∫ −208x5+16x6+e2x(−50x3+4x4)+ex(2x3−206x4+16x5)+(308x4−24x5+e2x(74x2−6x3)+ex(−2x2+304x3−24x4)) log(ex(12−x)+25x−2x2 6ex+12x )+(−100x3+8x4+e2x(−24x+2x2)+ex(−98x2+8x3)) log2(ex(12−x)+25x−2x2 6ex+12x ) ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

3.34.15 \(\int \frac {-208 x^5+16 x^6+e^{2 x} (-50 x^3+4 x^4)+e^x (2 x^3-206 x^4+16 x^5)+(308 x^4-24 x^5+e^{2 x} (74 x^2-6 x^3)+e^x (-2 x^2+304 x^3-24 x^4)) \log (\frac {e^x (12-x)+25 x-2 x^2}{6 e^x+12 x})+(-100 x^3+8 x^4+e^{2 x} (-24 x+2 x^2)+e^x (-98 x^2+8 x^3)) \log ^2(\frac {e^x (12-x)+25 x-2 x^2}{6 e^x+12 x})}{e^{2 x} (-12+x)-50 x^2+4 x^3+e^x (-49 x+4 x^2)} \, dx\)

Optimal. Leaf size=32 \[ x^2 \left (x-\log \left (2+\frac {1}{6} \left (-x+\frac {x}{e^x+2 x}\right )\right )\right )^2 \]

________________________________________________________________________________________

Rubi [F] time = 21.74, 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 {-208 x^5+16 x^6+e^{2 x} \left (-50 x^3+4 x^4\right )+e^x \left (2 x^3-206 x^4+16 x^5\right )+\left (308 x^4-24 x^5+e^{2 x} \left (74 x^2-6 x^3\right )+e^x \left (-2 x^2+304 x^3-24 x^4\right )\right ) \log \left (\frac {e^x (12-x)+25 x-2 x^2}{6 e^x+12 x}\right )+\left (-100 x^3+8 x^4+e^{2 x} \left (-24 x+2 x^2\right )+e^x \left (-98 x^2+8 x^3\right )\right ) \log ^2\left (\frac {e^x (12-x)+25 x-2 x^2}{6 e^x+12 x}\right )}{e^{2 x} (-12+x)-50 x^2+4 x^3+e^x \left (-49 x+4 x^2\right )} \, dx \end {gather*}

Veriﬁcation is not applicable to the result.

[In]

Int[(-208*x^5 + 16*x^6 + E^(2*x)*(-50*x^3 + 4*x^4) + E^x*(2*x^3 - 206*x^4 + 16*x^5) + (308*x^4 - 24*x^5 + E^(2

*x)*(74*x^2 - 6*x^3) + E^x*(-2*x^2 + 304*x^3 - 24*x^4))*Log[(E^x*(12 - x) + 25*x - 2*x^2)/(6*E^x + 12*x)] + (-

100*x^3 + 8*x^4 + E^(2*x)*(-24*x + 2*x^2) + E^x*(-98*x^2 + 8*x^3))*Log[(E^x*(12 - x) + 25*x - 2*x^2)/(6*E^x +

12*x)]^2)/(E^(2*x)*(-12 + x) - 50*x^2 + 4*x^3 + E^x*(-49*x + 4*x^2)),x]

[Out]

-36*x - x^2/2 + x^4 - 432*Log[12 - x] + 24*x*Log[(E^x*(12 - x) + (25 - 2*x)*x)/(6*(E^x + 2*x))] + x^2*Log[(E^x

*(12 - x) + (25 - 2*x)*x)/(6*(E^x + 2*x))] - 2*x^3*Log[(E^x*(12 - x) + (25 - 2*x)*x)/(6*(E^x + 2*x))] + 48*Def

er[Int][x/(E^x + 2*x), x] - 46*Defer[Int][x^2/(E^x + 2*x), x] - 4*Log[(E^x*(12 - x) + (25 - 2*x)*x)/(6*(E^x +

2*x))]*Defer[Int][x^2/(E^x + 2*x), x] - 2*Defer[Int][x^3/(E^x + 2*x), x] + 4*Log[(E^x*(12 - x) + (25 - 2*x)*x)

/(6*(E^x + 2*x))]*Defer[Int][x^3/(E^x + 2*x), x] - 432*Defer[Int][(-12*E^x - 25*x + E^x*x + 2*x^2)^(-1), x] +

288*Log[(E^x*(12 - x) + (25 - 2*x)*x)/(6*(E^x + 2*x))]*Defer[Int][(-12*E^x - 25*x + E^x*x + 2*x^2)^(-1), x] -

5184*Defer[Int][1/((-12 + x)*(-12*E^x - 25*x + E^x*x + 2*x^2)), x] + 3456*Log[(E^x*(12 - x) + (25 - 2*x)*x)/(6

*(E^x + 2*x))]*Defer[Int][1/((-12 + x)*(-12*E^x - 25*x + E^x*x + 2*x^2)), x] + 564*Defer[Int][x/(-12*E^x - 25*

x + E^x*x + 2*x^2), x] + 24*Log[(E^x*(12 - x) + (25 - 2*x)*x)/(6*(E^x + 2*x))]*Defer[Int][x/(-12*E^x - 25*x +

E^x*x + 2*x^2), x] - 624*Defer[Int][x^2/(-12*E^x - 25*x + E^x*x + 2*x^2), x] - 48*Log[(E^x*(12 - x) + (25 - 2*

x)*x)/(6*(E^x + 2*x))]*Defer[Int][x^2/(-12*E^x - 25*x + E^x*x + 2*x^2), x] + 21*Defer[Int][x^3/(-12*E^x - 25*x

+ E^x*x + 2*x^2), x] + 54*Log[(E^x*(12 - x) + (25 - 2*x)*x)/(6*(E^x + 2*x))]*Defer[Int][x^3/(-12*E^x - 25*x +

E^x*x + 2*x^2), x] + 2*Defer[Int][x^4/(-12*E^x - 25*x + E^x*x + 2*x^2), x] - 4*Log[(E^x*(12 - x) + (25 - 2*x)

