3.56.20 \(\int \frac {2+e (432+14256 x+20880 x^2+230416 x^3+185600 x^4+1216512 x^5+458752 x^6+2097152 x^7)+e (-432-14112 x-13872 x^2-150528 x^3-61440 x^4-393216 x^5) \log (4)+e (144+4656 x+2304 x^2+24576 x^3) \log ^2(4)+e (-16-512 x) \log ^3(4)}{x+e (162+216 x+3564 x^2+3480 x^3+28802 x^4+18560 x^5+101376 x^6+32768 x^7+131072 x^8)+e (-216-216 x-3528 x^2-2312 x^3-18816 x^4-6144 x^5-32768 x^6) \log (4)+e (108+72 x+1164 x^2+384 x^3+3072 x^4) \log ^2(4)+e (-24-8 x-128 x^2) \log ^3(4)+2 e \log ^4(4)} \, dx\)

Optimal. Leaf size=22 \[ \log \left (\left (x+2 e \left (3+x+16 x^2-\log (4)\right )^4\right )^2\right ) \]

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Rubi [B]  time = 0.13, antiderivative size = 132, normalized size of antiderivative = 6.00, number of steps used = 1, number of rules used = 1, integrand size = 230, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.004, Rules used = {1587} \begin {gather*} 2 \log \left (-8 e \left (16 x^2+x+3\right ) \log ^3(4)+12 e \left (256 x^4+32 x^3+97 x^2+6 x+9\right ) \log ^2(4)-8 e \left (4096 x^6+768 x^5+2352 x^4+289 x^3+441 x^2+27 x+27\right ) \log (4)+2 e \left (65536 x^8+16384 x^7+50688 x^6+9280 x^5+14401 x^4+1740 x^3+1782 x^2+108 x+81\right )+x+2 e \log ^4(4)\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(2 + E*(432 + 14256*x + 20880*x^2 + 230416*x^3 + 185600*x^4 + 1216512*x^5 + 458752*x^6 + 2097152*x^7) + E*
(-432 - 14112*x - 13872*x^2 - 150528*x^3 - 61440*x^4 - 393216*x^5)*Log[4] + E*(144 + 4656*x + 2304*x^2 + 24576
*x^3)*Log[4]^2 + E*(-16 - 512*x)*Log[4]^3)/(x + E*(162 + 216*x + 3564*x^2 + 3480*x^3 + 28802*x^4 + 18560*x^5 +
101376*x^6 + 32768*x^7 + 131072*x^8) + E*(-216 - 216*x - 3528*x^2 - 2312*x^3 - 18816*x^4 - 6144*x^5 - 32768*x
^6)*Log[4] + E*(108 + 72*x + 1164*x^2 + 384*x^3 + 3072*x^4)*Log[4]^2 + E*(-24 - 8*x - 128*x^2)*Log[4]^3 + 2*E*
Log[4]^4),x]

[Out]

2*Log[x + 2*E*(81 + 108*x + 1782*x^2 + 1740*x^3 + 14401*x^4 + 9280*x^5 + 50688*x^6 + 16384*x^7 + 65536*x^8) -
8*E*(27 + 27*x + 441*x^2 + 289*x^3 + 2352*x^4 + 768*x^5 + 4096*x^6)*Log[4] + 12*E*(9 + 6*x + 97*x^2 + 32*x^3 +
256*x^4)*Log[4]^2 - 8*E*(3 + x + 16*x^2)*Log[4]^3 + 2*E*Log[4]^4]

