∫ (−520+944x−656x2+156x3+40x4−28x5+4x6+e2x(−128+320x−320x2+160x3−40x4+4x5)+ex(−576+1232x−992x2+324x3−24x5+4x6)) log(185−240x+62x2+34x3−14x4−2x5+x6+e2x(16−32x+24x2−8x3+x4)+ex(104−168x+82x2−10x4+2x5) 16−32x+24x2−8x3+x4 ) _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________−370+665x−364x2 −6x3 +62x4 −10x5 −4x6 +x7 +e2x (−32+80x−80x2 +40x3 −10x4 +x5 )+ex (−208+440x−332x2 +82x3 +20x4 −14x5 +2x6 ) dx [534]

3.6.34 $\int \frac {(-520+944 x-656 x^2+156 x^3+40 x^4-28 x^5+4 x^6+e^{2 x} (-128+320 x-320 x^2+160 x^3-40 x^4+4 x^5)+e^x (-576+1232 x-992 x^2+324 x^3-24 x^5+4 x^6)) \log (\frac {185-240 x+62 x^2+34 x^3-14 x^4-2 x^5+x^6+e^{2 x} (16-32 x+24 x^2-8 x^3+x^4)+e^x (104-168 x+82 x^2-10 x^4+2 x^5)}{16-32 x+24 x^2-8 x^3+x^4})}{-370+665 x-364 x^2-6 x^3+62 x^4-10 x^5-4 x^6+x^7+e^{2 x} (-32+80 x-80 x^2+40 x^3-10 x^4+x^5)+e^x (-208+440 x-332 x^2+82 x^3+20 x^4-14 x^5+2 x^6)} \, dx$ [534]

Optimal. Leaf size=20 \[ -3+\log ^2\left (1+\left (3+e^x+\frac {1}{(-2+x)^2}+x\right )^2\right ) \]

[Out]

ln((exp(x)+3+x+1/(-2+x)^2)^2+1)^2-3

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Rubi [F]
time = 180.00, 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*} \text {\$Aborted} \end {gather*}

Veriﬁcation is not applicable to the result.

[In]

Int[((-520 + 944*x - 656*x^2 + 156*x^3 + 40*x^4 - 28*x^5 + 4*x^6 + E^(2*x)*(-128 + 320*x - 320*x^2 + 160*x^3 -

40*x^4 + 4*x^5) + E^x*(-576 + 1232*x - 992*x^2 + 324*x^3 - 24*x^5 + 4*x^6))*Log[(185 - 240*x + 62*x^2 + 34*x^

3 - 14*x^4 - 2*x^5 + x^6 + E^(2*x)*(16 - 32*x + 24*x^2 - 8*x^3 + x^4) + E^x*(104 - 168*x + 82*x^2 - 10*x^4 + 2

*x^5))/(16 - 32*x + 24*x^2 - 8*x^3 + x^4)])/(-370 + 665*x - 364*x^2 - 6*x^3 + 62*x^4 - 10*x^5 - 4*x^6 + x^7 +

E^(2*x)*(-32 + 80*x - 80*x^2 + 40*x^3 - 10*x^4 + x^5) + E^x*(-208 + 440*x - 332*x^2 + 82*x^3 + 20*x^4 - 14*x^5

+ 2*x^6)),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. $71$ vs. $2(20)=40$.
time = 0.11, size = 71, normalized size = 3.55 \begin {gather*} \log ^2\left (\frac {185+e^{2 x} (-2+x)^4-240 x+62 x^2+34 x^3-14 x^4-2 x^5+x^6+2 e^x (-2+x)^2 \left (13-8 x-x^2+x^3\right )}{(-2+x)^4}\right ) \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Integrate[((-520 + 944*x - 656*x^2 + 156*x^3 + 40*x^4 - 28*x^5 + 4*x^6 + E^(2*x)*(-128 + 320*x - 320*x^2 + 160

*x^3 - 40*x^4 + 4*x^5) + E^x*(-576 + 1232*x - 992*x^2 + 324*x^3 - 24*x^5 + 4*x^6))*Log[(185 - 240*x + 62*x^2 +

34*x^3 - 14*x^4 - 2*x^5 + x^6 + E^(2*x)*(16 - 32*x + 24*x^2 - 8*x^3 + x^4) + E^x*(104 - 168*x + 82*x^2 - 10*x

^4 + 2*x^5))/(16 - 32*x + 24*x^2 - 8*x^3 + x^4)])/(-370 + 665*x - 364*x^2 - 6*x^3 + 62*x^4 - 10*x^5 - 4*x^6 +

x^7 + E^(2*x)*(-32 + 80*x - 80*x^2 + 40*x^3 - 10*x^4 + x^5) + E^x*(-208 + 440*x - 332*x^2 + 82*x^3 + 20*x^4 -