*x)/(6*(E^x + 2*x))]*Defer[Int][x^4/(-12*E^x - 25*x + E^x*x + 2*x^2), x] + 288*Defer[Int][Log[(-(E^x*(-12 + x)

) + (25 - 2*x)*x)/(6*(E^x + 2*x))]/(-12 + x), x] + 2*Defer[Int][x*Log[(-(E^x*(-12 + x)) + (25 - 2*x)*x)/(6*(E^

x + 2*x))]^2, x] + 4*Defer[Int][Defer[Int][x^2/(E^x + 2*x), x]/(-12 + x), x] - 8*Defer[Int][Defer[Int][x^2/(E^

x + 2*x), x]/(E^x + 2*x), x] + 8*Defer[Int][(x*Defer[Int][x^2/(E^x + 2*x), x])/(E^x + 2*x), x] - 96*Defer[Int]

[Defer[Int][x^2/(E^x + 2*x), x]/(-12*E^x - 25*x + E^x*x + 2*x^2), x] + 48*Defer[Int][Defer[Int][x^2/(E^x + 2*x

), x]/((-12 + x)*(-12*E^x - 25*x + E^x*x + 2*x^2)), x] + 108*Defer[Int][(x*Defer[Int][x^2/(E^x + 2*x), x])/(-1

2*E^x - 25*x + E^x*x + 2*x^2), x] - 8*Defer[Int][(x^2*Defer[Int][x^2/(E^x + 2*x), x])/(-12*E^x - 25*x + E^x*x

+ 2*x^2), x] - 4*Defer[Int][Defer[Int][x^3/(E^x + 2*x), x]/(-12 + x), x] + 8*Defer[Int][Defer[Int][x^3/(E^x +

2*x), x]/(E^x + 2*x), x] - 8*Defer[Int][(x*Defer[Int][x^3/(E^x + 2*x), x])/(E^x + 2*x), x] + 96*Defer[Int][Def

er[Int][x^3/(E^x + 2*x), x]/(-12*E^x - 25*x + E^x*x + 2*x^2), x] - 48*Defer[Int][Defer[Int][x^3/(E^x + 2*x), x

]/((-12 + x)*(-12*E^x - 25*x + E^x*x + 2*x^2)), x] - 108*Defer[Int][(x*Defer[Int][x^3/(E^x + 2*x), x])/(-12*E^

x - 25*x + E^x*x + 2*x^2), x] + 8*Defer[Int][(x^2*Defer[Int][x^3/(E^x + 2*x), x])/(-12*E^x - 25*x + E^x*x + 2*

x^2), x] - 288*Defer[Int][Defer[Int][(E^x*(-12 + x) + x*(-25 + 2*x))^(-1), x]/(-12 + x), x] + 576*Defer[Int][D

efer[Int][(E^x*(-12 + x) + x*(-25 + 2*x))^(-1), x]/(E^x + 2*x), x] - 576*Defer[Int][(x*Defer[Int][(E^x*(-12 +

x) + x*(-25 + 2*x))^(-1), x])/(E^x + 2*x), x] + 6912*Defer[Int][Defer[Int][(E^x*(-12 + x) + x*(-25 + 2*x))^(-1

), x]/(-12*E^x - 25*x + E^x*x + 2*x^2), x] - 3456*Defer[Int][Defer[Int][(E^x*(-12 + x) + x*(-25 + 2*x))^(-1),

x]/((-12 + x)*(-12*E^x - 25*x + E^x*x + 2*x^2)), x] - 7776*Defer[Int][(x*Defer[Int][(E^x*(-12 + x) + x*(-25 +

2*x))^(-1), x])/(-12*E^x - 25*x + E^x*x + 2*x^2), x] + 576*Defer[Int][(x^2*Defer[Int][(E^x*(-12 + x) + x*(-25

+ 2*x))^(-1), x])/(-12*E^x - 25*x + E^x*x + 2*x^2), x] - 3456*Defer[Int][Defer[Int][1/((-12 + x)*(E^x*(-12 + x

) + x*(-25 + 2*x))), x]/(-12 + x), x] + 6912*Defer[Int][Defer[Int][1/((-12 + x)*(E^x*(-12 + x) + x*(-25 + 2*x)

)), x]/(E^x + 2*x), x] - 6912*Defer[Int][(x*Defer[Int][1/((-12 + x)*(E^x*(-12 + x) + x*(-25 + 2*x))), x])/(E^x

+ 2*x), x] + 82944*Defer[Int][Defer[Int][1/((-12 + x)*(E^x*(-12 + x) + x*(-25 + 2*x))), x]/(-12*E^x - 25*x +

E^x*x + 2*x^2), x] - 41472*Defer[Int][Defer[Int][1/((-12 + x)*(E^x*(-12 + x) + x*(-25 + 2*x))), x]/((-12 + x)*

(-12*E^x - 25*x + E^x*x + 2*x^2)), x] - 93312*Defer[Int][(x*Defer[Int][1/((-12 + x)*(E^x*(-12 + x) + x*(-25 +

2*x))), x])/(-12*E^x - 25*x + E^x*x + 2*x^2), x] + 6912*Defer[Int][(x^2*Defer[Int][1/((-12 + x)*(E^x*(-12 + x)

+ x*(-25 + 2*x))), x])/(-12*E^x - 25*x + E^x*x + 2*x^2), x] - 24*Defer[Int][Defer[Int][x/(E^x*(-12 + x) + x*(

-25 + 2*x)), x]/(-12 + x), x] + 48*Defer[Int][Defer[Int][x/(E^x*(-12 + x) + x*(-25 + 2*x)), x]/(E^x + 2*x), x]

- 48*Defer[Int][(x*Defer[Int][x/(E^x*(-12 + x) + x*(-25 + 2*x)), x])/(E^x + 2*x), x] + 576*Defer[Int][Defer[I

nt][x/(E^x*(-12 + x) + x*(-25 + 2*x)), x]/(-12*E^x - 25*x + E^x*x + 2*x^2), x] - 288*Defer[Int][Defer[Int][x/(

