∫ −2x2−2x3−2x4−2x5+(4x2+6x3+6x4) log(x)+(−4x2−6x3) log2(x)+2x2 log3(x)+(−524288x3+1572864x2 log(x)−1572864x log2(x)+524288 log3(x)) log3(x2)_______________________________________________________________________________________________________________ −x4−2x5−x6+(x3+4x4+3x5) log(x)+(−2x3−3x4) log2(x)+x3 log3(x)+(−65536x4+196608x3 log(x)−196608x2 log2(x)+65536x log3(x)) log4(x2) dx [8787]

3.88.87 \(\int \frac {-2 x^2-2 x^3-2 x^4-2 x^5+(4 x^2+6 x^3+6 x^4) \log (x)+(-4 x^2-6 x^3) \log ^2(x)+2 x^2 \log ^3(x)+(-524288 x^3+1572864 x^2 \log (x)-1572864 x \log ^2(x)+524288 \log ^3(x)) \log ^3(x^2)}{-x^4-2 x^5-x^6+(x^3+4 x^4+3 x^5) \log (x)+(-2 x^3-3 x^4) \log ^2(x)+x^3 \log ^3(x)+(-65536 x^4+196608 x^3 \log (x)-196608 x^2 \log ^2(x)+65536 x \log ^3(x)) \log ^4(x^2)} \, dx\) [8787]

Optimal. Leaf size=24 \[ \log \left (\left (x+\frac {x}{x-\log (x)}\right )^2+65536 \log ^4\left (x^2\right )\right ) \]

[Out]

ln(65536*ln(x^2)^4+(1/(x-ln(x))*x+x)^2)

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Rubi [F]
time = 10.99, 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 {-2 x^2-2 x^3-2 x^4-2 x^5+\left (4 x^2+6 x^3+6 x^4\right ) \log (x)+\left (-4 x^2-6 x^3\right ) \log ^2(x)+2 x^2 \log ^3(x)+\left (-524288 x^3+1572864 x^2 \log (x)-1572864 x \log ^2(x)+524288 \log ^3(x)\right ) \log ^3\left (x^2\right )}{-x^4-2 x^5-x^6+\left (x^3+4 x^4+3 x^5\right ) \log (x)+\left (-2 x^3-3 x^4\right ) \log ^2(x)+x^3 \log ^3(x)+\left (-65536 x^4+196608 x^3 \log (x)-196608 x^2 \log ^2(x)+65536 x \log ^3(x)\right ) \log ^4\left (x^2\right )} \, dx \end {gather*}

Veriﬁcation is not applicable to the result.

[In]

Int[(-2*x^2 - 2*x^3 - 2*x^4 - 2*x^5 + (4*x^2 + 6*x^3 + 6*x^4)*Log[x] + (-4*x^2 - 6*x^3)*Log[x]^2 + 2*x^2*Log[x

]^3 + (-524288*x^3 + 1572864*x^2*Log[x] - 1572864*x*Log[x]^2 + 524288*Log[x]^3)*Log[x^2]^3)/(-x^4 - 2*x^5 - x^

6 + (x^3 + 4*x^4 + 3*x^5)*Log[x] + (-2*x^3 - 3*x^4)*Log[x]^2 + x^3*Log[x]^3 + (-65536*x^4 + 196608*x^3*Log[x]

- 196608*x^2*Log[x]^2 + 65536*x*Log[x]^3)*Log[x^2]^4),x]

[Out]

2*Defer[Int][x/((x - Log[x])*(x^2 + 2*x^3 + x^4 - 2*x^2*Log[x] - 2*x^3*Log[x] + x^2*Log[x]^2 + 65536*x^2*Log[x

^2]^4 - 131072*x*Log[x]*Log[x^2]^4 + 65536*Log[x]^2*Log[x^2]^4)), x] + 2*Defer[Int][x^2/((x - Log[x])*(x^2 + 2

*x^3 + x^4 - 2*x^2*Log[x] - 2*x^3*Log[x] + x^2*Log[x]^2 + 65536*x^2*Log[x^2]^4 - 131072*x*Log[x]*Log[x^2]^4 +

65536*Log[x]^2*Log[x^2]^4)), x] + 2*Defer[Int][x^3/((x - Log[x])*(x^2 + 2*x^3 + x^4 - 2*x^2*Log[x] - 2*x^3*Log

