x^3\right ) \log ^2(x)+\left (-16-32 x-8 x^4-12 x^5+\left (-16-16 x^3-24 x^4\right ) \log (x)+\left (-8 x^2-12 x^3\right ) \log ^2(x)\right ) \log \left (\frac {8-2 x^2-4 x^3-3 x^4+\left (-2 x-4 x^2-3 x^3\right ) \log (x)}{x^2+x \log (x)}\right )+\left (8 x-2 x^3-4 x^4-3 x^5+\left (8-4 x^2-8 x^3-6 x^4\right ) \log (x)+\left (-2 x-4 x^2-3 x^3\right ) \log ^2(x)\right ) \log ^2\left (\frac {8-2 x^2-4 x^3-3 x^4+\left (-2 x-4 x^2-3 x^3\right ) \log (x)}{x^2+x \log (x)}\right )}{-8 x+2 x^3+4 x^4+3 x^5+\left (-8+4 x^2+8 x^3+6 x^4\right ) \log (x)+\left (2 x+4 x^2+3 x^3\right ) \log ^2(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(-32*x + 8*x^3 + 16*x^4 + 12*x^5 + (-32 + 16*x^2 + 32*x^3 + 24*x^4)*Log[x] + (8*x + 16*x^2 + 12*x^3)
*Log[x]^2 + (-16 - 32*x - 8*x^4 - 12*x^5 + (-16 - 16*x^3 - 24*x^4)*Log[x] + (-8*x^2 - 12*x^3)*Log[x]^2)*Log[(8
- 2*x^2 - 4*x^3 - 3*x^4 + (-2*x - 4*x^2 - 3*x^3)*Log[x])/(x^2 + x*Log[x])] + (8*x - 2*x^3 - 4*x^4 - 3*x^5 + (
8 - 4*x^2 - 8*x^3 - 6*x^4)*Log[x] + (-2*x - 4*x^2 - 3*x^3)*Log[x]^2)*Log[(8 - 2*x^2 - 4*x^3 - 3*x^4 + (-2*x -
4*x^2 - 3*x^3)*Log[x])/(x^2 + x*Log[x])]^2)/(-8*x + 2*x^3 + 4*x^4 + 3*x^5 + (-8 + 4*x^2 + 8*x^3 + 6*x^4)*Log[x
] + (2*x + 4*x^2 + 3*x^3)*Log[x]^2),x]

[Out]

Integrate[(-32*x + 8*x^3 + 16*x^4 + 12*x^5 + (-32 + 16*x^2 + 32*x^3 + 24*x^4)*Log[x] + (8*x + 16*x^2 + 12*x^3)
*Log[x]^2 + (-16 - 32*x - 8*x^4 - 12*x^5 + (-16 - 16*x^3 - 24*x^4)*Log[x] + (-8*x^2 - 12*x^3)*Log[x]^2)*Log[(8
- 2*x^2 - 4*x^3 - 3*x^4 + (-2*x - 4*x^2 - 3*x^3)*Log[x])/(x^2 + x*Log[x])] + (8*x - 2*x^3 - 4*x^4 - 3*x^5 + (
8 - 4*x^2 - 8*x^3 - 6*x^4)*Log[x] + (-2*x - 4*x^2 - 3*x^3)*Log[x]^2)*Log[(8 - 2*x^2 - 4*x^3 - 3*x^4 + (-2*x -
4*x^2 - 3*x^3)*Log[x])/(x^2 + x*Log[x])]^2)/(-8*x + 2*x^3 + 4*x^4 + 3*x^5 + (-8 + 4*x^2 + 8*x^3 + 6*x^4)*Log[x
] + (2*x + 4*x^2 + 3*x^3)*Log[x]^2), x]

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Maple [C] Result contains higher order function than in optimal. Order 9 vs. order 3.
time = 7.76, size = 7087, normalized size = 228.61

method	result	size
risch	\(\text {Expression too large to display}\)	\(7087\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-3*x^3-4*x^2-2*x)*ln(x)^2+(-6*x^4-8*x^3-4*x^2+8)*ln(x)-3*x^5-4*x^4-2*x^3+8*x)*ln(((-3*x^3-4*x^2-2*x)*ln
(x)-3*x^4-4*x^3-2*x^2+8)/(x*ln(x)+x^2))^2+((-12*x^3-8*x^2)*ln(x)^2+(-24*x^4-16*x^3-16)*ln(x)-12*x^5-8*x^4-32*x
-16)*ln(((-3*x^3-4*x^2-2*x)*ln(x)-3*x^4-4*x^3-2*x^2+8)/(x*ln(x)+x^2))+(12*x^3+16*x^2+8*x)*ln(x)^2+(24*x^4+32*x
^3+16*x^2-32)*ln(x)+12*x^5+16*x^4+8*x^3-32*x)/((3*x^3+4*x^2+2*x)*ln(x)^2+(6*x^4+8*x^3+4*x^2-8)*ln(x)+3*x^5+4*x
^4+2*x^3-8*x),x,method=_RETURNVERBOSE)

