3.78.28 \(\int \frac {64 x^6-16 x^2 \log (5)+e^{e^3} (4+2 x+256 x^7+128 x^8+(-64 x^3-32 x^4) \log (5))+(4+2 x+256 x^7+128 x^8+(-64 x^3-32 x^4) \log (5)) \log (2+x)+(192 x^4-16 \log (5)+e^{e^3} (768 x^5+384 x^6+(-64 x-32 x^2) \log (5))+(768 x^5+384 x^6+(-64 x-32 x^2) \log (5)) \log (2+x)) \log (e^{e^3}+\log (2+x))+(192 x^2+e^{e^3} (768 x^3+384 x^4)+(768 x^3+384 x^4) \log (2+x)) \log ^2(e^{e^3}+\log (2+x))+(64+e^{e^3} (256 x+128 x^2)+(256 x+128 x^2) \log (2+x)) \log ^3(e^{e^3}+\log (2+x))}{e^{e^3} (2+x)+(2+x) \log (2+x)} \, dx\)

Optimal. Leaf size=28 \[ 2 x+\left (\log (5)-4 \left (x^2+\log \left (e^{e^3}+\log (2+x)\right )\right )^2\right )^2 \]

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Rubi [F]  time = 36.89, 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 {64 x^6-16 x^2 \log (5)+e^{e^3} \left (4+2 x+256 x^7+128 x^8+\left (-64 x^3-32 x^4\right ) \log (5)\right )+\left (4+2 x+256 x^7+128 x^8+\left (-64 x^3-32 x^4\right ) \log (5)\right ) \log (2+x)+\left (192 x^4-16 \log (5)+e^{e^3} \left (768 x^5+384 x^6+\left (-64 x-32 x^2\right ) \log (5)\right )+\left (768 x^5+384 x^6+\left (-64 x-32 x^2\right ) \log (5)\right ) \log (2+x)\right ) \log \left (e^{e^3}+\log (2+x)\right )+\left (192 x^2+e^{e^3} \left (768 x^3+384 x^4\right )+\left (768 x^3+384 x^4\right ) \log (2+x)\right ) \log ^2\left (e^{e^3}+\log (2+x)\right )+\left (64+e^{e^3} \left (256 x+128 x^2\right )+\left (256 x+128 x^2\right ) \log (2+x)\right ) \log ^3\left (e^{e^3}+\log (2+x)\right )}{e^{e^3} (2+x)+(2+x) \log (2+x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(64*x^6 - 16*x^2*Log[5] + E^E^3*(4 + 2*x + 256*x^7 + 128*x^8 + (-64*x^3 - 32*x^4)*Log[5]) + (4 + 2*x + 256
*x^7 + 128*x^8 + (-64*x^3 - 32*x^4)*Log[5])*Log[2 + x] + (192*x^4 - 16*Log[5] + E^E^3*(768*x^5 + 384*x^6 + (-6
4*x - 32*x^2)*Log[5]) + (768*x^5 + 384*x^6 + (-64*x - 32*x^2)*Log[5])*Log[2 + x])*Log[E^E^3 + Log[2 + x]] + (1
92*x^2 + E^E^3*(768*x^3 + 384*x^4) + (768*x^3 + 384*x^4)*Log[2 + x])*Log[E^E^3 + Log[2 + x]]^2 + (64 + E^E^3*(
256*x + 128*x^2) + (256*x + 128*x^2)*Log[2 + x])*Log[E^E^3 + Log[2 + x]]^3)/(E^E^3*(2 + x) + (2 + x)*Log[2 + x
]),x]

[Out]

