3.75.2 \(\int \frac {e^{12} (128-320 x+352 x^2-240 x^3+120 x^4-44 x^5+10 x^6-x^7)+e^{\frac {1+4 e^3 x+e^6 (-8 x+14 x^2-2 x^3)+e^9 (-16 x^2+20 x^3-4 x^4)+e^{12} (16 x^2-40 x^3+33 x^4-10 x^5+x^6)}{e^{12} (16-32 x+24 x^2-8 x^3+x^4)}} (-4 x+e^3 (-8 x-12 x^2)+e^6 (16 x-32 x^2-16 x^3+2 x^4)+e^9 (64 x^2-88 x^3+12 x^4)+e^{12} (32-80 x+16 x^2+168 x^3-214 x^4+99 x^5-22 x^6+2 x^7))}{e^{12} (-32 x^2+80 x^3-80 x^4+40 x^5-10 x^6+x^7)} \, dx\)

Optimal. Leaf size=34 \[ \frac {4+e^{\left (x-\frac {\left (\frac {1}{e^3}+x\right )^2}{(-2+x)^2}\right )^2}-2 x-x^2}{x} \]

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Rubi [F]  time = 13.21, 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 {e^{12} \left (128-320 x+352 x^2-240 x^3+120 x^4-44 x^5+10 x^6-x^7\right )+\exp \left (\frac {1+4 e^3 x+e^6 \left (-8 x+14 x^2-2 x^3\right )+e^9 \left (-16 x^2+20 x^3-4 x^4\right )+e^{12} \left (16 x^2-40 x^3+33 x^4-10 x^5+x^6\right )}{e^{12} \left (16-32 x+24 x^2-8 x^3+x^4\right )}\right ) \left (-4 x+e^3 \left (-8 x-12 x^2\right )+e^6 \left (16 x-32 x^2-16 x^3+2 x^4\right )+e^9 \left (64 x^2-88 x^3+12 x^4\right )+e^{12} \left (32-80 x+16 x^2+168 x^3-214 x^4+99 x^5-22 x^6+2 x^7\right )\right )}{e^{12} \left (-32 x^2+80 x^3-80 x^4+40 x^5-10 x^6+x^7\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^12*(128 - 320*x + 352*x^2 - 240*x^3 + 120*x^4 - 44*x^5 + 10*x^6 - x^7) + E^((1 + 4*E^3*x + E^6*(-8*x +
14*x^2 - 2*x^3) + E^9*(-16*x^2 + 20*x^3 - 4*x^4) + E^12*(16*x^2 - 40*x^3 + 33*x^4 - 10*x^5 + x^6))/(E^12*(16 -
32*x + 24*x^2 - 8*x^3 + x^4)))*(-4*x + E^3*(-8*x - 12*x^2) + E^6*(16*x - 32*x^2 - 16*x^3 + 2*x^4) + E^9*(64*x
^2 - 88*x^3 + 12*x^4) + E^12*(32 - 80*x + 16*x^2 + 168*x^3 - 214*x^4 + 99*x^5 - 22*x^6 + 2*x^7)))/(E^12*(-32*x
^2 + 80*x^3 - 80*x^4 + 40*x^5 - 10*x^6 + x^7)),x]

[Out]

4/x - x + (2*Defer[Int][E^(12 + (1 + 2*E^3*(1 - 2*E^3)*x + 5*E^6*x^2 - E^6*x^3)^2/(E^12*(-2 + x)^4)), x])/E^12
- (2*(1 + 2*E^3)^4*Defer[Int][E^((1 + 2*E^3*(1 - 2*E^3)*x + 5*E^6*x^2 - E^6*x^3)^2/(E^12*(-2 + x)^4))/(-2 + x
)^5, x])/E^12 + ((1 - 4*E^3)*(1 + 2*E^3)^3*Defer[Int][E^((1 + 2*E^3*(1 - 2*E^3)*x + 5*E^6*x^2 - E^6*x^3)^2/(E^
12*(-2 + x)^4))/(-2 + x)^4, x])/E^12 - ((1 + 2*E^3)^2*(1 - 2*E^3 - 4*E^6)*Defer[Int][E^((1 + 2*E^3*(1 - 2*E^3)
*x + 5*E^6*x^2 - E^6*x^3)^2/(E^12*(-2 + x)^4))/(-2 + x)^3, x])/(2*E^12) + ((1 + 2*E^3 - 4*E^6 + 16*E^12)*Defer
[Int][E^((1 + 2*E^3*(1 - 2*E^3)*x + 5*E^6*x^2 - E^6*x^3)^2/(E^12*(-2 + x)^4))/(-2 + x)^2, x])/(4*E^12) - ((1 +
2*E^3 - 4*E^6 + 16*E^12)*Defer[Int][E^((1 + 2*E^3*(1 - 2*E^3)*x + 5*E^6*x^2 - E^6*x^3)^2/(E^12*(-2 + x)^4))/(
-2 + x), x])/(8*E^12) - Defer[Int][E^(12 + (1 + 2*E^3*(1 - 2*E^3)*x + 5*E^6*x^2 - E^6*x^3)^2/(E^12*(-2 + x)^4)
)/x^2, x]/E^12 + ((1 + 2*E^3 - 4*E^6)*Defer[Int][E^((1 + 2*E^3*(1 - 2*E^3)*x + 5*E^6*x^2 - E^6*x^3)^2/(E^12*(-
2 + x)^4))/x, x])/(8*E^12)