[Out]

result too large to display

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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 122 vs. \(2 (30) = 60\).
time = 0.32, size = 122, normalized size = 3.94 \begin {gather*} -x \log \left (-3 \, x^{4} - 4 \, x^{3} - 2 \, x^{2} - {\left (3 \, x^{3} + 4 \, x^{2} + 2 \, x\right )} \log \left (x\right ) + 8\right )^{2} - x \log \left (x + \log \left (x\right )\right )^{2} - 2 \, x \log \left (x + \log \left (x\right )\right ) \log \left (x\right ) - x \log \left (x\right )^{2} + 2 \, {\left (x \log \left (x + \log \left (x\right )\right ) + x \log \left (x\right )\right )} \log \left (-3 \, x^{4} - 4 \, x^{3} - 2 \, x^{2} - {\left (3 \, x^{3} + 4 \, x^{2} + 2 \, x\right )} \log \left (x\right ) + 8\right ) + 4 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-3*x^3-4*x^2-2*x)*log(x)^2+(-6*x^4-8*x^3-4*x^2+8)*log(x)-3*x^5-4*x^4-2*x^3+8*x)*log(((-3*x^3-4*x^
2-2*x)*log(x)-3*x^4-4*x^3-2*x^2+8)/(x*log(x)+x^2))^2+((-12*x^3-8*x^2)*log(x)^2+(-24*x^4-16*x^3-16)*log(x)-12*x
^5-8*x^4-32*x-16)*log(((-3*x^3-4*x^2-2*x)*log(x)-3*x^4-4*x^3-2*x^2+8)/(x*log(x)+x^2))+(12*x^3+16*x^2+8*x)*log(
x)^2+(24*x^4+32*x^3+16*x^2-32)*log(x)+12*x^5+16*x^4+8*x^3-32*x)/((3*x^3+4*x^2+2*x)*log(x)^2+(6*x^4+8*x^3+4*x^2
-8)*log(x)+3*x^5+4*x^4+2*x^3-8*x),x, algorithm="maxima")

[Out]

-x*log(-3*x^4 - 4*x^3 - 2*x^2 - (3*x^3 + 4*x^2 + 2*x)*log(x) + 8)^2 - x*log(x + log(x))^2 - 2*x*log(x + log(x)
)*log(x) - x*log(x)^2 + 2*(x*log(x + log(x)) + x*log(x))*log(-3*x^4 - 4*x^3 - 2*x^2 - (3*x^3 + 4*x^2 + 2*x)*lo
g(x) + 8) + 4*x

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Fricas [A]
time = 0.38, size = 56, normalized size = 1.81 \begin {gather*} -x \log \left (-\frac {3 \, x^{4} + 4 \, x^{3} + 2 \, x^{2} + {\left (3 \, x^{3} + 4 \, x^{2} + 2 \, x\right )} \log \left (x\right ) - 8}{x^{2} + x \log \left (x\right )}\right )^{2} + 4 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-3*x^3-4*x^2-2*x)*log(x)^2+(-6*x^4-8*x^3-4*x^2+8)*log(x)-3*x^5-4*x^4-2*x^3+8*x)*log(((-3*x^3-4*x^
2-2*x)*log(x)-3*x^4-4*x^3-2*x^2+8)/(x*log(x)+x^2))^2+((-12*x^3-8*x^2)*log(x)^2+(-24*x^4-16*x^3-16)*log(x)-12*x
^5-8*x^4-32*x-16)*log(((-3*x^3-4*x^2-2*x)*log(x)-3*x^4-4*x^3-2*x^2+8)/(x*log(x)+x^2))+(12*x^3+16*x^2+8*x)*log(
x)^2+(24*x^4+32*x^3+16*x^2-32)*log(x)+12*x^5+16*x^4+8*x^3-32*x)/((3*x^3+4*x^2+2*x)*log(x)^2+(6*x^4+8*x^3+4*x^2
-8)*log(x)+3*x^5+4*x^4+2*x^3-8*x),x, algorithm="fricas")

[Out]

-x*log(-(3*x^4 + 4*x^3 + 2*x^2 + (3*x^3 + 4*x^2 + 2*x)*log(x) - 8)/(x^2 + x*log(x)))^2 + 4*x

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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 51 vs. \(2 (24) = 48\).
time = 0.54, size = 51, normalized size = 1.65 \begin {gather*} - x \log {\left (\frac {- 3 x^{4} - 4 x^{3} - 2 x^{2} + \left (- 3 x^{3} - 4 x^{2} - 2 x\right ) \log {\left (x \right )} + 8}{x^{2} + x \log {\left (x \right )}} \right )}^{2} + 4 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-3*x**3-4*x**2-2*x)*ln(x)**2+(-6*x**4-8*x**3-4*x**2+8)*ln(x)-3*x**5-4*x**4-2*x**3+8*x)*ln(((-3*x*
*3-4*x**2-2*x)*ln(x)-3*x**4-4*x**3-2*x**2+8)/(x*ln(x)+x**2))**2+((-12*x**3-8*x**2)*ln(x)**2+(-24*x**4-16*x**3-
16)*ln(x)-12*x**5-8*x**4-32*x-16)*ln(((-3*x**3-4*x**2-2*x)*ln(x)-3*x**4-4*x**3-2*x**2+8)/(x*ln(x)+x**2))+(12*x
**3+16*x**2+8*x)*ln(x)**2+(24*x**4+32*x**3+16*x**2-32)*ln(x)+12*x**5+16*x**4+8*x**3-32*x)/((3*x**3+4*x**2+2*x)
*ln(x)**2+(6*x**4+8*x**3+4*x**2-8)*ln(x)+3*x**5+4*x**4+2*x**3-8*x),x)