E^x*(-12 + x) + x*(-25 + 2*x)), x]/((-12 + x)*(-12*E^x - 25*x + E^x*x + 2*x^2)), x] - 648*Defer[Int][(x*Defer[

Int][x/(E^x*(-12 + x) + x*(-25 + 2*x)), x])/(-12*E^x - 25*x + E^x*x + 2*x^2), x] + 48*Defer[Int][(x^2*Defer[In

t][x/(E^x*(-12 + x) + x*(-25 + 2*x)), x])/(-12*E^x - 25*x + E^x*x + 2*x^2), x] + 48*Defer[Int][Defer[Int][x^2/

(E^x*(-12 + x) + x*(-25 + 2*x)), x]/(-12 + x), x] - 96*Defer[Int][Defer[Int][x^2/(E^x*(-12 + x) + x*(-25 + 2*x

)), x]/(E^x + 2*x), x] + 96*Defer[Int][(x*Defer[Int][x^2/(E^x*(-12 + x) + x*(-25 + 2*x)), x])/(E^x + 2*x), x]

- 1152*Defer[Int][Defer[Int][x^2/(E^x*(-12 + x) + x*(-25 + 2*x)), x]/(-12*E^x - 25*x + E^x*x + 2*x^2), x] + 57

6*Defer[Int][Defer[Int][x^2/(E^x*(-12 + x) + x*(-25 + 2*x)), x]/((-12 + x)*(-12*E^x - 25*x + E^x*x + 2*x^2)),

x] + 1296*Defer[Int][(x*Defer[Int][x^2/(E^x*(-12 + x) + x*(-25 + 2*x)), x])/(-12*E^x - 25*x + E^x*x + 2*x^2),

x] - 96*Defer[Int][(x^2*Defer[Int][x^2/(E^x*(-12 + x) + x*(-25 + 2*x)), x])/(-12*E^x - 25*x + E^x*x + 2*x^2),

x] - 54*Defer[Int][Defer[Int][x^3/(E^x*(-12 + x) + x*(-25 + 2*x)), x]/(-12 + x), x] + 108*Defer[Int][Defer[Int

][x^3/(E^x*(-12 + x) + x*(-25 + 2*x)), x]/(E^x + 2*x), x] - 108*Defer[Int][(x*Defer[Int][x^3/(E^x*(-12 + x) +

x*(-25 + 2*x)), x])/(E^x + 2*x), x] + 1296*Defer[Int][Defer[Int][x^3/(E^x*(-12 + x) + x*(-25 + 2*x)), x]/(-12*

E^x - 25*x + E^x*x + 2*x^2), x] - 648*Defer[Int][Defer[Int][x^3/(E^x*(-12 + x) + x*(-25 + 2*x)), x]/((-12 + x)

*(-12*E^x - 25*x + E^x*x + 2*x^2)), x] - 1458*Defer[Int][(x*Defer[Int][x^3/(E^x*(-12 + x) + x*(-25 + 2*x)), x]

)/(-12*E^x - 25*x + E^x*x + 2*x^2), x] + 108*Defer[Int][(x^2*Defer[Int][x^3/(E^x*(-12 + x) + x*(-25 + 2*x)), x

])/(-12*E^x - 25*x + E^x*x + 2*x^2), x] + 4*Defer[Int][Defer[Int][x^4/(E^x*(-12 + x) + x*(-25 + 2*x)), x]/(-12

+ x), x] - 8*Defer[Int][Defer[Int][x^4/(E^x*(-12 + x) + x*(-25 + 2*x)), x]/(E^x + 2*x), x] + 8*Defer[Int][(x*

Defer[Int][x^4/(E^x*(-12 + x) + x*(-25 + 2*x)), x])/(E^x + 2*x), x] - 96*Defer[Int][Defer[Int][x^4/(E^x*(-12 +

x) + x*(-25 + 2*x)), x]/(-12*E^x - 25*x + E^x*x + 2*x^2), x] + 48*Defer[Int][Defer[Int][x^4/(E^x*(-12 + x) +

x*(-25 + 2*x)), x]/((-12 + x)*(-12*E^x - 25*x + E^x*x + 2*x^2)), x] + 108*Defer[Int][(x*Defer[Int][x^4/(E^x*(-

12 + x) + x*(-25 + 2*x)), x])/(-12*E^x - 25*x + E^x*x + 2*x^2), x] - 8*Defer[Int][(x^2*Defer[Int][x^4/(E^x*(-1