[x] + x^2*Log[x]^2 + 65536*x^2*Log[x^2]^4 - 131072*x*Log[x]*Log[x^2]^4 + 65536*Log[x]^2*Log[x^2]^4)), x] + 2*D

efer[Int][x^4/((x - Log[x])*(x^2 + 2*x^3 + x^4 - 2*x^2*Log[x] - 2*x^3*Log[x] + x^2*Log[x]^2 + 65536*x^2*Log[x^

2]^4 - 131072*x*Log[x]*Log[x^2]^4 + 65536*Log[x]^2*Log[x^2]^4)), x] - 4*Defer[Int][(x*Log[x])/((x - Log[x])*(x

^2 + 2*x^3 + x^4 - 2*x^2*Log[x] - 2*x^3*Log[x] + x^2*Log[x]^2 + 65536*x^2*Log[x^2]^4 - 131072*x*Log[x]*Log[x^2

]^4 + 65536*Log[x]^2*Log[x^2]^4)), x] - 6*Defer[Int][(x^2*Log[x])/((x - Log[x])*(x^2 + 2*x^3 + x^4 - 2*x^2*Log

[x] - 2*x^3*Log[x] + x^2*Log[x]^2 + 65536*x^2*Log[x^2]^4 - 131072*x*Log[x]*Log[x^2]^4 + 65536*Log[x]^2*Log[x^2

]^4)), x] - 6*Defer[Int][(x^3*Log[x])/((x - Log[x])*(x^2 + 2*x^3 + x^4 - 2*x^2*Log[x] - 2*x^3*Log[x] + x^2*Log

[x]^2 + 65536*x^2*Log[x^2]^4 - 131072*x*Log[x]*Log[x^2]^4 + 65536*Log[x]^2*Log[x^2]^4)), x] + 4*Defer[Int][(x*

Log[x]^2)/((x - Log[x])*(x^2 + 2*x^3 + x^4 - 2*x^2*Log[x] - 2*x^3*Log[x] + x^2*Log[x]^2 + 65536*x^2*Log[x^2]^4

- 131072*x*Log[x]*Log[x^2]^4 + 65536*Log[x]^2*Log[x^2]^4)), x] + 6*Defer[Int][(x^2*Log[x]^2)/((x - Log[x])*(x

^2 + 2*x^3 + x^4 - 2*x^2*Log[x] - 2*x^3*Log[x] + x^2*Log[x]^2 + 65536*x^2*Log[x^2]^4 - 131072*x*Log[x]*Log[x^2

]^4 + 65536*Log[x]^2*Log[x^2]^4)), x] - 2*Defer[Int][(x*Log[x]^3)/((x - Log[x])*(x^2 + 2*x^3 + x^4 - 2*x^2*Log

[x] - 2*x^3*Log[x] + x^2*Log[x]^2 + 65536*x^2*Log[x^2]^4 - 131072*x*Log[x]*Log[x^2]^4 + 65536*Log[x]^2*Log[x^2

]^4)), x] + 524288*Defer[Int][(x^2*Log[x^2]^3)/((x - Log[x])*(x^2 + 2*x^3 + x^4 - 2*x^2*Log[x] - 2*x^3*Log[x]

+ x^2*Log[x]^2 + 65536*x^2*Log[x^2]^4 - 131072*x*Log[x]*Log[x^2]^4 + 65536*Log[x]^2*Log[x^2]^4)), x] - 1572864

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

2 + 65536*x^2*Log[x^2]^4 - 131072*x*Log[x]*Log[x^2]^4 + 65536*Log[x]^2*Log[x^2]^4)), x] + 1572864*Defer[Int][(

Log[x]^2*Log[x^2]^3)/((x - Log[x])*(x^2 + 2*x^3 + x^4 - 2*x^2*Log[x] - 2*x^3*Log[x] + x^2*Log[x]^2 + 65536*x^2

*Log[x^2]^4 - 131072*x*Log[x]*Log[x^2]^4 + 65536*Log[x]^2*Log[x^2]^4)), x] - 524288*Defer[Int][(Log[x]^3*Log[x

^2]^3)/(x*(x - Log[x])*(x^2 + 2*x^3 + x^4 - 2*x^2*Log[x] - 2*x^3*Log[x] + x^2*Log[x]^2 + 65536*x^2*Log[x^2]^4