2*x + 16*x^8 - (8192*ExpIntegralEi[E^E^3 + Log[2 + x]])/E^E^E^3 + (14336*ExpIntegralEi[2*(E^E^3 + Log[2 + x])]
)/E^(2*E^E^3) - (10240*ExpIntegralEi[3*(E^E^3 + Log[2 + x])])/E^(3*E^E^3) + (3840*ExpIntegralEi[4*(E^E^3 + Log
[2 + x])])/E^(4*E^E^3) - (768*ExpIntegralEi[5*(E^E^3 + Log[2 + x])])/E^(5*E^E^3) + (64*ExpIntegralEi[6*(E^E^3
+ Log[2 + x])])/E^(6*E^E^3) - (64*ExpIntegralEi[E^E^3 + Log[2 + x]]*(64 - Log[5]))/E^E^E^3 + (16*ExpIntegralEi
[2*(E^E^3 + Log[2 + x])]*(64 - Log[5]))/E^(2*E^E^3) - 8*x^4*Log[5] + 64*(64 - Log[5])*Log[E^E^3 + Log[2 + x]]
+ 8*(192 - Log[5])*Log[E^E^3 + Log[2 + x]]^2 + 256*Log[E^E^3 + Log[2 + x]]^3 + 16*Log[E^E^3 + Log[2 + x]]^4 +
768*Defer[Int][(x*Log[E^E^3 + Log[2 + x]])/(E^E^3 + Log[2 + x]), x] - 6144*E^E^3*Defer[Int][(x*Log[E^E^3 + Log
[2 + x]])/(E^E^3 + Log[2 + x]), x] + 32*E^E^3*(192 - Log[5])*Defer[Int][(x*Log[E^E^3 + Log[2 + x]])/(E^E^3 + L
og[2 + x]), x] - 384*Defer[Int][(x^2*Log[E^E^3 + Log[2 + x]])/(E^E^3 + Log[2 + x]), x] + 192*Defer[Int][(x^3*L
og[E^E^3 + Log[2 + x]])/(E^E^3 + Log[2 + x]), x] + 384*E^E^3*Defer[Int][(x^5*Log[E^E^3 + Log[2 + x]])/(E^E^3 +
Log[2 + x]), x] - 6144*Defer[Int][(x*Log[2 + x]*Log[E^E^3 + Log[2 + x]])/(E^E^3 + Log[2 + x]), x] + 32*(192 -
Log[5])*Defer[Int][(x*Log[2 + x]*Log[E^E^3 + Log[2 + x]])/(E^E^3 + Log[2 + x]), x] + 384*Defer[Int][(x^5*Log[
2 + x]*Log[E^E^3 + Log[2 + x]])/(E^E^3 + Log[2 + x]), x] + 192*Defer[Int][(x*Log[E^E^3 + Log[2 + x]]^2)/(E^E^3
+ Log[2 + x]), x] + 384*E^E^3*Defer[Int][(x^3*Log[E^E^3 + Log[2 + x]]^2)/(E^E^3 + Log[2 + x]), x] + 384*Defer
[Int][(x^3*Log[2 + x]*Log[E^E^3 + Log[2 + x]]^2)/(E^E^3 + Log[2 + x]), x] + 128*E^E^3*Defer[Int][(x*Log[E^E^3
+ Log[2 + x]]^3)/(E^E^3 + Log[2 + x]), x] + 128*Defer[Int][(x*Log[2 + x]*Log[E^E^3 + Log[2 + x]]^3)/(E^E^3 + L
og[2 + x]), x] - 1536*Defer[Subst][Defer[Int][Log[E^E^3 + Log[x]]/(E^E^3 + Log[x]), x], x, 2 + x] - 384*Defer[
Subst][Defer[Int][Log[E^E^3 + Log[x]]^2/(E^E^3 + Log[x]), x], x, 2 + x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {64 x^6-16 x^2 \log (5)+e^{e^3} \left (4+2 x+256 x^7+128 x^8+\left (-64 x^3-32 x^4\right ) \log (5)\right )+\left (4+2 x+256 x^7+128 x^8+\left (-64 x^3-32 x^4\right ) \log (5)\right ) \log (2+x)+\left (192 x^4-16 \log (5)+e^{e^3} \left (768 x^5+384 x^6+\left (-64 x-32 x^2\right ) \log (5)\right )+\left (768 x^5+384 x^6+\left (-64 x-32 x^2\right ) \log (5)\right ) \log (2+x)\right ) \log \left (e^{e^3}+\log (2+x)\right )+\left (192 x^2+e^{e^3} \left (768 x^3+384 x^4\right )+\left (768 x^3+384 x^4\right ) \log (2+x)\right ) \log ^2\left (e^{e^3}+\log (2+x)\right )+\left (64+e^{e^3} \left (256 x+128 x^2\right )+\left (256 x+128 x^2\right ) \log (2+x)\right ) \log ^3\left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )} \, dx\\ &=\int \left (\frac {2 \left (2 e^{e^3}+e^{e^3} x+32 x^6+128 e^{e^3} x^7+64 e^{e^3} x^8-8 x^2 \log (5)-32 e^{e^3} x^3 \log (5)-16 e^{e^3} x^4 \log (5)+2 \log (2+x)+x \log (2+x)+128 x^7 \log (2+x)+64 x^8 \log (2+x)-32 x^3 \log (5) \log (2+x)-16 x^4 \log (5) \log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )}+\frac {16 \left (12 x^4-\log (5)\right ) \left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log \left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )}+\frac {192 x^2 \left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log ^2\left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )}+\frac {64 \left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log ^3\left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )}\right ) \, dx\\ &=2 \int \frac {2 e^{e^3}+e^{e^3} x+32 x^6+128 e^{e^3} x^7+64 e^{e^3} x^8-8 x^2 \log (5)-32 e^{e^3} x^3 \log (5)-16 e^{e^3} x^4 \log (5)+2 \log (2+x)+x \log (2+x)+128 x^7 \log (2+x)+64 x^8 \log (2+x)-32 x^3 \log (5) \log (2+x)-16 x^4 \log (5) \log (2+x)}{(2+x) \left (e^{e^3}+\log (2+x)\right )} \, dx+16 \int \frac {\left (12 x^4-\log (5)\right ) \left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log \left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )} \, dx+64 \int \frac {\left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log ^3\left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )} \, dx+192 \int \frac {x^2 \left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log ^2\left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )} \, dx\\ &=2 \int \frac {32 x^6-8 x^2 \log (5)+e^{e^3} (2+x) \left (1+64 x^7-16 x^3 \log (5)\right )+(2+x) \left (1+64 x^7-16 x^3 \log (5)\right ) \log (2+x)}{(2+x) \left (e^{e^3}+\log (2+x)\right )} \, dx+16 \int \frac {\left (12 x^4-\log (5)\right ) \left (1+2 e^{e^3} x (2+x)+2 x (2+x) \log (2+x)\right ) \log \left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )} \, dx+64 \int \frac {\left (1+2 e^{e^3} x (2+x)+2 x (2+x) \log (2+x)\right ) \log ^3\left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )} \, dx+192 \int \frac {x^2 \left (1+2 e^{e^3} x (2+x)+2 x (2+x) \log (2+x)\right ) \log ^2\left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )} \, dx\\ &=2 \int \left (1+64 x^7-16 x^3 \log (5)+\frac {8 x^2 \left (4 x^4-\log (5)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )}\right ) \, dx+16 \int \left (-\frac {96 \left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log \left (e^{e^3}+\log (2+x)\right )}{e^{e^3}+\log (2+x)}+\frac {48 x \left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log \left (e^{e^3}+\log (2+x)\right )}{e^{e^3}+\log (2+x)}-\frac {24 x^2 \left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log \left (e^{e^3}+\log (2+x)\right )}{e^{e^3}+\log (2+x)}+\frac {12 x^3 \left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log \left (e^{e^3}+\log (2+x)\right )}{e^{e^3}+\log (2+x)}-\frac {(-192+\log (5)) \left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log \left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )}\right ) \, dx+64 \int \left (\frac {\log ^3\left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )}+\frac {4 e^{e^3} x \log ^3\left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )}+\frac {2 e^{e^3} x^2 \log ^3\left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )}+\frac {4 x \log (2+x) \log ^3\left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )}+\frac {2 x^2 \log (2+x) \log ^3\left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )}\right ) \, dx+192 \int \left (-\frac {2 \left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log ^2\left (e^{e^3}+\log (2+x)\right )}{e^{e^3}+\log (2+x)}+\frac {x \left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log ^2\left (e^{e^3}+\log (2+x)\right )}{e^{e^3}+\log (2+x)}+\frac {4 \left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log ^2\left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )}\right ) \, dx\\ &=2 x+16 x^8-8 x^4 \log (5)+16 \int \frac {x^2 \left (4 x^4-\log (5)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )} \, dx+64 \int \frac {\log ^3\left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )} \, dx+128 \int \frac {x^2 \log (2+x) \log ^3\left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )} \, dx+192 \int \frac {x^3 \left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log \left (e^{e^3}+\log (2+x)\right )}{e^{e^3}+\log (2+x)} \, dx+192 \int \frac {x \left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log ^2\left (e^{e^3}+\log (2+x)\right )}{e^{e^3}+\log (2+x)} \, dx+256 \int \frac {x \log (2+x) \log ^3\left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )} \, dx-384 \int \frac {x^2 \left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log \left (e^{e^3}+\log (2+x)\right )}{e^{e^3}+\log (2+x)} \, dx-384 \int \frac {\left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log ^2\left (e^{e^3}+\log (2+x)\right )}{e^{e^3}+\log (2+x)} \, dx+768 \int \frac {x \left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log \left (e^{e^3}+\log (2+x)\right )}{e^{e^3}+\log (2+x)} \, dx+768 \int \frac {\left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log ^2\left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )} \, dx-1536 \int \frac {\left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log \left (e^{e^3}+\log (2+x)\right )}{e^{e^3}+\log (2+x)} \, dx+\left (128 e^{e^3}\right ) \int \frac {x^2 \log ^3\left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )} \, dx+\left (256 e^{e^3}\right ) \int \frac {x \log ^3\left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )} \, dx+(16 (192-\log (5))) \int \frac {\left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log \left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.25, size = 100, normalized size = 3.57 \begin {gather*} 2 \left (x+8 x^8-4 x^4 \log (5)+8 x^2 \left (4 x^4-\log (5)\right ) \log \left (e^{e^3}+\log (2+x)\right )+4 \left (12 x^4-\log (5)\right ) \log ^2\left (e^{e^3}+\log (2+x)\right )+32 x^2 \log ^3\left (e^{e^3}+\log (2+x)\right )+8 \log ^4\left (e^{e^3}+\log (2+x)\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(64*x^6 - 16*x^2*Log[5] + E^E^3*(4 + 2*x + 256*x^7 + 128*x^8 + (-64*x^3 - 32*x^4)*Log[5]) + (4 + 2*x
+ 256*x^7 + 128*x^8 + (-64*x^3 - 32*x^4)*Log[5])*Log[2 + x] + (192*x^4 - 16*Log[5] + E^E^3*(768*x^5 + 384*x^6
+ (-64*x - 32*x^2)*Log[5]) + (768*x^5 + 384*x^6 + (-64*x - 32*x^2)*Log[5])*Log[2 + x])*Log[E^E^3 + Log[2 + x]
] + (192*x^2 + E^E^3*(768*x^3 + 384*x^4) + (768*x^3 + 384*x^4)*Log[2 + x])*Log[E^E^3 + Log[2 + x]]^2 + (64 + E
^E^3*(256*x + 128*x^2) + (256*x + 128*x^2)*Log[2 + x])*Log[E^E^3 + Log[2 + x]]^3)/(E^E^3*(2 + x) + (2 + x)*Log
[2 + x]),x]