14*x^5 + 2*x^6)),x]

[Out]

Log[(185 + E^(2*x)*(-2 + x)^4 - 240*x + 62*x^2 + 34*x^3 - 14*x^4 - 2*x^5 + x^6 + 2*E^x*(-2 + x)^2*(13 - 8*x -

x^2 + x^3))/(-2 + x)^4]^2

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Maple [F]
time = 0.08, size = 0, normalized size = 0.00 \[\int \frac {\left (\left (4 x^{5}-40 x^{4}+160 x^{3}-320 x^{2}+320 x -128\right ) {\mathrm e}^{2 x}+\left (4 x^{6}-24 x^{5}+324 x^{3}-992 x^{2}+1232 x -576\right ) {\mathrm e}^{x}+4 x^{6}-28 x^{5}+40 x^{4}+156 x^{3}-656 x^{2}+944 x -520\right ) \ln \left (\frac {\left (x^{4}-8 x^{3}+24 x^{2}-32 x +16\right ) {\mathrm e}^{2 x}+\left (2 x^{5}-10 x^{4}+82 x^{2}-168 x +104\right ) {\mathrm e}^{x}+x^{6}-2 x^{5}-14 x^{4}+34 x^{3}+62 x^{2}-240 x +185}{x^{4}-8 x^{3}+24 x^{2}-32 x +16}\right )}{\left (x^{5}-10 x^{4}+40 x^{3}-80 x^{2}+80 x -32\right ) {\mathrm e}^{2 x}+\left (2 x^{6}-14 x^{5}+20 x^{4}+82 x^{3}-332 x^{2}+440 x -208\right ) {\mathrm e}^{x}+x^{7}-4 x^{6}-10 x^{5}+62 x^{4}-6 x^{3}-364 x^{2}+665 x -370}\, dx\]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(((4*x^5-40*x^4+160*x^3-320*x^2+320*x-128)*exp(x)^2+(4*x^6-24*x^5+324*x^3-992*x^2+1232*x-576)*exp(x)+4*x^6-

28*x^5+40*x^4+156*x^3-656*x^2+944*x-520)*ln(((x^4-8*x^3+24*x^2-32*x+16)*exp(x)^2+(2*x^5-10*x^4+82*x^2-168*x+10

4)*exp(x)+x^6-2*x^5-14*x^4+34*x^3+62*x^2-240*x+185)/(x^4-8*x^3+24*x^2-32*x+16))/((x^5-10*x^4+40*x^3-80*x^2+80*

x-32)*exp(x)^2+(2*x^6-14*x^5+20*x^4+82*x^3-332*x^2+440*x-208)*exp(x)+x^7-4*x^6-10*x^5+62*x^4-6*x^3-364*x^2+665

*x-370),x)

[Out]

int(((4*x^5-40*x^4+160*x^3-320*x^2+320*x-128)*exp(x)^2+(4*x^6-24*x^5+324*x^3-992*x^2+1232*x-576)*exp(x)+4*x^6-

28*x^5+40*x^4+156*x^3-656*x^2+944*x-520)*ln(((x^4-8*x^3+24*x^2-32*x+16)*exp(x)^2+(2*x^5-10*x^4+82*x^2-168*x+10

4)*exp(x)+x^6-2*x^5-14*x^4+34*x^3+62*x^2-240*x+185)/(x^4-8*x^3+24*x^2-32*x+16))/((x^5-10*x^4+40*x^3-80*x^2+80*

x-32)*exp(x)^2+(2*x^6-14*x^5+20*x^4+82*x^3-332*x^2+440*x-208)*exp(x)+x^7-4*x^6-10*x^5+62*x^4-6*x^3-364*x^2+665

*x-370),x)

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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 97 vs. $2 (19) = 38$.
time = 0.44, size = 97, normalized size = 4.85 \begin {gather*} \log \left (\frac {x^{6} - 2 \, x^{5} - 14 \, x^{4} + 34 \, x^{3} + 62 \, x^{2} + {\left (x^{4} - 8 \, x^{3} + 24 \, x^{2} - 32 \, x + 16\right )} e^{\left (2 \, x\right )} + 2 \, {\left (x^{5} - 5 \, x^{4} + 41 \, x^{2} - 84 \, x + 52\right )} e^{x} - 240 \, x + 185}{x^{4} - 8 \, x^{3} + 24 \, x^{2} - 32 \, x + 16}\right )^{2} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^5-40*x^4+160*x^3-320*x^2+320*x-128)*exp(x)^2+(4*x^6-24*x^5+324*x^3-992*x^2+1232*x-576)*exp(x)+