- 131072*x*Log[x]*Log[x^2]^4 + 65536*Log[x]^2*Log[x^2]^4)), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(244\) vs. \(2(24)=48\).
time = 36.59, size = 244, normalized size = 10.17 \begin {gather*} -2 \log (x-\log (x))+\log \left (x^2+2 x^3+x^4+1048576 \log ^6(x)+65536 x^2 \left (-2 \log (x)+\log \left (x^2\right )\right )^4+\log ^5(x) \left (-2097152 x+2097152 \left (-2 \log (x)+\log \left (x^2\right )\right )\right )+\log ^4(x) \left (1048576 x^2-4194304 x \left (-2 \log (x)+\log \left (x^2\right )\right )+1572864 \left (-2 \log (x)+\log \left (x^2\right )\right )^2\right )+\log ^3(x) \left (2097152 x^2 \left (-2 \log (x)+\log \left (x^2\right )\right )-3145728 x \left (-2 \log (x)+\log \left (x^2\right )\right )^2+524288 \left (-2 \log (x)+\log \left (x^2\right )\right )^3\right )+\log ^2(x) \left (x^2+1572864 x^2 \left (-2 \log (x)+\log \left (x^2\right )\right )^2-1048576 x \left (-2 \log (x)+\log \left (x^2\right )\right )^3+65536 \left (-2 \log (x)+\log \left (x^2\right )\right )^4\right )+\log (x) \left (-2 x^2-2 x^3+524288 x^2 \left (-2 \log (x)+\log \left (x^2\right )\right )^3-131072 x \left (-2 \log (x)+\log \left (x^2\right )\right )^4\right )\right ) \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Integrate[(-2*x^2 - 2*x^3 - 2*x^4 - 2*x^5 + (4*x^2 + 6*x^3 + 6*x^4)*Log[x] + (-4*x^2 - 6*x^3)*Log[x]^2 + 2*x^2

*Log[x]^3 + (-524288*x^3 + 1572864*x^2*Log[x] - 1572864*x*Log[x]^2 + 524288*Log[x]^3)*Log[x^2]^3)/(-x^4 - 2*x^

5 - x^6 + (x^3 + 4*x^4 + 3*x^5)*Log[x] + (-2*x^3 - 3*x^4)*Log[x]^2 + x^3*Log[x]^3 + (-65536*x^4 + 196608*x^3*L

og[x] - 196608*x^2*Log[x]^2 + 65536*x*Log[x]^3)*Log[x^2]^4),x]

[Out]

-2*Log[x - Log[x]] + Log[x^2 + 2*x^3 + x^4 + 1048576*Log[x]^6 + 65536*x^2*(-2*Log[x] + Log[x^2])^4 + Log[x]^5*

(-2097152*x + 2097152*(-2*Log[x] + Log[x^2])) + Log[x]^4*(1048576*x^2 - 4194304*x*(-2*Log[x] + Log[x^2]) + 157

2864*(-2*Log[x] + Log[x^2])^2) + Log[x]^3*(2097152*x^2*(-2*Log[x] + Log[x^2]) - 3145728*x*(-2*Log[x] + Log[x^2

])^2 + 524288*(-2*Log[x] + Log[x^2])^3) + Log[x]^2*(x^2 + 1572864*x^2*(-2*Log[x] + Log[x^2])^2 - 1048576*x*(-2

*Log[x] + Log[x^2])^3 + 65536*(-2*Log[x] + Log[x^2])^4) + Log[x]*(-2*x^2 - 2*x^3 + 524288*x^2*(-2*Log[x] + Log

[x^2])^3 - 131072*x*(-2*Log[x] + Log[x^2])^4)]

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Maple [C] Result contains higher order function than in optimal. Order 9 vs. order 3.
time = 40.35, size = 939, normalized size = 39.12


method	result	size

default	\(\text {Expression too large to display}\)	\(939\)
risch	\(\text {Expression too large to display}\)	\(1587\)

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(((524288*ln(x)^3-1572864*x*ln(x)^2+1572864*x^2*ln(x)-524288*x^3)*ln(x^2)^3+2*x^2*ln(x)^3+(-6*x^3-4*x^2)*ln

(x)^2+(6*x^4+6*x^3+4*x^2)*ln(x)-2*x^5-2*x^4-2*x^3-2*x^2)/((65536*x*ln(x)^3-196608*x^2*ln(x)^2+196608*x^3*ln(x)

-65536*x^4)*ln(x^2)^4+x^3*ln(x)^3+(-3*x^4-2*x^3)*ln(x)^2+(3*x^5+4*x^4+x^3)*ln(x)-x^6-2*x^5-x^4),x,method=_RETU