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {e^{12} \left (128-320 x+352 x^2-240 x^3+120 x^4-44 x^5+10 x^6-x^7\right )+\exp \left (\frac {1+4 e^3 x+e^6 \left (-8 x+14 x^2-2 x^3\right )+e^9 \left (-16 x^2+20 x^3-4 x^4\right )+e^{12} \left (16 x^2-40 x^3+33 x^4-10 x^5+x^6\right )}{e^{12} \left (16-32 x+24 x^2-8 x^3+x^4\right )}\right ) \left (-4 x+e^3 \left (-8 x-12 x^2\right )+e^6 \left (16 x-32 x^2-16 x^3+2 x^4\right )+e^9 \left (64 x^2-88 x^3+12 x^4\right )+e^{12} \left (32-80 x+16 x^2+168 x^3-214 x^4+99 x^5-22 x^6+2 x^7\right )\right )}{-32 x^2+80 x^3-80 x^4+40 x^5-10 x^6+x^7} \, dx}{e^{12}}\\ &=\frac {\int \frac {-e^{12} \left (4+x^2\right )+\frac {\exp \left (\frac {\left (1+2 e^3 x-e^6 x \left (4-5 x+x^2\right )\right )^2}{e^{12} (-2+x)^4}\right ) \left (-4 x-4 e^3 x (2+3 x)+4 e^9 x^2 \left (16-22 x+3 x^2\right )+2 e^6 x \left (8-16 x-8 x^2+x^3\right )+e^{12} \left (32-80 x+16 x^2+168 x^3-214 x^4+99 x^5-22 x^6+2 x^7\right )\right )}{(-2+x)^5}}{x^2} \, dx}{e^{12}}\\ &=\frac {\int \left (-\frac {e^{12} \left (4+x^2\right )}{x^2}+\frac {\exp \left (\frac {\left (1+2 e^3 \left (1-2 e^3\right ) x+5 e^6 x^2-e^6 x^3\right )^2}{e^{12} (-2+x)^4}\right ) \left (-32 e^{12}+4 \left (1+2 e^3 \left (1-2 e^3+10 e^9\right )\right ) x+12 e^3 \left (1-\frac {4}{3} e^3 \left (-2+4 e^3+e^6\right )\right ) x^2+16 e^6 \left (1-\frac {1}{2} e^3 \left (-11+21 e^3\right )\right ) x^3-2 e^6 \left (1+6 e^3-107 e^6\right ) x^4-99 e^{12} x^5+22 e^{12} x^6-2 e^{12} x^7\right )}{(2-x)^5 x^2}\right ) \, dx}{e^{12}}\\ &=\frac {\int \frac {\exp \left (\frac {\left (1+2 e^3 \left (1-2 e^3\right ) x+5 e^6 x^2-e^6 x^3\right )^2}{e^{12} (-2+x)^4}\right ) \left (-32 e^{12}+4 \left (1+2 e^3 \left (1-2 e^3+10 e^9\right )\right ) x+12 e^3 \left (1-\frac {4}{3} e^3 \left (-2+4 e^3+e^6\right )\right ) x^2+16 e^6 \left (1-\frac {1}{2} e^3 \left (-11+21 e^3\right )\right ) x^3-2 e^6 \left (1+6 e^3-107 e^6\right ) x^4-99 e^{12} x^5+22 e^{12} x^6-2 e^{12} x^7\right )}{(2-x)^5 x^2} \, dx}{e^{12}}-\int \frac {4+x^2}{x^2} \, dx\\ &=\frac {\int \frac {\exp \left (\frac {\left (1+2 e^3 \left (1-2 e^3\right ) x+5 e^6 x^2-e^6 x^3\right )^2}{e^{12} (-2+x)^4}\right ) \left (4 x+4 e^3 x (2+3 x)-4 e^9 x^2 \left (16-22 x+3 x^2\right )-2 e^6 x \left (8-16 x-8 x^2+x^3\right )-e^{12} \left (32-80 x+16 x^2+168 x^3-214 x^4+99 x^5-22 x^6+2 x^7\right )\right )}{(2-x)^5 x^2} \, dx}{e^{12}}-\int \left (1+\frac {4}{x^2}\right ) \, dx\\ &=\frac {4}{x}-x+\frac {\int \left (2 \exp \left (12+\frac {\left (1+2 e^3 \left (1-2 e^3\right ) x+5 e^6 x^2-e^6 x^3\right )^2}{e^{12} (-2+x)^4}\right )-\frac {2 \exp \left (\frac {\left (1+2 e^3 \left (1-2 e^3\right ) x+5 e^6 x^2-e^6 x^3\right )^2}{e^{12} (-2+x)^4}\right ) \left (1+2 e^3\right )^4}{(-2+x)^5}-\frac {\exp \left (\frac {\left (1+2 e^3 \left (1-2 e^3\right ) x+5 e^6 x^2-e^6 x^3\right )^2}{e^{12} (-2+x)^4}\right ) \left (1+2 e^3\right )^3 \left (-1+4 e^3\right )}{(-2+x)^4}+\frac {\exp \left (\frac {\left (1+2 e^3 \left (1-2 e^3\right ) x+5 e^6 x^2-e^6 x^3\right )^2}{e^{12} (-2+x)^4}\right ) \left (1+2 e^3\right )^2 \left (-1+2 e^3+4 e^6\right )}{2 (-2+x)^3}+\frac {\exp \left (\frac {\left (1+2 e^3 \left (1-2 e^3\right ) x+5 e^6 x^2-e^6 x^3\right )^2}{e^{12} (-2+x)^4}\right ) \left (1+2 e^3-4 e^6+16 e^{12}\right )}{4 (-2+x)^2}+\frac {\exp \left (\frac {\left (1+2 e^3 \left (1-2 e^3\right ) x+5 e^6 x^2-e^6 x^3\right )^2}{e^{12} (-2+x)^4}\right ) \left (-1-2 e^3+4 e^6-16 e^{12}\right )}{8 (-2+x)}-\frac {\exp \left (12+\frac {\left (1+2 e^3 \left (1-2 e^3\right ) x+5 e^6 x^2-e^6 x^3\right )^2}{e^{12} (-2+x)^4}\right )}{x^2}+\frac {\exp \left (\frac {\left (1+2 e^3 \left (1-2 e^3\right ) x+5 e^6 x^2-e^6 x^3\right )^2}{e^{12} (-2+x)^4}\right ) \left (1+2 e^3-4 e^6\right )}{8 x}\right ) \, dx}{e^{12}}\\ &=\frac {4}{x}-x-\frac {\int \frac {\exp \left (12+\frac {\left (1+2 e^3 \left (1-2 e^3\right ) x+5 e^6 x^2-e^6 x^3\right )^2}{e^{12} (-2+x)^4}\right )}{x^2} \, dx}{e^{12}}+\frac {2 \int \exp \left (12+\frac {\left (1+2 e^3 \left (1-2 e^3\right ) x+5 e^6 x^2-e^6 x^3\right )^2}{e^{12} (-2+x)^4}\right ) \, dx}{e^{12}}+\frac {\left (\left (1-4 e^3\right ) \left (1+2 e^3\right )^3\right ) \int \frac {\exp \left (\frac {\left (1+2 e^3 \left (1-2 e^3\right ) x+5 e^6 x^2-e^6 x^3\right )^2}{e^{12} (-2+x)^4}\right )}{(-2+x)^4} \, dx}{e^{12}}-\frac {\left (2 \left (1+2 e^3\right )^4\right ) \int \frac {\exp \left (\frac {\left (1+2 e^3 \left (1-2 e^3\right ) x+5 e^6 x^2-e^6 x^3\right )^2}{e^{12} (-2+x)^4}\right )}{(-2+x)^5} \, dx}{e^{12}}-\frac {\left (\left (1+2 e^3\right )^2 \left (1-2 e^3-4 e^6\right )\right ) \int \frac {\exp \left (\frac {\left (1+2 e^3 \left (1-2 e^3\right ) x+5 e^6 x^2-e^6 x^3\right )^2}{e^{12} (-2+x)^4}\right )}{(-2+x)^3} \, dx}{2 e^{12}}+\frac {\left (1+2 e^3-4 e^6\right ) \int \frac {\exp \left (\frac {\left (1+2 e^3 \left (1-2 e^3\right ) x+5 e^6 x^2-e^6 x^3\right )^2}{e^{12} (-2+x)^4}\right )}{x} \, dx}{8 e^{12}}-\frac {\left (1+2 e^3-4 e^6+16 e^{12}\right ) \int \frac {\exp \left (\frac {\left (1+2 e^3 \left (1-2 e^3\right ) x+5 e^6 x^2-e^6 x^3\right )^2}{e^{12} (-2+x)^4}\right )}{-2+x} \, dx}{8 e^{12}}+\frac {\left (1+2 e^3-4 e^6+16 e^{12}\right ) \int \frac {\exp \left (\frac {\left (1+2 e^3 \left (1-2 e^3\right ) x+5 e^6 x^2-e^6 x^3\right )^2}{e^{12} (-2+x)^4}\right )}{(-2+x)^2} \, dx}{4 e^{12}}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.53, size = 46, normalized size = 1.35 \begin {gather*} \frac {4+e^{\frac {\left (1+2 e^3 x-e^6 x \left (4-5 x+x^2\right )\right )^2}{e^{12} (-2+x)^4}}-x^2}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^12*(128 - 320*x + 352*x^2 - 240*x^3 + 120*x^4 - 44*x^5 + 10*x^6 - x^7) + E^((1 + 4*E^3*x + E^6*(-
8*x + 14*x^2 - 2*x^3) + E^9*(-16*x^2 + 20*x^3 - 4*x^4) + E^12*(16*x^2 - 40*x^3 + 33*x^4 - 10*x^5 + x^6))/(E^12
*(16 - 32*x + 24*x^2 - 8*x^3 + x^4)))*(-4*x + E^3*(-8*x - 12*x^2) + E^6*(16*x - 32*x^2 - 16*x^3 + 2*x^4) + E^9
*(64*x^2 - 88*x^3 + 12*x^4) + E^12*(32 - 80*x + 16*x^2 + 168*x^3 - 214*x^4 + 99*x^5 - 22*x^6 + 2*x^7)))/(E^12*
(-32*x^2 + 80*x^3 - 80*x^4 + 40*x^5 - 10*x^6 + x^7)),x]