Rule 1587

Int[(Pp_)/(Qq_), x_Symbol] :> With[{p = Expon[Pp, x], q = Expon[Qq, x]}, Simp[(Coeff[Pp, x, p]*Log[RemoveConte
nt[Qq, x]])/(q*Coeff[Qq, x, q]), x] /; EqQ[p, q - 1] && EqQ[Pp, Simplify[(Coeff[Pp, x, p]*D[Qq, x])/(q*Coeff[Q
q, x, q])]]] /; PolyQ[Pp, x] && PolyQ[Qq, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=2 \log \left (x+2 e \left (81+108 x+1782 x^2+1740 x^3+14401 x^4+9280 x^5+50688 x^6+16384 x^7+65536 x^8\right )-8 e \left (27+27 x+441 x^2+289 x^3+2352 x^4+768 x^5+4096 x^6\right ) \log (4)+12 e \left (9+6 x+97 x^2+32 x^3+256 x^4\right ) \log ^2(4)-8 e \left (3+x+16 x^2\right ) \log ^3(4)+2 e \log ^4(4)\right )\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.14, size = 182, normalized size = 8.27 \begin {gather*} 2 \log \left (162 e+x+216 e x+3564 e x^2+3480 e x^3+28802 e x^4+18560 e x^5+101376 e x^6+32768 e x^7+131072 e x^8-216 e \log (4)-216 e x \log (4)-3528 e x^2 \log (4)-2312 e x^3 \log (4)-18816 e x^4 \log (4)-6144 e x^5 \log (4)-32768 e x^6 \log (4)+108 e \log ^2(4)+72 e x \log ^2(4)+1164 e x^2 \log ^2(4)+384 e x^3 \log ^2(4)+3072 e x^4 \log ^2(4)-24 e \log ^3(4)-8 e x \log ^3(4)-128 e x^2 \log ^3(4)+2 e \log ^4(4)\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(2 + E*(432 + 14256*x + 20880*x^2 + 230416*x^3 + 185600*x^4 + 1216512*x^5 + 458752*x^6 + 2097152*x^7
) + E*(-432 - 14112*x - 13872*x^2 - 150528*x^3 - 61440*x^4 - 393216*x^5)*Log[4] + E*(144 + 4656*x + 2304*x^2 +
24576*x^3)*Log[4]^2 + E*(-16 - 512*x)*Log[4]^3)/(x + E*(162 + 216*x + 3564*x^2 + 3480*x^3 + 28802*x^4 + 18560
*x^5 + 101376*x^6 + 32768*x^7 + 131072*x^8) + E*(-216 - 216*x - 3528*x^2 - 2312*x^3 - 18816*x^4 - 6144*x^5 - 3
2768*x^6)*Log[4] + E*(108 + 72*x + 1164*x^2 + 384*x^3 + 3072*x^4)*Log[4]^2 + E*(-24 - 8*x - 128*x^2)*Log[4]^3
+ 2*E*Log[4]^4),x]

[Out]

2*Log[162*E + x + 216*E*x + 3564*E*x^2 + 3480*E*x^3 + 28802*E*x^4 + 18560*E*x^5 + 101376*E*x^6 + 32768*E*x^7 +
131072*E*x^8 - 216*E*Log[4] - 216*E*x*Log[4] - 3528*E*x^2*Log[4] - 2312*E*x^3*Log[4] - 18816*E*x^4*Log[4] - 6
144*E*x^5*Log[4] - 32768*E*x^6*Log[4] + 108*E*Log[4]^2 + 72*E*x*Log[4]^2 + 1164*E*x^2*Log[4]^2 + 384*E*x^3*Log
[4]^2 + 3072*E*x^4*Log[4]^2 - 24*E*Log[4]^3 - 8*E*x*Log[4]^3 - 128*E*x^2*Log[4]^3 + 2*E*Log[4]^4]

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fricas [B]  time = 1.08, size = 137, normalized size = 6.23 \begin {gather*} 2 \, \log \left (-64 \, {\left (16 \, x^{2} + x + 3\right )} e \log \relax (2)^{3} + 32 \, e \log \relax (2)^{4} + 48 \, {\left (256 \, x^{4} + 32 \, x^{3} + 97 \, x^{2} + 6 \, x + 9\right )} e \log \relax (2)^{2} - 16 \, {\left (4096 \, x^{6} + 768 \, x^{5} + 2352 \, x^{4} + 289 \, x^{3} + 441 \, x^{2} + 27 \, x + 27\right )} e \log \relax (2) + 2 \, {\left (65536 \, x^{8} + 16384 \, x^{7} + 50688 \, x^{6} + 9280 \, x^{5} + 14401 \, x^{4} + 1740 \, x^{3} + 1782 \, x^{2} + 108 \, x + 81\right )} e + x\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((8*(-512*x-16)*exp(1)*log(2)^3+4*(24576*x^3+2304*x^2+4656*x+144)*exp(1)*log(2)^2+2*(-393216*x^5-6144
0*x^4-150528*x^3-13872*x^2-14112*x-432)*exp(1)*log(2)+(2097152*x^7+458752*x^6+1216512*x^5+185600*x^4+230416*x^
3+20880*x^2+14256*x+432)*exp(1)+2)/(32*exp(1)*log(2)^4+8*(-128*x^2-8*x-24)*exp(1)*log(2)^3+4*(3072*x^4+384*x^3
+1164*x^2+72*x+108)*exp(1)*log(2)^2+2*(-32768*x^6-6144*x^5-18816*x^4-2312*x^3-3528*x^2-216*x-216)*exp(1)*log(2
)+(131072*x^8+32768*x^7+101376*x^6+18560*x^5+28802*x^4+3480*x^3+3564*x^2+216*x+162)*exp(1)+x),x, algorithm="fr
icas")