4*x^6-28*x^5+40*x^4+156*x^3-656*x^2+944*x-520)*log(((x^4-8*x^3+24*x^2-32*x+16)*exp(x)^2+(2*x^5-10*x^4+82*x^2-1

68*x+104)*exp(x)+x^6-2*x^5-14*x^4+34*x^3+62*x^2-240*x+185)/(x^4-8*x^3+24*x^2-32*x+16))/((x^5-10*x^4+40*x^3-80*

x^2+80*x-32)*exp(x)^2+(2*x^6-14*x^5+20*x^4+82*x^3-332*x^2+440*x-208)*exp(x)+x^7-4*x^6-10*x^5+62*x^4-6*x^3-364*

x^2+665*x-370),x, algorithm="maxima")

[Out]

log((x^6 - 2*x^5 - 14*x^4 + 34*x^3 + 62*x^2 + (x^4 - 8*x^3 + 24*x^2 - 32*x + 16)*e^(2*x) + 2*(x^5 - 5*x^4 + 41

*x^2 - 84*x + 52)*e^x - 240*x + 185)/(x^4 - 8*x^3 + 24*x^2 - 32*x + 16))^2

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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 97 vs. $2 (19) = 38$.
time = 0.32, size = 97, normalized size = 4.85 \begin {gather*} \log \left (\frac {x^{6} - 2 \, x^{5} - 14 \, x^{4} + 34 \, x^{3} + 62 \, x^{2} + {\left (x^{4} - 8 \, x^{3} + 24 \, x^{2} - 32 \, x + 16\right )} e^{\left (2 \, x\right )} + 2 \, {\left (x^{5} - 5 \, x^{4} + 41 \, x^{2} - 84 \, x + 52\right )} e^{x} - 240 \, x + 185}{x^{4} - 8 \, x^{3} + 24 \, x^{2} - 32 \, x + 16}\right )^{2} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^5-40*x^4+160*x^3-320*x^2+320*x-128)*exp(x)^2+(4*x^6-24*x^5+324*x^3-992*x^2+1232*x-576)*exp(x)+

4*x^6-28*x^5+40*x^4+156*x^3-656*x^2+944*x-520)*log(((x^4-8*x^3+24*x^2-32*x+16)*exp(x)^2+(2*x^5-10*x^4+82*x^2-1

68*x+104)*exp(x)+x^6-2*x^5-14*x^4+34*x^3+62*x^2-240*x+185)/(x^4-8*x^3+24*x^2-32*x+16))/((x^5-10*x^4+40*x^3-80*

x^2+80*x-32)*exp(x)^2+(2*x^6-14*x^5+20*x^4+82*x^3-332*x^2+440*x-208)*exp(x)+x^7-4*x^6-10*x^5+62*x^4-6*x^3-364*

x^2+665*x-370),x, algorithm="fricas")

[Out]

log((x^6 - 2*x^5 - 14*x^4 + 34*x^3 + 62*x^2 + (x^4 - 8*x^3 + 24*x^2 - 32*x + 16)*e^(2*x) + 2*(x^5 - 5*x^4 + 41

*x^2 - 84*x + 52)*e^x - 240*x + 185)/(x^4 - 8*x^3 + 24*x^2 - 32*x + 16))^2

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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 97 vs. $2 (20) = 40$.
time = 0.83, size = 97, normalized size = 4.85 \begin {gather*} \log {\left (\frac {x^{6} - 2 x^{5} - 14 x^{4} + 34 x^{3} + 62 x^{2} - 240 x + \left (x^{4} - 8 x^{3} + 24 x^{2} - 32 x + 16\right ) e^{2 x} + \left (2 x^{5} - 10 x^{4} + 82 x^{2} - 168 x + 104\right ) e^{x} + 185}{x^{4} - 8 x^{3} + 24 x^{2} - 32 x + 16} \right )}^{2} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x**5-40*x**4+160*x**3-320*x**2+320*x-128)*exp(x)**2+(4*x**6-24*x**5+324*x**3-992*x**2+1232*x-576

)*exp(x)+4*x**6-28*x**5+40*x**4+156*x**3-656*x**2+944*x-520)*ln(((x**4-8*x**3+24*x**2-32*x+16)*exp(x)**2+(2*x*

*5-10*x**4+82*x**2-168*x+104)*exp(x)+x**6-2*x**5-14*x**4+34*x**3+62*x**2-240*x+185)/(x**4-8*x**3+24*x**2-32*x+

16))/((x**5-10*x**4+40*x**3-80*x**2+80*x-32)*exp(x)**2+(2*x**6-14*x**5+20*x**4+82*x**3-332*x**2+440*x-208)*exp

(x)+x**7-4*x**6-10*x**5+62*x**4-6*x**3-364*x**2+665*x-370),x)