[Out]

2*(x + 8*x^8 - 4*x^4*Log[5] + 8*x^2*(4*x^4 - Log[5])*Log[E^E^3 + Log[2 + x]] + 4*(12*x^4 - Log[5])*Log[E^E^3 +
Log[2 + x]]^2 + 32*x^2*Log[E^E^3 + Log[2 + x]]^3 + 8*Log[E^E^3 + Log[2 + x]]^4)

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fricas [B]  time = 2.04, size = 92, normalized size = 3.29 \begin {gather*} 16 \, x^{8} - 8 \, x^{4} \log \relax (5) + 64 \, x^{2} \log \left (e^{\left (e^{3}\right )} + \log \left (x + 2\right )\right )^{3} + 16 \, \log \left (e^{\left (e^{3}\right )} + \log \left (x + 2\right )\right )^{4} + 8 \, {\left (12 \, x^{4} - \log \relax (5)\right )} \log \left (e^{\left (e^{3}\right )} + \log \left (x + 2\right )\right )^{2} + 16 \, {\left (4 \, x^{6} - x^{2} \log \relax (5)\right )} \log \left (e^{\left (e^{3}\right )} + \log \left (x + 2\right )\right ) + 2 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((128*x^2+256*x)*log(2+x)+(128*x^2+256*x)*exp(exp(3))+64)*log(log(2+x)+exp(exp(3)))^3+((384*x^4+768
*x^3)*log(2+x)+(384*x^4+768*x^3)*exp(exp(3))+192*x^2)*log(log(2+x)+exp(exp(3)))^2+(((-32*x^2-64*x)*log(5)+384*
x^6+768*x^5)*log(2+x)+((-32*x^2-64*x)*log(5)+384*x^6+768*x^5)*exp(exp(3))-16*log(5)+192*x^4)*log(log(2+x)+exp(
exp(3)))+((-32*x^4-64*x^3)*log(5)+128*x^8+256*x^7+2*x+4)*log(2+x)+((-32*x^4-64*x^3)*log(5)+128*x^8+256*x^7+2*x
+4)*exp(exp(3))-16*x^2*log(5)+64*x^6)/((2+x)*log(2+x)+(2+x)*exp(exp(3))),x, algorithm="fricas")