[Out]

2*log(-64*(16*x^2 + x + 3)*e*log(2)^3 + 32*e*log(2)^4 + 48*(256*x^4 + 32*x^3 + 97*x^2 + 6*x + 9)*e*log(2)^2 -
16*(4096*x^6 + 768*x^5 + 2352*x^4 + 289*x^3 + 441*x^2 + 27*x + 27)*e*log(2) + 2*(65536*x^8 + 16384*x^7 + 50688
*x^6 + 9280*x^5 + 14401*x^4 + 1740*x^3 + 1782*x^2 + 108*x + 81)*e + x)

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giac [B]  time = 0.19, size = 159, normalized size = 7.23 \begin {gather*} 2 \, \log \left (-64 \, {\left (16 \, x^{2} + x\right )} e \log \relax (2)^{3} + 32 \, e \log \relax (2)^{4} + 48 \, {\left (256 \, x^{4} + 32 \, x^{3} + 97 \, x^{2} + 6 \, x\right )} e \log \relax (2)^{2} - 192 \, e \log \relax (2)^{3} - 16 \, {\left (4096 \, x^{6} + 768 \, x^{5} + 2352 \, x^{4} + 289 \, x^{3} + 441 \, x^{2} + 27 \, x\right )} e \log \relax (2) + 432 \, e \log \relax (2)^{2} + 2 \, {\left (65536 \, x^{8} + 16384 \, x^{7} + 50688 \, x^{6} + 9280 \, x^{5} + 14401 \, x^{4} + 1740 \, x^{3} + 1782 \, x^{2} + 108 \, x\right )} e - 432 \, e \log \relax (2) + x + 162 \, e\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((8*(-512*x-16)*exp(1)*log(2)^3+4*(24576*x^3+2304*x^2+4656*x+144)*exp(1)*log(2)^2+2*(-393216*x^5-6144
0*x^4-150528*x^3-13872*x^2-14112*x-432)*exp(1)*log(2)+(2097152*x^7+458752*x^6+1216512*x^5+185600*x^4+230416*x^
3+20880*x^2+14256*x+432)*exp(1)+2)/(32*exp(1)*log(2)^4+8*(-128*x^2-8*x-24)*exp(1)*log(2)^3+4*(3072*x^4+384*x^3
+1164*x^2+72*x+108)*exp(1)*log(2)^2+2*(-32768*x^6-6144*x^5-18816*x^4-2312*x^3-3528*x^2-216*x-216)*exp(1)*log(2
)+(131072*x^8+32768*x^7+101376*x^6+18560*x^5+28802*x^4+3480*x^3+3564*x^2+216*x+162)*exp(1)+x),x, algorithm="gi
ac")

[Out]

2*log(-64*(16*x^2 + x)*e*log(2)^3 + 32*e*log(2)^4 + 48*(256*x^4 + 32*x^3 + 97*x^2 + 6*x)*e*log(2)^2 - 192*e*lo
g(2)^3 - 16*(4096*x^6 + 768*x^5 + 2352*x^4 + 289*x^3 + 441*x^2 + 27*x)*e*log(2) + 432*e*log(2)^2 + 2*(65536*x^
8 + 16384*x^7 + 50688*x^6 + 9280*x^5 + 14401*x^4 + 1740*x^3 + 1782*x^2 + 108*x)*e - 432*e*log(2) + x + 162*e)

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maple [B]  time = 0.19, size = 190, normalized size = 8.64