RNVERBOSE)

[Out]

ln(1/1048576*(x^2*ln(x)^2-2*x^3*ln(x)-2*x^2*ln(x)+x^4+2*x^3+x^2+4096*Pi^4*ln(x)^2*csgn(I*x^2)^12+4096*Pi^4*x^2

*csgn(I*x^2)^12+4096*Pi^4*ln(x)^2*csgn(I*x)^8*csgn(I*x^2)^4-32768*Pi^4*ln(x)^2*csgn(I*x)^7*csgn(I*x^2)^5+11468

8*Pi^4*ln(x)^2*csgn(I*x)^6*csgn(I*x^2)^6-229376*Pi^4*ln(x)^2*csgn(I*x)^5*csgn(I*x^2)^7+286720*Pi^4*ln(x)^2*csg

n(I*x)^4*csgn(I*x^2)^8-229376*Pi^4*ln(x)^2*csgn(I*x)^3*csgn(I*x^2)^9+114688*Pi^4*ln(x)^2*csgn(I*x)^2*csgn(I*x^

2)^10-32768*Pi^4*ln(x)^2*csgn(I*x)*csgn(I*x^2)^11-8192*ln(x)*Pi^4*csgn(I*x)^8*csgn(I*x^2)^4*x+65536*ln(x)*Pi^4

*csgn(I*x)^7*csgn(I*x^2)^5*x-229376*ln(x)*Pi^4*csgn(I*x)^6*csgn(I*x^2)^6*x+458752*ln(x)*Pi^4*csgn(I*x)^5*csgn(

I*x^2)^7*x-573440*ln(x)*Pi^4*csgn(I*x)^4*csgn(I*x^2)^8*x+458752*ln(x)*Pi^4*csgn(I*x)^3*csgn(I*x^2)^9*x-229376*

ln(x)*Pi^4*csgn(I*x)^2*csgn(I*x^2)^10*x+65536*ln(x)*Pi^4*csgn(I*x)*csgn(I*x^2)^11*x+4096*Pi^4*x^2*csgn(I*x)^8*

csgn(I*x^2)^4-32768*Pi^4*x^2*csgn(I*x)^7*csgn(I*x^2)^5+114688*Pi^4*x^2*csgn(I*x)^6*csgn(I*x^2)^6-229376*Pi^4*x

^2*csgn(I*x)^5*csgn(I*x^2)^7+286720*Pi^4*x^2*csgn(I*x)^4*csgn(I*x^2)^8-229376*Pi^4*x^2*csgn(I*x)^3*csgn(I*x^2)

^9+114688*Pi^4*x^2*csgn(I*x)^2*csgn(I*x^2)^10-32768*Pi^4*x^2*csgn(I*x)*csgn(I*x^2)^11-8192*ln(x)*Pi^4*csgn(I*x

^2)^12*x)/(ln(x)^2-2*x*ln(x)+x^2)+1/16*I*(csgn(I*x)^6-6*csgn(I*x)^5*csgn(I*x^2)+15*csgn(I*x)^4*csgn(I*x^2)^2-2

0*csgn(I*x)^3*csgn(I*x^2)^3+15*csgn(I*x)^2*csgn(I*x^2)^4-6*csgn(I*x)*csgn(I*x^2)^5+csgn(I*x^2)^6)*Pi^3*csgn(I*

x^2)^3*ln(x)-3/8*(csgn(I*x)^4-4*csgn(I*x)^3*csgn(I*x^2)+6*csgn(I*x)^2*csgn(I*x^2)^2-4*csgn(I*x)*csgn(I*x^2)^3+

csgn(I*x^2)^4)*Pi^2*csgn(I*x^2)^2*ln(x)^2+ln(x)^4-I*Pi*csgn(I*x^2)*(csgn(I*x)^2-2*csgn(I*x^2)*csgn(I*x)+csgn(I

*x^2)^2)*ln(x)^3)

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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 66 vs. \(2 (24) = 48\).
time = 0.31, size = 66, normalized size = 2.75 \begin {gather*} \log \left (x^{2} \log \left (x\right )^{4} - 2 \, x \log \left (x\right )^{5} + \log \left (x\right )^{6} + \frac {1}{1048576} \, x^{4} + \frac {1}{1048576} \, x^{2} \log \left (x\right )^{2} + \frac {1}{524288} \, x^{3} + \frac {1}{1048576} \, x^{2} - \frac {1}{524288} \, {\left (x^{3} + x^{2}\right )} \log \left (x\right )\right ) - 2 \, \log \left (-x + \log \left (x\right )\right ) \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((524288*log(x)^3-1572864*x*log(x)^2+1572864*x^2*log(x)-524288*x^3)*log(x^2)^3+2*x^2*log(x)^3+(-6*x^