[Out]

16*x^8 - 8*x^4*log(5) + 64*x^2*log(e^(e^3) + log(x + 2))^3 + 16*log(e^(e^3) + log(x + 2))^4 + 8*(12*x^4 - log(
5))*log(e^(e^3) + log(x + 2))^2 + 16*(4*x^6 - x^2*log(5))*log(e^(e^3) + log(x + 2)) + 2*x

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giac [B]  time = 0.44, size = 106, normalized size = 3.79 \begin {gather*} 16 \, x^{8} + 64 \, x^{6} \log \left (e^{\left (e^{3}\right )} + \log \left (x + 2\right )\right ) + 96 \, x^{4} \log \left (e^{\left (e^{3}\right )} + \log \left (x + 2\right )\right )^{2} - 8 \, x^{4} \log \relax (5) + 64 \, x^{2} \log \left (e^{\left (e^{3}\right )} + \log \left (x + 2\right )\right )^{3} - 16 \, x^{2} \log \relax (5) \log \left (e^{\left (e^{3}\right )} + \log \left (x + 2\right )\right ) + 16 \, \log \left (e^{\left (e^{3}\right )} + \log \left (x + 2\right )\right )^{4} - 8 \, \log \relax (5) \log \left (e^{\left (e^{3}\right )} + \log \left (x + 2\right )\right )^{2} + 2 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((128*x^2+256*x)*log(2+x)+(128*x^2+256*x)*exp(exp(3))+64)*log(log(2+x)+exp(exp(3)))^3+((384*x^4+768
*x^3)*log(2+x)+(384*x^4+768*x^3)*exp(exp(3))+192*x^2)*log(log(2+x)+exp(exp(3)))^2+(((-32*x^2-64*x)*log(5)+384*
x^6+768*x^5)*log(2+x)+((-32*x^2-64*x)*log(5)+384*x^6+768*x^5)*exp(exp(3))-16*log(5)+192*x^4)*log(log(2+x)+exp(
exp(3)))+((-32*x^4-64*x^3)*log(5)+128*x^8+256*x^7+2*x+4)*log(2+x)+((-32*x^4-64*x^3)*log(5)+128*x^8+256*x^7+2*x
+4)*exp(exp(3))-16*x^2*log(5)+64*x^6)/((2+x)*log(2+x)+(2+x)*exp(exp(3))),x, algorithm="giac")

[Out]

16*x^8 + 64*x^6*log(e^(e^3) + log(x + 2)) + 96*x^4*log(e^(e^3) + log(x + 2))^2 - 8*x^4*log(5) + 64*x^2*log(e^(
e^3) + log(x + 2))^3 - 16*x^2*log(5)*log(e^(e^3) + log(x + 2)) + 16*log(e^(e^3) + log(x + 2))^4 - 8*log(5)*log
(e^(e^3) + log(x + 2))^2 + 2*x

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maple [B]  time = 0.11, size = 91, normalized size = 3.25