method	result	size
risch	\(2 \ln \left (131072 x^{8} {\mathrm e}+32768 x^{7} {\mathrm e}+\left (-65536 \,{\mathrm e} \ln \relax (2)+101376 \,{\mathrm e}\right ) x^{6}+\left (-12288 \,{\mathrm e} \ln \relax (2)+18560 \,{\mathrm e}\right ) x^{5}+\left (12288 \,{\mathrm e} \ln \relax (2)^{2}-37632 \,{\mathrm e} \ln \relax (2)+28802 \,{\mathrm e}\right ) x^{4}+\left (1536 \,{\mathrm e} \ln \relax (2)^{2}-4624 \,{\mathrm e} \ln \relax (2)+3480 \,{\mathrm e}\right ) x^{3}+\left (-1024 \,{\mathrm e} \ln \relax (2)^{3}+4656 \,{\mathrm e} \ln \relax (2)^{2}-7056 \,{\mathrm e} \ln \relax (2)+3564 \,{\mathrm e}\right ) x^{2}+\left (-64 \,{\mathrm e} \ln \relax (2)^{3}+288 \,{\mathrm e} \ln \relax (2)^{2}-432 \,{\mathrm e} \ln \relax (2)+216 \,{\mathrm e}+1\right ) x +32 \,{\mathrm e} \ln \relax (2)^{4}-192 \,{\mathrm e} \ln \relax (2)^{3}+432 \,{\mathrm e} \ln \relax (2)^{2}-432 \,{\mathrm e} \ln \relax (2)+162 \,{\mathrm e}\right )\)	\(190\)
default	\(2 \ln \left (-432 x \,{\mathrm e} \ln \relax (2)+x +4656 x^{2} {\mathrm e} \ln \relax (2)^{2}+131072 x^{8} {\mathrm e}+32 \,{\mathrm e} \ln \relax (2)^{4}+32768 x^{7} {\mathrm e}+162 \,{\mathrm e}+288 \ln \relax (2)^{2} {\mathrm e} x +18560 x^{5} {\mathrm e}-432 \,{\mathrm e} \ln \relax (2)+432 \,{\mathrm e} \ln \relax (2)^{2}-65536 \,{\mathrm e} \ln \relax (2) x^{6}+12288 \,{\mathrm e} \ln \relax (2)^{2} x^{4}-12288 \,{\mathrm e} \ln \relax (2) x^{5}-1024 \,{\mathrm e} \ln \relax (2)^{3} x^{2}+1536 \,{\mathrm e} \ln \relax (2)^{2} x^{3}-37632 \,{\mathrm e} \ln \relax (2) x^{4}-64 \,{\mathrm e} \ln \relax (2)^{3} x -4624 \,{\mathrm e} \ln \relax (2) x^{3}-7056 \,{\mathrm e} \ln \relax (2) x^{2}+28802 x^{4} {\mathrm e}+216 x \,{\mathrm e}+3564 x^{2} {\mathrm e}+3480 x^{3} {\mathrm e}-192 \,{\mathrm e} \ln \relax (2)^{3}+101376 x^{6} {\mathrm e}\right )\)	\(208\)
norman	\(2 \ln \left (-432 x \,{\mathrm e} \ln \relax (2)+x +4656 x^{2} {\mathrm e} \ln \relax (2)^{2}+131072 x^{8} {\mathrm e}+32 \,{\mathrm e} \ln \relax (2)^{4}+32768 x^{7} {\mathrm e}+162 \,{\mathrm e}+288 \ln \relax (2)^{2} {\mathrm e} x +18560 x^{5} {\mathrm e}-432 \,{\mathrm e} \ln \relax (2)+432 \,{\mathrm e} \ln \relax (2)^{2}-65536 \,{\mathrm e} \ln \relax (2) x^{6}+12288 \,{\mathrm e} \ln \relax (2)^{2} x^{4}-12288 \,{\mathrm e} \ln \relax (2) x^{5}-1024 \,{\mathrm e} \ln \relax (2)^{3} x^{2}+1536 \,{\mathrm e} \ln \relax (2)^{2} x^{3}-37632 \,{\mathrm e} \ln \relax (2) x^{4}-64 \,{\mathrm e} \ln \relax (2)^{3} x -4624 \,{\mathrm e} \ln \relax (2) x^{3}-7056 \,{\mathrm e} \ln \relax (2) x^{2}+28802 x^{4} {\mathrm e}+216 x \,{\mathrm e}+3564 x^{2} {\mathrm e}+3480 x^{3} {\mathrm e}-192 \,{\mathrm e} \ln \relax (2)^{3}+101376 x^{6} {\mathrm e}\right )\)	\(208\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((8*(-512*x-16)*exp(1)*ln(2)^3+4*(24576*x^3+2304*x^2+4656*x+144)*exp(1)*ln(2)^2+2*(-393216*x^5-61440*x^4-15
0528*x^3-13872*x^2-14112*x-432)*exp(1)*ln(2)+(2097152*x^7+458752*x^6+1216512*x^5+185600*x^4+230416*x^3+20880*x
^2+14256*x+432)*exp(1)+2)/(32*exp(1)*ln(2)^4+8*(-128*x^2-8*x-24)*exp(1)*ln(2)^3+4*(3072*x^4+384*x^3+1164*x^2+7
2*x+108)*exp(1)*ln(2)^2+2*(-32768*x^6-6144*x^5-18816*x^4-2312*x^3-3528*x^2-216*x-216)*exp(1)*ln(2)+(131072*x^8
+32768*x^7+101376*x^6+18560*x^5+28802*x^4+3480*x^3+3564*x^2+216*x+162)*exp(1)+x),x,method=_RETURNVERBOSE)