2 + x) + x*(-25 + 2*x)), x])/(-12*E^x - 25*x + E^x*x + 2*x^2), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 x \left (x-\log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )\right ) \left (x \left (8 (-13+x) x^2+e^{2 x} (-25+2 x)+e^x \left (1-103 x+8 x^2\right )\right )+\left (-e^{2 x} (-12+x)+2 (25-2 x) x^2-e^x x (-49+4 x)\right ) \log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )\right )}{e^{2 x} (-12+x)+2 x^2 (-25+2 x)+e^x x (-49+4 x)} \, dx\\ &=2 \int \frac {x \left (x-\log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )\right ) \left (x \left (8 (-13+x) x^2+e^{2 x} (-25+2 x)+e^x \left (1-103 x+8 x^2\right )\right )+\left (-e^{2 x} (-12+x)+2 (25-2 x) x^2-e^x x (-49+4 x)\right ) \log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )\right )}{e^{2 x} (-12+x)+2 x^2 (-25+2 x)+e^x x (-49+4 x)} \, dx\\ &=2 \int \left (-\frac {2 (-1+x) x^2 \left (x-\log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )\right )}{e^x+2 x}+\frac {x^2 \left (-300+348 x-51 x^2+2 x^3\right ) \left (x-\log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )\right )}{(-12+x) \left (-12 e^x-25 x+e^x x+2 x^2\right )}+\frac {x \left (-25 x^2+2 x^3+37 x \log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )-3 x^2 \log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )-12 \log ^2\left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )+x \log ^2\left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )\right )}{-12+x}\right ) \, dx\\ &=2 \int \frac {x^2 \left (-300+348 x-51 x^2+2 x^3\right ) \left (x-\log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )\right )}{(-12+x) \left (-12 e^x-25 x+e^x x+2 x^2\right )} \, dx+2 \int \frac {x \left (-25 x^2+2 x^3+37 x \log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )-3 x^2 \log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )-12 \log ^2\left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )+x \log ^2\left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )\right )}{-12+x} \, dx-4 \int \frac {(-1+x) x^2 \left (x-\log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )\right )}{e^x+2 x} \, dx\\ &=2 \int \left (-\frac {144 \left (x-\log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )\right )}{-12 e^x-25 x+e^x x+2 x^2}-\frac {1728 \left (x-\log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )\right )}{(-12+x) \left (-12 e^x-25 x+e^x x+2 x^2\right )}-\frac {12 x \left (x-\log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )\right )}{-12 e^x-25 x+e^x x+2 x^2}+\frac {24 x^2 \left (x-\log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )\right )}{-12 e^x-25 x+e^x x+2 x^2}-\frac {27 x^3 \left (x-\log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )\right )}{-12 e^x-25 x+e^x x+2 x^2}+\frac {2 x^4 \left (x-\log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )\right )}{-12 e^x-25 x+e^x x+2 x^2}\right ) \, dx+2 \int \frac {x \left (-x^2 (-25+2 x)-(37-3 x) x \log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )-(-12+x) \log ^2\left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )\right )}{12-x} \, dx-4 \int \left (-\frac {x^2 \left (x-\log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )\right )}{e^x+2 x}+\frac {x^3 \left (x-\log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )\right )}{e^x+2 x}\right ) \, dx\\ &=2 \int \left (\frac {x^3 (-25+2 x)}{-12+x}-\frac {x^2 (-37+3 x) \log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )}{-12+x}+x \log ^2\left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )\right ) \, dx+4 \int \frac {x^2 \left (x-\log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )\right )}{e^x+2 x} \, dx-4 \int \frac {x^3 \left (x-\log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )\right )}{e^x+2 x} \, dx+4 \int \frac {x^4 \left (x-\log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )\right )}{-12 e^x-25 x+e^x x+2 x^2} \, dx-24 \int \frac {x \left (x-\log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )\right )}{-12 e^x-25 x+e^x x+2 x^2} \, dx+48 \int \frac {x^2 \left (x-\log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )\right )}{-12 e^x-25 x+e^x x+2 x^2} \, dx-54 \int \frac {x^3 \left (x-\log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )\right )}{-12 e^x-25 x+e^x x+2 x^2} \, dx-288 \int \frac {x-\log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )}{-12 e^x-25 x+e^x x+2 x^2} \, dx-3456 \int \frac {x-\log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )}{(-12+x) \left (-12 e^x-25 x+e^x x+2 x^2\right )} \, dx\\ &=2 \int \frac {x^3 (-25+2 x)}{-12+x} \, dx-2 \int \frac {x^2 (-37+3 x) \log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )}{-12+x} \, dx+2 \int x \log ^2\left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right ) \, dx+4 \int \left (\frac {x^3}{e^x+2 x}-\frac {x^2 \log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )}{e^x+2 x}\right ) \, dx-4 \int \left (\frac {x^4}{e^x+2 x}-\frac {x^3 \log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )}{e^x+2 x}\right ) \, dx+4 \int \left (\frac {x^5}{-12 e^x-25 x+e^x x+2 x^2}-\frac {x^4 \log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )}{-12 e^x-25 x+e^x x+2 x^2}\right ) \, dx-24 \int \left (\frac {x^2}{-12 e^x-25 x+e^x x+2 x^2}-\frac {x \log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )}{-12 e^x-25 x+e^x x+2 x^2}\right ) \, dx+48 \int \left (\frac {x^3}{-12 e^x-25 x+e^x x+2 x^2}-\frac {x^2 \log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )}{-12 e^x-25 x+e^x x+2 x^2}\right ) \, dx-54 \int \left (\frac {x^4}{-12 e^x-25 x+e^x x+2 x^2}-\frac {x^3 \log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )}{-12 e^x-25 x+e^x x+2 x^2}\right ) \, dx-288 \int \left (\frac {x}{-12 e^x-25 x+e^x x+2 x^2}-\frac {\log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )}{-12 e^x-25 x+e^x x+2 x^2}\right ) \, dx-3456 \int \left (\frac {x}{(-12+x) \left (-12 e^x-25 x+e^x x+2 x^2\right )}-\frac {\log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )}{(-12+x) \left (-12 e^x-25 x+e^x x+2 x^2\right )}\right ) \, dx\\ &=2 \int \left (-144-\frac {1728}{-12+x}-12 x-x^2+2 x^3\right ) \, dx+2 \int x \log ^2\left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right ) \, dx-2 \int \left (-12 \log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )-\frac {144 \log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )}{-12+x}-x \log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )+3 x^2 \log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )\right ) \, dx+4 \int \frac {x^3}{e^x+2 x} \, dx-4 \int \frac {x^4}{e^x+2 x} \, dx+4 \int \frac {x^5}{-12 e^x-25 x+e^x x+2 x^2} \, dx-4 \int \frac {x^2 \log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )}{e^x+2 x} \, dx+4 \int \frac {x^3 \log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )}{e^x+2 x} \, dx-4 \int \frac {x^4 \log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )}{-12 e^x-25 x+e^x x+2 x^2} \, dx-24 \int \frac {x^2}{-12 e^x-25 x+e^x x+2 x^2} \, dx+24 \int \frac {x \log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )}{-12 e^x-25 x+e^x x+2 x^2} \, dx+48 \int \frac {x^3}{-12 e^x-25 x+e^x x+2 x^2} \, dx-48 \int \frac {x^2 \log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )}{-12 e^x-25 x+e^x x+2 x^2} \, dx-54 \int \frac {x^4}{-12 e^x-25 x+e^x x+2 x^2} \, dx+54 \int \frac {x^3 \log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )}{-12 e^x-25 x+e^x x+2 x^2} \, dx-288 \int \frac {x}{-12 e^x-25 x+e^x x+2 x^2} \, dx+288 \int \frac {\log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )}{-12 e^x-25 x+e^x x+2 x^2} \, dx-3456 \int \frac {x}{(-12+x) \left (-12 e^x-25 x+e^x x+2 x^2\right )} \, dx+3456 \int \frac {\log \left (\frac {-e^x (-12+x)+(25-2 x) x}{6 \left (e^x+2 x\right )}\right )}{(-12+x) \left (-12 e^x-25 x+e^x x+2 x^2\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [F] time = 1.90, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {-208 x^5+16 x^6+e^{2 x} \left (-50 x^3+4 x^4\right )+e^x \left (2 x^3-206 x^4+16 x^5\right )+\left (308 x^4-24 x^5+e^{2 x} \left (74 x^2-6 x^3\right )+e^x \left (-2 x^2+304 x^3-24 x^4\right )\right ) \log \left (\frac {e^x (12-x)+25 x-2 x^2}{6 e^x+12 x}\right )+\left (-100 x^3+8 x^4+e^{2 x} \left (-24 x+2 x^2\right )+e^x \left (-98 x^2+8 x^3\right )\right ) \log ^2\left (\frac {e^x (12-x)+25 x-2 x^2}{6 e^x+12 x}\right )}{e^{2 x} (-12+x)-50 x^2+4 x^3+e^x \left (-49 x+4 x^2\right )} \, dx \end {gather*}