[Out]

log((x**6 - 2*x**5 - 14*x**4 + 34*x**3 + 62*x**2 - 240*x + (x**4 - 8*x**3 + 24*x**2 - 32*x + 16)*exp(2*x) + (2

*x**5 - 10*x**4 + 82*x**2 - 168*x + 104)*exp(x) + 185)/(x**4 - 8*x**3 + 24*x**2 - 32*x + 16))**2

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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^5-40*x^4+160*x^3-320*x^2+320*x-128)*exp(x)^2+(4*x^6-24*x^5+324*x^3-992*x^2+1232*x-576)*exp(x)+

4*x^6-28*x^5+40*x^4+156*x^3-656*x^2+944*x-520)*log(((x^4-8*x^3+24*x^2-32*x+16)*exp(x)^2+(2*x^5-10*x^4+82*x^2-1

68*x+104)*exp(x)+x^6-2*x^5-14*x^4+34*x^3+62*x^2-240*x+185)/(x^4-8*x^3+24*x^2-32*x+16))/((x^5-10*x^4+40*x^3-80*

x^2+80*x-32)*exp(x)^2+(2*x^6-14*x^5+20*x^4+82*x^3-332*x^2+440*x-208)*exp(x)+x^7-4*x^6-10*x^5+62*x^4-6*x^3-364*

x^2+665*x-370),x, algorithm="giac")

[Out]

integrate(4*(x^6 - 7*x^5 + 10*x^4 + 39*x^3 - 164*x^2 + (x^5 - 10*x^4 + 40*x^3 - 80*x^2 + 80*x - 32)*e^(2*x) +

(x^6 - 6*x^5 + 81*x^3 - 248*x^2 + 308*x - 144)*e^x + 236*x - 130)*log((x^6 - 2*x^5 - 14*x^4 + 34*x^3 + 62*x^2

+ (x^4 - 8*x^3 + 24*x^2 - 32*x + 16)*e^(2*x) + 2*(x^5 - 5*x^4 + 41*x^2 - 84*x + 52)*e^x - 240*x + 185)/(x^4 -

8*x^3 + 24*x^2 - 32*x + 16))/(x^7 - 4*x^6 - 10*x^5 + 62*x^4 - 6*x^3 - 364*x^2 + (x^5 - 10*x^4 + 40*x^3 - 80*x^

2 + 80*x - 32)*e^(2*x) + 2*(x^6 - 7*x^5 + 10*x^4 + 41*x^3 - 166*x^2 + 220*x - 104)*e^x + 665*x - 370), x)

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Mupad [B]
time = 2.19, size = 98, normalized size = 4.90 \begin {gather*} {\ln \left (\frac {{\mathrm {e}}^{2\,x}\,\left (x^4-8\,x^3+24\,x^2-32\,x+16\right )-240\,x+{\mathrm {e}}^x\,\left (2\,x^5-10\,x^4+82\,x^2-168\,x+104\right )+62\,x^2+34\,x^3-14\,x^4-2\,x^5+x^6+185}{x^4-8\,x^3+24\,x^2-32\,x+16}\right )}^2 \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((log((exp(2*x)*(24*x^2 - 32*x - 8*x^3 + x^4 + 16) - 240*x + exp(x)*(82*x^2 - 168*x - 10*x^4 + 2*x^5 + 104)

+ 62*x^2 + 34*x^3 - 14*x^4 - 2*x^5 + x^6 + 185)/(24*x^2 - 32*x - 8*x^3 + x^4 + 16))*(944*x + exp(x)*(1232*x -

992*x^2 + 324*x^3 - 24*x^5 + 4*x^6 - 576) + exp(2*x)*(320*x - 320*x^2 + 160*x^3 - 40*x^4 + 4*x^5 - 128) - 656

*x^2 + 156*x^3 + 40*x^4 - 28*x^5 + 4*x^6 - 520))/(665*x + exp(2*x)*(80*x - 80*x^2 + 40*x^3 - 10*x^4 + x^5 - 32

) + exp(x)*(440*x - 332*x^2 + 82*x^3 + 20*x^4 - 14*x^5 + 2*x^6 - 208) - 364*x^2 - 6*x^3 + 62*x^4 - 10*x^5 - 4*

x^6 + x^7 - 370),x)

[Out]

log((exp(2*x)*(24*x^2 - 32*x - 8*x^3 + x^4 + 16) - 240*x + exp(x)*(82*x^2 - 168*x - 10*x^4 + 2*x^5 + 104) + 62

*x^2 + 34*x^3 - 14*x^4 - 2*x^5 + x^6 + 185)/(24*x^2 - 32*x - 8*x^3 + x^4 + 16))^2

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