[Out]

2*ln(131072*x^8*exp(1)+32768*x^7*exp(1)+(-65536*exp(1)*ln(2)+101376*exp(1))*x^6+(-12288*exp(1)*ln(2)+18560*exp
(1))*x^5+(12288*exp(1)*ln(2)^2-37632*exp(1)*ln(2)+28802*exp(1))*x^4+(1536*exp(1)*ln(2)^2-4624*exp(1)*ln(2)+348
0*exp(1))*x^3+(-1024*exp(1)*ln(2)^3+4656*exp(1)*ln(2)^2-7056*exp(1)*ln(2)+3564*exp(1))*x^2+(-64*exp(1)*ln(2)^3
+288*exp(1)*ln(2)^2-432*exp(1)*ln(2)+216*exp(1)+1)*x+32*exp(1)*ln(2)^4-192*exp(1)*ln(2)^3+432*exp(1)*ln(2)^2-4
32*exp(1)*ln(2)+162*exp(1))

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maxima [B]  time = 0.37, size = 195, normalized size = 8.86 \begin {gather*} 2 \, \log \left (131072 \, x^{8} e + 32768 \, x^{7} e - 1024 \, {\left (64 \, e \log \relax (2) - 99 \, e\right )} x^{6} - 128 \, {\left (96 \, e \log \relax (2) - 145 \, e\right )} x^{5} + 2 \, {\left (6144 \, e \log \relax (2)^{2} - 18816 \, e \log \relax (2) + 14401 \, e\right )} x^{4} + 32 \, e \log \relax (2)^{4} + 8 \, {\left (192 \, e \log \relax (2)^{2} - 578 \, e \log \relax (2) + 435 \, e\right )} x^{3} - 192 \, e \log \relax (2)^{3} - 4 \, {\left (256 \, e \log \relax (2)^{3} - 1164 \, e \log \relax (2)^{2} + 1764 \, e \log \relax (2) - 891 \, e\right )} x^{2} + 432 \, e \log \relax (2)^{2} - {\left (64 \, e \log \relax (2)^{3} - 288 \, e \log \relax (2)^{2} + 432 \, e \log \relax (2) - 216 \, e - 1\right )} x - 432 \, e \log \relax (2) + 162 \, e\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((8*(-512*x-16)*exp(1)*log(2)^3+4*(24576*x^3+2304*x^2+4656*x+144)*exp(1)*log(2)^2+2*(-393216*x^5-6144
0*x^4-150528*x^3-13872*x^2-14112*x-432)*exp(1)*log(2)+(2097152*x^7+458752*x^6+1216512*x^5+185600*x^4+230416*x^
3+20880*x^2+14256*x+432)*exp(1)+2)/(32*exp(1)*log(2)^4+8*(-128*x^2-8*x-24)*exp(1)*log(2)^3+4*(3072*x^4+384*x^3
+1164*x^2+72*x+108)*exp(1)*log(2)^2+2*(-32768*x^6-6144*x^5-18816*x^4-2312*x^3-3528*x^2-216*x-216)*exp(1)*log(2
)+(131072*x^8+32768*x^7+101376*x^6+18560*x^5+28802*x^4+3480*x^3+3564*x^2+216*x+162)*exp(1)+x),x, algorithm="ma
xima")

[Out]

2*log(131072*x^8*e + 32768*x^7*e - 1024*(64*e*log(2) - 99*e)*x^6 - 128*(96*e*log(2) - 145*e)*x^5 + 2*(6144*e*l
og(2)^2 - 18816*e*log(2) + 14401*e)*x^4 + 32*e*log(2)^4 + 8*(192*e*log(2)^2 - 578*e*log(2) + 435*e)*x^3 - 192*
e*log(2)^3 - 4*(256*e*log(2)^3 - 1164*e*log(2)^2 + 1764*e*log(2) - 891*e)*x^2 + 432*e*log(2)^2 - (64*e*log(2)^
3 - 288*e*log(2)^2 + 432*e*log(2) - 216*e - 1)*x - 432*e*log(2) + 162*e)