3-4*x^2)*log(x)^2+(6*x^4+6*x^3+4*x^2)*log(x)-2*x^5-2*x^4-2*x^3-2*x^2)/((65536*x*log(x)^3-196608*x^2*log(x)^2+1

96608*x^3*log(x)-65536*x^4)*log(x^2)^4+x^3*log(x)^3+(-3*x^4-2*x^3)*log(x)^2+(3*x^5+4*x^4+x^3)*log(x)-x^6-2*x^5

-x^4),x, algorithm="maxima")

[Out]

log(x^2*log(x)^4 - 2*x*log(x)^5 + log(x)^6 + 1/1048576*x^4 + 1/1048576*x^2*log(x)^2 + 1/524288*x^3 + 1/1048576

*x^2 - 1/524288*(x^3 + x^2)*log(x)) - 2*log(-x + log(x))

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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 64 vs. \(2 (24) = 48\).
time = 0.42, size = 64, normalized size = 2.67 \begin {gather*} \log \left (1048576 \, x^{2} \log \left (x\right )^{4} - 2097152 \, x \log \left (x\right )^{5} + 1048576 \, \log \left (x\right )^{6} + x^{4} + x^{2} \log \left (x\right )^{2} + 2 \, x^{3} + x^{2} - 2 \, {\left (x^{3} + x^{2}\right )} \log \left (x\right )\right ) - 2 \, \log \left (-x + \log \left (x\right )\right ) \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((524288*log(x)^3-1572864*x*log(x)^2+1572864*x^2*log(x)-524288*x^3)*log(x^2)^3+2*x^2*log(x)^3+(-6*x^

3-4*x^2)*log(x)^2+(6*x^4+6*x^3+4*x^2)*log(x)-2*x^5-2*x^4-2*x^3-2*x^2)/((65536*x*log(x)^3-196608*x^2*log(x)^2+1

96608*x^3*log(x)-65536*x^4)*log(x^2)^4+x^3*log(x)^3+(-3*x^4-2*x^3)*log(x)^2+(3*x^5+4*x^4+x^3)*log(x)-x^6-2*x^5

-x^4),x, algorithm="fricas")

[Out]

log(1048576*x^2*log(x)^4 - 2097152*x*log(x)^5 + 1048576*log(x)^6 + x^4 + x^2*log(x)^2 + 2*x^3 + x^2 - 2*(x^3 +

x^2)*log(x)) - 2*log(-x + log(x))

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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 71 vs. \(2 (19) = 38\).
time = 0.98, size = 71, normalized size = 2.96 \begin {gather*} - 2 \log {\left (- x + \log {\left (x \right )} \right )} + \log {\left (\frac {x^{4}}{1048576} + \frac {x^{3}}{524288} + x^{2} \log {\left (x \right )}^{4} + \frac {x^{2} \log {\left (x \right )}^{2}}{1048576} + \frac {x^{2}}{1048576} - 2 x \log {\left (x \right )}^{5} + \left (- \frac {x^{3}}{524288} - \frac {x^{2}}{524288}\right ) \log {\left (x \right )} + \log {\left (x \right )}^{6} \right )} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((524288*ln(x)**3-1572864*x*ln(x)**2+1572864*x**2*ln(x)-524288*x**3)*ln(x**2)**3+2*x**2*ln(x)**3+(-6

*x**3-4*x**2)*ln(x)**2+(6*x**4+6*x**3+4*x**2)*ln(x)-2*x**5-2*x**4-2*x**3-2*x**2)/((65536*x*ln(x)**3-196608*x**

2*ln(x)**2+196608*x**3*ln(x)-65536*x**4)*ln(x**2)**4+x**3*ln(x)**3+(-3*x**4-2*x**3)*ln(x)**2+(3*x**5+4*x**4+x*

*3)*ln(x)-x**6-2*x**5-x**4),x)

[Out]

-2*log(-x + log(x)) + log(x**4/1048576 + x**3/524288 + x**2*log(x)**4 + x**2*log(x)**2/1048576 + x**2/1048576