method	result	size
risch	\(16 \ln \left (\ln \left (2+x \right )+{\mathrm e}^{{\mathrm e}^{3}}\right )^{4}+64 x^{2} \ln \left (\ln \left (2+x \right )+{\mathrm e}^{{\mathrm e}^{3}}\right )^{3}+\left (96 x^{4}-8 \ln \relax (5)\right ) \ln \left (\ln \left (2+x \right )+{\mathrm e}^{{\mathrm e}^{3}}\right )^{2}+\left (64 x^{6}-16 x^{2} \ln \relax (5)\right ) \ln \left (\ln \left (2+x \right )+{\mathrm e}^{{\mathrm e}^{3}}\right )+16 x^{8}-8 x^{4} \ln \relax (5)+2 x\)	\(91\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((128*x^2+256*x)*ln(2+x)+(128*x^2+256*x)*exp(exp(3))+64)*ln(ln(2+x)+exp(exp(3)))^3+((384*x^4+768*x^3)*ln(
2+x)+(384*x^4+768*x^3)*exp(exp(3))+192*x^2)*ln(ln(2+x)+exp(exp(3)))^2+(((-32*x^2-64*x)*ln(5)+384*x^6+768*x^5)*
ln(2+x)+((-32*x^2-64*x)*ln(5)+384*x^6+768*x^5)*exp(exp(3))-16*ln(5)+192*x^4)*ln(ln(2+x)+exp(exp(3)))+((-32*x^4
-64*x^3)*ln(5)+128*x^8+256*x^7+2*x+4)*ln(2+x)+((-32*x^4-64*x^3)*ln(5)+128*x^8+256*x^7+2*x+4)*exp(exp(3))-16*x^
2*ln(5)+64*x^6)/((2+x)*ln(2+x)+(2+x)*exp(exp(3))),x,method=_RETURNVERBOSE)

[Out]

16*ln(ln(2+x)+exp(exp(3)))^4+64*x^2*ln(ln(2+x)+exp(exp(3)))^3+(96*x^4-8*ln(5))*ln(ln(2+x)+exp(exp(3)))^2+(64*x
^6-16*x^2*ln(5))*ln(ln(2+x)+exp(exp(3)))+16*x^8-8*x^4*ln(5)+2*x

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maxima [B]  time = 0.51, size = 111, normalized size = 3.96 \begin {gather*} 16 \, x^{8} - 8 \, x^{4} \log \relax (5) + 64 \, x^{2} \log \left (e^{\left (e^{3}\right )} + \log \left (x + 2\right )\right )^{3} + 16 \, \log \left (e^{\left (e^{3}\right )} + \log \left (x + 2\right )\right )^{4} + 8 \, {\left (12 \, x^{4} - \log \relax (5)\right )} \log \left (e^{\left (e^{3}\right )} + \log \left (x + 2\right )\right )^{2} + 4 \, {\left (16 \, x^{6} - 4 \, x^{2} \log \relax (5) - e^{\left (e^{3}\right )}\right )} \log \left (e^{\left (e^{3}\right )} + \log \left (x + 2\right )\right ) + 4 \, e^{\left (e^{3}\right )} \log \left (e^{\left (e^{3}\right )} + \log \left (x + 2\right )\right ) + 2 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((128*x^2+256*x)*log(2+x)+(128*x^2+256*x)*exp(exp(3))+64)*log(log(2+x)+exp(exp(3)))^3+((384*x^4+768
*x^3)*log(2+x)+(384*x^4+768*x^3)*exp(exp(3))+192*x^2)*log(log(2+x)+exp(exp(3)))^2+(((-32*x^2-64*x)*log(5)+384*
x^6+768*x^5)*log(2+x)+((-32*x^2-64*x)*log(5)+384*x^6+768*x^5)*exp(exp(3))-16*log(5)+192*x^4)*log(log(2+x)+exp(
exp(3)))+((-32*x^4-64*x^3)*log(5)+128*x^8+256*x^7+2*x+4)*log(2+x)+((-32*x^4-64*x^3)*log(5)+128*x^8+256*x^7+2*x
+4)*exp(exp(3))-16*x^2*log(5)+64*x^6)/((2+x)*log(2+x)+(2+x)*exp(exp(3))),x, algorithm="maxima")

[Out]

16*x^8 - 8*x^4*log(5) + 64*x^2*log(e^(e^3) + log(x + 2))^3 + 16*log(e^(e^3) + log(x + 2))^4 + 8*(12*x^4 - log(
5))*log(e^(e^3) + log(x + 2))^2 + 4*(16*x^6 - 4*x^2*log(5) - e^(e^3))*log(e^(e^3) + log(x + 2)) + 4*e^(e^3)*lo
g(e^(e^3) + log(x + 2)) + 2*x