Veriﬁcation is not applicable to the result.

[In]

Integrate[(-208*x^5 + 16*x^6 + E^(2*x)*(-50*x^3 + 4*x^4) + E^x*(2*x^3 - 206*x^4 + 16*x^5) + (308*x^4 - 24*x^5

+ E^(2*x)*(74*x^2 - 6*x^3) + E^x*(-2*x^2 + 304*x^3 - 24*x^4))*Log[(E^x*(12 - x) + 25*x - 2*x^2)/(6*E^x + 12*x)

] + (-100*x^3 + 8*x^4 + E^(2*x)*(-24*x + 2*x^2) + E^x*(-98*x^2 + 8*x^3))*Log[(E^x*(12 - x) + 25*x - 2*x^2)/(6*

E^x + 12*x)]^2)/(E^(2*x)*(-12 + x) - 50*x^2 + 4*x^3 + E^x*(-49*x + 4*x^2)),x]

[Out]

Integrate[(-208*x^5 + 16*x^6 + E^(2*x)*(-50*x^3 + 4*x^4) + E^x*(2*x^3 - 206*x^4 + 16*x^5) + (308*x^4 - 24*x^5

+ E^(2*x)*(74*x^2 - 6*x^3) + E^x*(-2*x^2 + 304*x^3 - 24*x^4))*Log[(E^x*(12 - x) + 25*x - 2*x^2)/(6*E^x + 12*x)

] + (-100*x^3 + 8*x^4 + E^(2*x)*(-24*x + 2*x^2) + E^x*(-98*x^2 + 8*x^3))*Log[(E^x*(12 - x) + 25*x - 2*x^2)/(6*

E^x + 12*x)]^2)/(E^(2*x)*(-12 + x) - 50*x^2 + 4*x^3 + E^x*(-49*x + 4*x^2)), x]

________________________________________________________________________________________

fricas [B] time = 0.49, size = 67, normalized size = 2.09 \begin {gather*} x^{4} - 2 \, x^{3} \log \left (-\frac {2 \, x^{2} + {\left (x - 12\right )} e^{x} - 25 \, x}{6 \, {\left (2 \, x + e^{x}\right )}}\right ) + x^{2} \log \left (-\frac {2 \, x^{2} + {\left (x - 12\right )} e^{x} - 25 \, x}{6 \, {\left (2 \, x + e^{x}\right )}}\right )^{2} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x^2-24*x)*exp(x)^2+(8*x^3-98*x^2)*exp(x)+8*x^4-100*x^3)*log(((12-x)*exp(x)-2*x^2+25*x)/(6*exp(x

)+12*x))^2+((-6*x^3+74*x^2)*exp(x)^2+(-24*x^4+304*x^3-2*x^2)*exp(x)-24*x^5+308*x^4)*log(((12-x)*exp(x)-2*x^2+2

5*x)/(6*exp(x)+12*x))+(4*x^4-50*x^3)*exp(x)^2+(16*x^5-206*x^4+2*x^3)*exp(x)+16*x^6-208*x^5)/((x-12)*exp(x)^2+(

4*x^2-49*x)*exp(x)+4*x^3-50*x^2),x, algorithm="fricas")

[Out]

x^4 - 2*x^3*log(-1/6*(2*x^2 + (x - 12)*e^x - 25*x)/(2*x + e^x)) + x^2*log(-1/6*(2*x^2 + (x - 12)*e^x - 25*x)/(

2*x + e^x))^2

________________________________________________________________________________________

giac [B] time = 15.18, size = 71, normalized size = 2.22 \begin {gather*} x^{4} - 2 \, x^{3} \log \left (-\frac {2 \, x^{2} + x e^{x} - 25 \, x - 12 \, e^{x}}{6 \, {\left (2 \, x + e^{x}\right )}}\right ) + x^{2} \log \left (-\frac {2 \, x^{2} + x e^{x} - 25 \, x - 12 \, e^{x}}{6 \, {\left (2 \, x + e^{x}\right )}}\right )^{2} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x^2-24*x)*exp(x)^2+(8*x^3-98*x^2)*exp(x)+8*x^4-100*x^3)*log(((12-x)*exp(x)-2*x^2+25*x)/(6*exp(x

)+12*x))^2+((-6*x^3+74*x^2)*exp(x)^2+(-24*x^4+304*x^3-2*x^2)*exp(x)-24*x^5+308*x^4)*log(((12-x)*exp(x)-2*x^2+2