[Out]

-x*log((-3*x**4 - 4*x**3 - 2*x**2 + (-3*x**3 - 4*x**2 - 2*x)*log(x) + 8)/(x**2 + x*log(x)))**2 + 4*x

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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 124 vs. \(2 (30) = 60\).
time = 2.67, size = 124, normalized size = 4.00 \begin {gather*} -x \log \left (-3 \, x^{4} - 3 \, x^{3} \log \left (x\right ) - 4 \, x^{3} - 4 \, x^{2} \log \left (x\right ) - 2 \, x^{2} - 2 \, x \log \left (x\right ) + 8\right )^{2} - x \log \left (x + \log \left (x\right )\right )^{2} - 2 \, x \log \left (x + \log \left (x\right )\right ) \log \left (x\right ) - x \log \left (x\right )^{2} + 2 \, {\left (x \log \left (x + \log \left (x\right )\right ) + x \log \left (x\right )\right )} \log \left (-3 \, x^{4} - 3 \, x^{3} \log \left (x\right ) - 4 \, x^{3} - 4 \, x^{2} \log \left (x\right ) - 2 \, x^{2} - 2 \, x \log \left (x\right ) + 8\right ) + 4 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-3*x^3-4*x^2-2*x)*log(x)^2+(-6*x^4-8*x^3-4*x^2+8)*log(x)-3*x^5-4*x^4-2*x^3+8*x)*log(((-3*x^3-4*x^
2-2*x)*log(x)-3*x^4-4*x^3-2*x^2+8)/(x*log(x)+x^2))^2+((-12*x^3-8*x^2)*log(x)^2+(-24*x^4-16*x^3-16)*log(x)-12*x
^5-8*x^4-32*x-16)*log(((-3*x^3-4*x^2-2*x)*log(x)-3*x^4-4*x^3-2*x^2+8)/(x*log(x)+x^2))+(12*x^3+16*x^2+8*x)*log(
x)^2+(24*x^4+32*x^3+16*x^2-32)*log(x)+12*x^5+16*x^4+8*x^3-32*x)/((3*x^3+4*x^2+2*x)*log(x)^2+(6*x^4+8*x^3+4*x^2
-8)*log(x)+3*x^5+4*x^4+2*x^3-8*x),x, algorithm="giac")

[Out]

-x*log(-3*x^4 - 3*x^3*log(x) - 4*x^3 - 4*x^2*log(x) - 2*x^2 - 2*x*log(x) + 8)^2 - x*log(x + log(x))^2 - 2*x*lo
g(x + log(x))*log(x) - x*log(x)^2 + 2*(x*log(x + log(x)) + x*log(x))*log(-3*x^4 - 3*x^3*log(x) - 4*x^3 - 4*x^2
*log(x) - 2*x^2 - 2*x*log(x) + 8) + 4*x

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Mupad [B]
time = 7.87, size = 54, normalized size = 1.74 \begin {gather*} -x\,\left ({\ln \left (-\frac {2\,x^2+4\,x^3+3\,x^4+\ln \left (x\right )\,\left (3\,x^3+4\,x^2+2\,x\right )-8}{x\,\ln \left (x\right )+x^2}\right )}^2-4\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(x)^2*(8*x + 16*x^2 + 12*x^3) - log(-(2*x^2 + 4*x^3 + 3*x^4 + log(x)*(2*x + 4*x^2 + 3*x^3) - 8)/(x*log
(x) + x^2))^2*(log(x)^2*(2*x + 4*x^2 + 3*x^3) - 8*x + log(x)*(4*x^2 + 8*x^3 + 6*x^4 - 8) + 2*x^3 + 4*x^4 + 3*x
^5) - 32*x + log(x)*(16*x^2 + 32*x^3 + 24*x^4 - 32) - log(-(2*x^2 + 4*x^3 + 3*x^4 + log(x)*(2*x + 4*x^2 + 3*x^
3) - 8)/(x*log(x) + x^2))*(32*x + log(x)*(16*x^3 + 24*x^4 + 16) + log(x)^2*(8*x^2 + 12*x^3) + 8*x^4 + 12*x^5 +
16) + 8*x^3 + 16*x^4 + 12*x^5)/(log(x)^2*(2*x + 4*x^2 + 3*x^3) - 8*x + log(x)*(4*x^2 + 8*x^3 + 6*x^4 - 8) + 2
*x^3 + 4*x^4 + 3*x^5),x)

[Out]

-x*(log(-(2*x^2 + 4*x^3 + 3*x^4 + log(x)*(2*x + 4*x^2 + 3*x^3) - 8)/(x*log(x) + x^2))^2 - 4)

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