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

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

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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 = {} $$\begin{array}{c}\text{\$Aborted}\end{array}$$

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]  time = 0.16, size = 71, normalized size = 3.55 $$\begin{array}{c}{\log }^2\left(\frac{185+e^{2x}(-2+x{)}^4-240x+62x^2+34x^3-14x^4-2x^5+x^6+2e^x(-2+x{)}^2(13-8x-x^2+x^3)}{(-2+x{)}^4}\right)\end{array}$$

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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fricas [B]  time = 0.77, size = 97, normalized size = 4.85 $$\begin{array}{c}\log {\left(\frac{x^6-2x^5-14x^4+34x^3+62x^2+(x^4-8x^3+24x^2-32x+16)e^{\left(2x\right)}+2(x^5-5x^4+41x^2-84x+52)e^x-240x+185}{x^4-8x^3+24x^2-32x+16}\right)}^2\end{array}$$

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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giac [F]  time = 0.00, size = 0, normalized size = 0.00 $$\begin{array}{c}\int \frac{4(x^6-7x^5+10x^4+39x^3-164x^2+(x^5-10x^4+40x^3-80x^2+80x-32)e^{\left(2x\right)}+(x^6-6x^5+81x^3-248x^2+308x-144)e^x+236x-130)\log \left(\frac{x^6-2x^5-14x^4+34x^3+62x^2+(x^4-8x^3+24x^2-32x+16)e^{\left(2x\right)}+2(x^5-5x^4+41x^2-84x+52)e^x-240x+185}{x^4-8x^3+24x^2-32x+16}\right)}{x^7-4x^6-10x^5+62x^4-6x^3-364x^2+(x^5-10x^4+40x^3-80x^2+80x-32)e^{\left(2x\right)}+2(x^6-7x^5+10x^4+41x^3-166x^2+220x-104)e^x+665x-370}dx\end{array}$$

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

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]  time = 1.05, size = 97, normalized size = 4.85 $$\begin{array}{c}\log {\left(\frac{x^6-2x^5-14x^4+34x^3+62x^2+(x^4-8x^3+24x^2-32x+16)e^{\left(2x\right)}+2(x^5-5x^4+41x^2-84x+52)e^x-240x+185}{x^4-8x^3+24x^2-32x+16}\right)}^2\end{array}$$

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

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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sympy [B]  time = 1.74, size = 97, normalized size = 4.85 $$\begin{array}{c}\log {\left(\frac{x^6-2x^5-14x^4+34x^3+62x^2-240x+(x^4-8x^3+24x^2-32x+16)e^{2x}+(2x^5-10x^4+82x^2-168x+104)e^x+185}{x^4-8x^3+24x^2-32x+16}\right)}^2\end{array}$$

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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