5*x)/(6*exp(x)+12*x))+(4*x^4-50*x^3)*exp(x)^2+(16*x^5-206*x^4+2*x^3)*exp(x)+16*x^6-208*x^5)/((x-12)*exp(x)^2+(

4*x^2-49*x)*exp(x)+4*x^3-50*x^2),x, algorithm="giac")

[Out]

x^4 - 2*x^3*log(-1/6*(2*x^2 + x*e^x - 25*x - 12*e^x)/(2*x + e^x)) + x^2*log(-1/6*(2*x^2 + x*e^x - 25*x - 12*e^

x)/(2*x + e^x))^2

________________________________________________________________________________________

maple [C] time = 0.45, size = 2492, normalized size = 77.88


method	result	size

risch	\(\text {Expression too large to display}\)	\(2492\)

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((((2*x^2-24*x)*exp(x)^2+(8*x^3-98*x^2)*exp(x)+8*x^4-100*x^3)*ln(((12-x)*exp(x)-2*x^2+25*x)/(6*exp(x)+12*x)

)^2+((-6*x^3+74*x^2)*exp(x)^2+(-24*x^4+304*x^3-2*x^2)*exp(x)-24*x^5+308*x^4)*ln(((12-x)*exp(x)-2*x^2+25*x)/(6*

exp(x)+12*x))+(4*x^4-50*x^3)*exp(x)^2+(16*x^5-206*x^4+2*x^3)*exp(x)+16*x^6-208*x^5)/((x-12)*exp(x)^2+(4*x^2-49

*x)*exp(x)+4*x^3-50*x^2),x,method=_RETURNVERBOSE)

[Out]

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

^2+(1/2*exp(x)-25/2)*x-6*exp(x)))^2-I*Pi*x^2*csgn(I/(1/2*exp(x)+x))*csgn(I*(x^2+(1/2*exp(x)-25/2)*x-6*exp(x)))

*csgn(I/(1/2*exp(x)+x)*(x^2+(1/2*exp(x)-25/2)*x-6*exp(x)))+I*Pi*x^2*csgn(I/(1/2*exp(x)+x))*csgn(I/(1/2*exp(x)+

x)*(x^2+(1/2*exp(x)-25/2)*x-6*exp(x)))^2+I*Pi*x^2*csgn(I*(x^2+(1/2*exp(x)-25/2)*x-6*exp(x)))*csgn(I/(1/2*exp(x

)+x)*(x^2+(1/2*exp(x)-25/2)*x-6*exp(x)))^2+I*Pi*x^2*csgn(I/(1/2*exp(x)+x)*(x^2+(1/2*exp(x)-25/2)*x-6*exp(x)))^

3+2*I*Pi*x^2-2*x^2*ln(2)-2*x^2*ln(3)-2*x^3)*ln(x^2+(1/2*exp(x)-25/2)*x-6*exp(x))+2*x^3*ln(1/2*exp(x)+x)+x^2*ln

(1/2*exp(x)+x)^2+x^2*ln(x^2+(1/2*exp(x)-25/2)*x-6*exp(x))^2-1/4*x^2*Pi^2*csgn(I/(1/2*exp(x)+x))^2*csgn(I/(1/2*

exp(x)+x)*(x^2+(1/2*exp(x)-25/2)*x-6*exp(x)))^4-1/2*x^2*Pi^2*csgn(I/(1/2*exp(x)+x))*csgn(I/(1/2*exp(x)+x)*(x^2

+(1/2*exp(x)-25/2)*x-6*exp(x)))^5-1/4*x^2*Pi^2*csgn(I*(x^2+(1/2*exp(x)-25/2)*x-6*exp(x)))^2*csgn(I/(1/2*exp(x)

+x)*(x^2+(1/2*exp(x)-25/2)*x-6*exp(x)))^4-1/2*x^2*Pi^2*csgn(I*(x^2+(1/2*exp(x)-25/2)*x-6*exp(x)))*csgn(I/(1/2*

exp(x)+x)*(x^2+(1/2*exp(x)-25/2)*x-6*exp(x)))^5+2*I*Pi*x^3*csgn(I/(1/2*exp(x)+x)*(x^2+(1/2*exp(x)-25/2)*x-6*ex

p(x)))^2-x^2*Pi^2*csgn(I/(1/2*exp(x)+x))*csgn(I/(1/2*exp(x)+x)*(x^2+(1/2*exp(x)-25/2)*x-6*exp(x)))^2-x^2*Pi^2*

csgn(I*(x^2+(1/2*exp(x)-25/2)*x-6*exp(x)))*csgn(I/(1/2*exp(x)+x)*(x^2+(1/2*exp(x)-25/2)*x-6*exp(x)))^2-2*I*Pi*

x^3+x^2*ln(3)^2+2*x^2*ln(2)*ln(1/2*exp(x)+x)+2*x^2*ln(3)*ln(1/2*exp(x)+x)+2*x^2*Pi^2*csgn(I/(1/2*exp(x)+x)*(x^

2+(1/2*exp(x)-25/2)*x-6*exp(x)))^2+2*ln(2)*ln(3)*x^2-2*I*Pi*ln(2)*x^2-2*I*Pi*ln(3)*x^2-2*I*Pi*x^2*ln(1/2*exp(x

)+x)-x^2*Pi^2*csgn(I/(1/2*exp(x)+x))*csgn(I*(x^2+(1/2*exp(x)-25/2)*x-6*exp(x)))*csgn(I/(1/2*exp(x)+x)*(x^2+(1/

2*exp(x)-25/2)*x-6*exp(x)))^3+x^2*Pi^2*csgn(I/(1/2*exp(x)+x))*csgn(I/(1/2*exp(x)+x)*(x^2+(1/2*exp(x)-25/2)*x-6

*exp(x)))^4+x^2*Pi^2*csgn(I*(x^2+(1/2*exp(x)-25/2)*x-6*exp(x)))*csgn(I/(1/2*exp(x)+x)*(x^2+(1/2*exp(x)-25/2)*x