- 2*x*log(x)**5 + (-x**3/524288 - x**2/524288)*log(x) + log(x)**6)

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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 67 vs. \(2 (24) = 48\).
time = 1.23, size = 67, normalized size = 2.79 \begin {gather*} \log \left (1048576 \, x^{2} \log \left (x\right )^{4} - 2097152 \, x \log \left (x\right )^{5} + 1048576 \, \log \left (x\right )^{6} + x^{4} - 2 \, x^{3} \log \left (x\right ) + x^{2} \log \left (x\right )^{2} + 2 \, x^{3} - 2 \, x^{2} \log \left (x\right ) + x^{2}\right ) - 2 \, \log \left (x - \log \left (x\right )\right ) \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((524288*log(x)^3-1572864*x*log(x)^2+1572864*x^2*log(x)-524288*x^3)*log(x^2)^3+2*x^2*log(x)^3+(-6*x^

3-4*x^2)*log(x)^2+(6*x^4+6*x^3+4*x^2)*log(x)-2*x^5-2*x^4-2*x^3-2*x^2)/((65536*x*log(x)^3-196608*x^2*log(x)^2+1

96608*x^3*log(x)-65536*x^4)*log(x^2)^4+x^3*log(x)^3+(-3*x^4-2*x^3)*log(x)^2+(3*x^5+4*x^4+x^3)*log(x)-x^6-2*x^5

-x^4),x, algorithm="giac")

[Out]

log(1048576*x^2*log(x)^4 - 2097152*x*log(x)^5 + 1048576*log(x)^6 + x^4 - 2*x^3*log(x) + x^2*log(x)^2 + 2*x^3 -

2*x^2*log(x) + x^2) - 2*log(x - log(x))

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Mupad [F]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {{\ln \left (x\right )}^2\,\left (6\,x^3+4\,x^2\right )-\ln \left (x\right )\,\left (6\,x^4+6\,x^3+4\,x^2\right )+{\ln \left (x^2\right )}^3\,\left (524288\,x^3-1572864\,x^2\,\ln \left (x\right )+1572864\,x\,{\ln \left (x\right )}^2-524288\,{\ln \left (x\right )}^3\right )-2\,x^2\,{\ln \left (x\right )}^3+2\,x^2+2\,x^3+2\,x^4+2\,x^5}{{\ln \left (x\right )}^2\,\left (3\,x^4+2\,x^3\right )-{\ln \left (x^2\right )}^4\,\left (-65536\,x^4+196608\,x^3\,\ln \left (x\right )-196608\,x^2\,{\ln \left (x\right )}^2+65536\,x\,{\ln \left (x\right )}^3\right )-x^3\,{\ln \left (x\right )}^3+x^4+2\,x^5+x^6-\ln \left (x\right )\,\left (3\,x^5+4\,x^4+x^3\right )} \,d x \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((log(x)^2*(4*x^2 + 6*x^3) - log(x)*(4*x^2 + 6*x^3 + 6*x^4) + log(x^2)^3*(1572864*x*log(x)^2 - 1572864*x^2*

log(x) - 524288*log(x)^3 + 524288*x^3) - 2*x^2*log(x)^3 + 2*x^2 + 2*x^3 + 2*x^4 + 2*x^5)/(log(x)^2*(2*x^3 + 3*

x^4) - log(x^2)^4*(65536*x*log(x)^3 + 196608*x^3*log(x) - 196608*x^2*log(x)^2 - 65536*x^4) - x^3*log(x)^3 + x^

4 + 2*x^5 + x^6 - log(x)*(x^3 + 4*x^4 + 3*x^5)),x)

[Out]

int((log(x)^2*(4*x^2 + 6*x^3) - log(x)*(4*x^2 + 6*x^3 + 6*x^4) + log(x^2)^3*(1572864*x*log(x)^2 - 1572864*x^2*

log(x) - 524288*log(x)^3 + 524288*x^3) - 2*x^2*log(x)^3 + 2*x^2 + 2*x^3 + 2*x^4 + 2*x^5)/(log(x)^2*(2*x^3 + 3*

x^4) - log(x^2)^4*(65536*x*log(x)^3 + 196608*x^3*log(x) - 196608*x^2*log(x)^2 - 65536*x^4) - x^3*log(x)^3 + x^

4 + 2*x^5 + x^6 - log(x)*(x^3 + 4*x^4 + 3*x^5)), x)

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