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mupad [F(-1)]  time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \text {Hanged} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(1)*(14256*x + 20880*x^2 + 230416*x^3 + 185600*x^4 + 1216512*x^5 + 458752*x^6 + 2097152*x^7 + 432) + 4
*exp(1)*log(2)^2*(4656*x + 2304*x^2 + 24576*x^3 + 144) - 2*exp(1)*log(2)*(14112*x + 13872*x^2 + 150528*x^3 + 6
1440*x^4 + 393216*x^5 + 432) - 8*exp(1)*log(2)^3*(512*x + 16) + 2)/(x + exp(1)*(216*x + 3564*x^2 + 3480*x^3 +
28802*x^4 + 18560*x^5 + 101376*x^6 + 32768*x^7 + 131072*x^8 + 162) + 32*exp(1)*log(2)^4 + 4*exp(1)*log(2)^2*(7
2*x + 1164*x^2 + 384*x^3 + 3072*x^4 + 108) - 2*exp(1)*log(2)*(216*x + 3528*x^2 + 2312*x^3 + 18816*x^4 + 6144*x
^5 + 32768*x^6 + 216) - 8*exp(1)*log(2)^3*(8*x + 128*x^2 + 24)),x)

[Out]

\text{Hanged}

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sympy [B]  time = 3.89, size = 226, normalized size = 10.27 \begin {gather*} 2 \log {\left (131072 e x^{8} + 32768 e x^{7} + x^{6} \left (- 65536 e \log {\relax (2 )} + 101376 e\right ) + x^{5} \left (- 12288 e \log {\relax (2 )} + 18560 e\right ) + x^{4} \left (- 37632 e \log {\relax (2 )} + 12288 e \log {\relax (2 )}^{2} + 28802 e\right ) + x^{3} \left (- 4624 e \log {\relax (2 )} + 1536 e \log {\relax (2 )}^{2} + 3480 e\right ) + x^{2} \left (- 7056 e \log {\relax (2 )} - 1024 e \log {\relax (2 )}^{3} + 4656 e \log {\relax (2 )}^{2} + 3564 e\right ) + x \left (- 432 e \log {\relax (2 )} - 64 e \log {\relax (2 )}^{3} + 1 + 288 e \log {\relax (2 )}^{2} + 216 e\right ) - 432 e \log {\relax (2 )} - 192 e \log {\relax (2 )}^{3} + 32 e \log {\relax (2 )}^{4} + 162 e + 432 e \log {\relax (2 )}^{2} \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((8*(-512*x-16)*exp(1)*ln(2)**3+4*(24576*x**3+2304*x**2+4656*x+144)*exp(1)*ln(2)**2+2*(-393216*x**5-6
1440*x**4-150528*x**3-13872*x**2-14112*x-432)*exp(1)*ln(2)+(2097152*x**7+458752*x**6+1216512*x**5+185600*x**4+
230416*x**3+20880*x**2+14256*x+432)*exp(1)+2)/(32*exp(1)*ln(2)**4+8*(-128*x**2-8*x-24)*exp(1)*ln(2)**3+4*(3072
*x**4+384*x**3+1164*x**2+72*x+108)*exp(1)*ln(2)**2+2*(-32768*x**6-6144*x**5-18816*x**4-2312*x**3-3528*x**2-216
*x-216)*exp(1)*ln(2)+(131072*x**8+32768*x**7+101376*x**6+18560*x**5+28802*x**4+3480*x**3+3564*x**2+216*x+162)*
exp(1)+x),x)

[Out]

2*log(131072*E*x**8 + 32768*E*x**7 + x**6*(-65536*E*log(2) + 101376*E) + x**5*(-12288*E*log(2) + 18560*E) + x*
*4*(-37632*E*log(2) + 12288*E*log(2)**2 + 28802*E) + x**3*(-4624*E*log(2) + 1536*E*log(2)**2 + 3480*E) + x**2*
(-7056*E*log(2) - 1024*E*log(2)**3 + 4656*E*log(2)**2 + 3564*E) + x*(-432*E*log(2) - 64*E*log(2)**3 + 1 + 288*
E*log(2)**2 + 216*E) - 432*E*log(2) - 192*E*log(2)**3 + 32*E*log(2)**4 + 162*E + 432*E*log(2)**2)

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