-6*exp(x)))^4+I*Pi*ln(2)*x^2*csgn(I/(1/2*exp(x)+x))*csgn(I*(x^2+(1/2*exp(x)-25/2)*x-6*exp(x)))*csgn(I/(1/2*exp

(x)+x)*(x^2+(1/2*exp(x)-25/2)*x-6*exp(x)))+I*Pi*ln(3)*x^2*csgn(I/(1/2*exp(x)+x))*csgn(I*(x^2+(1/2*exp(x)-25/2)

*x-6*exp(x)))*csgn(I/(1/2*exp(x)+x)*(x^2+(1/2*exp(x)-25/2)*x-6*exp(x)))+I*Pi*x^2*csgn(I/(1/2*exp(x)+x))*csgn(I

*(x^2+(1/2*exp(x)-25/2)*x-6*exp(x)))*csgn(I/(1/2*exp(x)+x)*(x^2+(1/2*exp(x)-25/2)*x-6*exp(x)))*ln(1/2*exp(x)+x

)-I*Pi*ln(2)*x^2*csgn(I/(1/2*exp(x)+x)*(x^2+(1/2*exp(x)-25/2)*x-6*exp(x)))^3-I*Pi*ln(3)*x^2*csgn(I/(1/2*exp(x)

+x)*(x^2+(1/2*exp(x)-25/2)*x-6*exp(x)))^3-I*Pi*ln(2)*x^2*csgn(I/(1/2*exp(x)+x))*csgn(I/(1/2*exp(x)+x)*(x^2+(1/

2*exp(x)-25/2)*x-6*exp(x)))^2-I*Pi*ln(2)*x^2*csgn(I*(x^2+(1/2*exp(x)-25/2)*x-6*exp(x)))*csgn(I/(1/2*exp(x)+x)*

(x^2+(1/2*exp(x)-25/2)*x-6*exp(x)))^2-I*Pi*ln(3)*x^2*csgn(I/(1/2*exp(x)+x))*csgn(I/(1/2*exp(x)+x)*(x^2+(1/2*ex

p(x)-25/2)*x-6*exp(x)))^2-I*Pi*ln(3)*x^2*csgn(I*(x^2+(1/2*exp(x)-25/2)*x-6*exp(x)))*csgn(I/(1/2*exp(x)+x)*(x^2

+(1/2*exp(x)-25/2)*x-6*exp(x)))^2-I*Pi*x^2*csgn(I/(1/2*exp(x)+x))*csgn(I/(1/2*exp(x)+x)*(x^2+(1/2*exp(x)-25/2)

*x-6*exp(x)))^2*ln(1/2*exp(x)+x)-I*Pi*x^2*csgn(I*(x^2+(1/2*exp(x)-25/2)*x-6*exp(x)))*csgn(I/(1/2*exp(x)+x)*(x^

2+(1/2*exp(x)-25/2)*x-6*exp(x)))^2*ln(1/2*exp(x)+x)+I*Pi*x^3*csgn(I/(1/2*exp(x)+x))*csgn(I*(x^2+(1/2*exp(x)-25

/2)*x-6*exp(x)))*csgn(I/(1/2*exp(x)+x)*(x^2+(1/2*exp(x)-25/2)*x-6*exp(x)))-I*Pi*x^2*csgn(I/(1/2*exp(x)+x)*(x^2

+(1/2*exp(x)-25/2)*x-6*exp(x)))^3*ln(1/2*exp(x)+x)-I*Pi*x^3*csgn(I/(1/2*exp(x)+x)*(x^2+(1/2*exp(x)-25/2)*x-6*e

xp(x)))^3-x^2*Pi^2*csgn(I/(1/2*exp(x)+x)*(x^2+(1/2*exp(x)-25/2)*x-6*exp(x)))^3-x^2*Pi^2*csgn(I/(1/2*exp(x)+x)*

(x^2+(1/2*exp(x)-25/2)*x-6*exp(x)))^4+x^2*Pi^2*csgn(I/(1/2*exp(x)+x)*(x^2+(1/2*exp(x)-25/2)*x-6*exp(x)))^5-1/4

*x^2*Pi^2*csgn(I/(1/2*exp(x)+x)*(x^2+(1/2*exp(x)-25/2)*x-6*exp(x)))^6+x^2*Pi^2*csgn(I/(1/2*exp(x)+x))*csgn(I*(

x^2+(1/2*exp(x)-25/2)*x-6*exp(x)))*csgn(I/(1/2*exp(x)+x)*(x^2+(1/2*exp(x)-25/2)*x-6*exp(x)))-I*Pi*x^3*csgn(I/(

1/2*exp(x)+x))*csgn(I/(1/2*exp(x)+x)*(x^2+(1/2*exp(x)-25/2)*x-6*exp(x)))^2-I*Pi*x^3*csgn(I*(x^2+(1/2*exp(x)-25

/2)*x-6*exp(x)))*csgn(I/(1/2*exp(x)+x)*(x^2+(1/2*exp(x)-25/2)*x-6*exp(x)))^2-1/4*x^2*Pi^2*csgn(I/(1/2*exp(x)+x

))^2*csgn(I*(x^2+(1/2*exp(x)-25/2)*x-6*exp(x)))^2*csgn(I/(1/2*exp(x)+x)*(x^2+(1/2*exp(x)-25/2)*x-6*exp(x)))^2+

1/2*x^2*Pi^2*csgn(I/(1/2*exp(x)+x))^2*csgn(I*(x^2+(1/2*exp(x)-25/2)*x-6*exp(x)))*csgn(I/(1/2*exp(x)+x)*(x^2+(1

/2*exp(x)-25/2)*x-6*exp(x)))^3+1/2*x^2*Pi^2*csgn(I/(1/2*exp(x)+x))*csgn(I*(x^2+(1/2*exp(x)-25/2)*x-6*exp(x)))^