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mupad [B]  time = 7.36, size = 92, normalized size = 3.29 \begin {gather*} 2\,x+16\,{\ln \left (\ln \left (x+2\right )+{\mathrm {e}}^{{\mathrm {e}}^3}\right )}^4+64\,x^2\,{\ln \left (\ln \left (x+2\right )+{\mathrm {e}}^{{\mathrm {e}}^3}\right )}^3-\ln \left (\ln \left (x+2\right )+{\mathrm {e}}^{{\mathrm {e}}^3}\right )\,\left (16\,x^2\,\ln \relax (5)-64\,x^6\right )-8\,x^4\,\ln \relax (5)+16\,x^8-{\ln \left (\ln \left (x+2\right )+{\mathrm {e}}^{{\mathrm {e}}^3}\right )}^2\,\left (8\,\ln \relax (5)-96\,x^4\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(exp(3))*(2*x - log(5)*(64*x^3 + 32*x^4) + 256*x^7 + 128*x^8 + 4) + log(log(x + 2) + exp(exp(3)))*(exp
(exp(3))*(768*x^5 - log(5)*(64*x + 32*x^2) + 384*x^6) - 16*log(5) + log(x + 2)*(768*x^5 - log(5)*(64*x + 32*x^
2) + 384*x^6) + 192*x^4) + log(log(x + 2) + exp(exp(3)))^2*(log(x + 2)*(768*x^3 + 384*x^4) + 192*x^2 + exp(exp
(3))*(768*x^3 + 384*x^4)) + log(log(x + 2) + exp(exp(3)))^3*(log(x + 2)*(256*x + 128*x^2) + exp(exp(3))*(256*x
+ 128*x^2) + 64) - 16*x^2*log(5) + 64*x^6 + log(x + 2)*(2*x - log(5)*(64*x^3 + 32*x^4) + 256*x^7 + 128*x^8 +
4))/(exp(exp(3))*(x + 2) + log(x + 2)*(x + 2)),x)

[Out]

2*x + 16*log(log(x + 2) + exp(exp(3)))^4 + 64*x^2*log(log(x + 2) + exp(exp(3)))^3 - log(log(x + 2) + exp(exp(3
)))*(16*x^2*log(5) - 64*x^6) - 8*x^4*log(5) + 16*x^8 - log(log(x + 2) + exp(exp(3)))^2*(8*log(5) - 96*x^4)

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sympy [B]  time = 1.56, size = 99, normalized size = 3.54 \begin {gather*} 16 x^{8} - 8 x^{4} \log {\relax (5 )} + 64 x^{2} \log {\left (\log {\left (x + 2 \right )} + e^{e^{3}} \right )}^{3} + 2 x + \left (96 x^{4} - 8 \log {\relax (5 )}\right ) \log {\left (\log {\left (x + 2 \right )} + e^{e^{3}} \right )}^{2} + \left (64 x^{6} - 16 x^{2} \log {\relax (5 )}\right ) \log {\left (\log {\left (x + 2 \right )} + e^{e^{3}} \right )} + 16 \log {\left (\log {\left (x + 2 \right )} + e^{e^{3}} \right )}^{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((128*x**2+256*x)*ln(2+x)+(128*x**2+256*x)*exp(exp(3))+64)*ln(ln(2+x)+exp(exp(3)))**3+((384*x**4+76
8*x**3)*ln(2+x)+(384*x**4+768*x**3)*exp(exp(3))+192*x**2)*ln(ln(2+x)+exp(exp(3)))**2+(((-32*x**2-64*x)*ln(5)+3
84*x**6+768*x**5)*ln(2+x)+((-32*x**2-64*x)*ln(5)+384*x**6+768*x**5)*exp(exp(3))-16*ln(5)+192*x**4)*ln(ln(2+x)+
exp(exp(3)))+((-32*x**4-64*x**3)*ln(5)+128*x**8+256*x**7+2*x+4)*ln(2+x)+((-32*x**4-64*x**3)*ln(5)+128*x**8+256
*x**7+2*x+4)*exp(exp(3))-16*x**2*ln(5)+64*x**6)/((2+x)*ln(2+x)+(2+x)*exp(exp(3))),x)

[Out]

16*x**8 - 8*x**4*log(5) + 64*x**2*log(log(x + 2) + exp(exp(3)))**3 + 2*x + (96*x**4 - 8*log(5))*log(log(x + 2)
+ exp(exp(3)))**2 + (64*x**6 - 16*x**2*log(5))*log(log(x + 2) + exp(exp(3))) + 16*log(log(x + 2) + exp(exp(3)
))**4

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