2*csgn(I/(1/2*exp(x)+x)*(x^2+(1/2*exp(x)-25/2)*x-6*exp(x)))^3+2*I*Pi*ln(3)*x^2*csgn(I/(1/2*exp(x)+x)*(x^2+(1/2

*exp(x)-25/2)*x-6*exp(x)))^2+2*I*Pi*ln(2)*x^2*csgn(I/(1/2*exp(x)+x)*(x^2+(1/2*exp(x)-25/2)*x-6*exp(x)))^2+2*I*

Pi*x^2*csgn(I/(1/2*exp(x)+x)*(x^2+(1/2*exp(x)-25/2)*x-6*exp(x)))^2*ln(1/2*exp(x)+x)

________________________________________________________________________________________

maxima [B] time = 0.78, size = 134, normalized size = 4.19 \begin {gather*} x^{4} + 2 \, x^{3} {\left (\log \relax (3) + \log \relax (2)\right )} + x^{2} \log \left (-2 \, x^{2} - {\left (x - 12\right )} e^{x} + 25 \, x\right )^{2} + x^{2} \log \left (2 \, x + e^{x}\right )^{2} + {\left (\log \relax (3)^{2} + 2 \, \log \relax (3) \log \relax (2) + \log \relax (2)^{2}\right )} x^{2} - 2 \, {\left (x^{3} + x^{2} {\left (\log \relax (3) + \log \relax (2)\right )} + x^{2} \log \left (2 \, x + e^{x}\right )\right )} \log \left (-2 \, x^{2} - {\left (x - 12\right )} e^{x} + 25 \, x\right ) + 2 \, {\left (x^{3} + x^{2} {\left (\log \relax (3) + \log \relax (2)\right )}\right )} \log \left (2 \, x + e^{x}\right ) \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x^2-24*x)*exp(x)^2+(8*x^3-98*x^2)*exp(x)+8*x^4-100*x^3)*log(((12-x)*exp(x)-2*x^2+25*x)/(6*exp(x

)+12*x))^2+((-6*x^3+74*x^2)*exp(x)^2+(-24*x^4+304*x^3-2*x^2)*exp(x)-24*x^5+308*x^4)*log(((12-x)*exp(x)-2*x^2+2

5*x)/(6*exp(x)+12*x))+(4*x^4-50*x^3)*exp(x)^2+(16*x^5-206*x^4+2*x^3)*exp(x)+16*x^6-208*x^5)/((x-12)*exp(x)^2+(

4*x^2-49*x)*exp(x)+4*x^3-50*x^2),x, algorithm="maxima")

[Out]

x^4 + 2*x^3*(log(3) + log(2)) + x^2*log(-2*x^2 - (x - 12)*e^x + 25*x)^2 + x^2*log(2*x + e^x)^2 + (log(3)^2 + 2

*log(3)*log(2) + log(2)^2)*x^2 - 2*(x^3 + x^2*(log(3) + log(2)) + x^2*log(2*x + e^x))*log(-2*x^2 - (x - 12)*e^

x + 25*x) + 2*(x^3 + x^2*(log(3) + log(2)))*log(2*x + e^x)

________________________________________________________________________________________

mupad [B] time = 2.41, size = 38, normalized size = 1.19 \begin {gather*} x^2\,{\left (x-\ln \left (-\frac {{\mathrm {e}}^x\,\left (x-12\right )-25\,x+2\,x^2}{12\,x+6\,{\mathrm {e}}^x}\right )\right )}^2 \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(2*x)*(50*x^3 - 4*x^4) - exp(x)*(2*x^3 - 206*x^4 + 16*x^5) + log(-(exp(x)*(x - 12) - 25*x + 2*x^2)/(1

2*x + 6*exp(x)))^2*(exp(2*x)*(24*x - 2*x^2) + exp(x)*(98*x^2 - 8*x^3) + 100*x^3 - 8*x^4) + 208*x^5 - 16*x^6 +

log(-(exp(x)*(x - 12) - 25*x + 2*x^2)/(12*x + 6*exp(x)))*(exp(x)*(2*x^2 - 304*x^3 + 24*x^4) - exp(2*x)*(74*x^2

- 6*x^3) - 308*x^4 + 24*x^5))/(exp(2*x)*(x - 12) - exp(x)*(49*x - 4*x^2) - 50*x^2 + 4*x^3),x)

[Out]

x^2*(x - log(-(exp(x)*(x - 12) - 25*x + 2*x^2)/(12*x + 6*exp(x))))^2

________________________________________________________________________________________

sympy [B] time = 0.66, size = 63, normalized size = 1.97 \begin {gather*} x^{4} - 2 x^{3} \log {\left (\frac {- 2 x^{2} + 25 x + \left (12 - x\right ) e^{x}}{12 x + 6 e^{x}} \right )} + x^{2} \log {\left (\frac {- 2 x^{2} + 25 x + \left (12 - x\right ) e^{x}}{12 x + 6 e^{x}} \right )}^{2} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x**2-24*x)*exp(x)**2+(8*x**3-98*x**2)*exp(x)+8*x**4-100*x**3)*ln(((12-x)*exp(x)-2*x**2+25*x)/(6

*exp(x)+12*x))**2+((-6*x**3+74*x**2)*exp(x)**2+(-24*x**4+304*x**3-2*x**2)*exp(x)-24*x**5+308*x**4)*ln(((12-x)*

exp(x)-2*x**2+25*x)/(6*exp(x)+12*x))+(4*x**4-50*x**3)*exp(x)**2+(16*x**5-206*x**4+2*x**3)*exp(x)+16*x**6-208*x

**5)/((x-12)*exp(x)**2+(4*x**2-49*x)*exp(x)+4*x**3-50*x**2),x)

[Out]

x**4 - 2*x**3*log((-2*x**2 + 25*x + (12 - x)*exp(x))/(12*x + 6*exp(x))) + x**2*log((-2*x**2 + 25*x + (12 - x)*

exp(x))/(12*x + 6*exp(x)))**2

________________________________________________________________________________________

[next] [prev] [prev-tail] [front] [up]