[Out]

(4 + E^((1 + 2*E^3*x - E^6*x*(4 - 5*x + x^2))^2/(E^12*(-2 + x)^4)) - x^2)/x

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fricas [B]  time = 0.56, size = 104, normalized size = 3.06 \begin {gather*} -\frac {x^{2} - e^{\left (\frac {{\left ({\left (x^{6} - 10 \, x^{5} + 33 \, x^{4} - 40 \, x^{3} + 16 \, x^{2}\right )} e^{12} - 4 \, {\left (x^{4} - 5 \, x^{3} + 4 \, x^{2}\right )} e^{9} - 2 \, {\left (x^{3} - 7 \, x^{2} + 4 \, x\right )} e^{6} + 4 \, x e^{3} + 1\right )} e^{\left (-12\right )}}{x^{4} - 8 \, x^{3} + 24 \, x^{2} - 32 \, x + 16}\right )} - 4}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x^7-22*x^6+99*x^5-214*x^4+168*x^3+16*x^2-80*x+32)*exp(3)^4+(12*x^4-88*x^3+64*x^2)*exp(3)^3+(2*x
^4-16*x^3-32*x^2+16*x)*exp(3)^2+(-12*x^2-8*x)*exp(3)-4*x)*exp(((x^6-10*x^5+33*x^4-40*x^3+16*x^2)*exp(3)^4+(-4*
x^4+20*x^3-16*x^2)*exp(3)^3+(-2*x^3+14*x^2-8*x)*exp(3)^2+4*x*exp(3)+1)/(x^4-8*x^3+24*x^2-32*x+16)/exp(3)^4)+(-
x^7+10*x^6-44*x^5+120*x^4-240*x^3+352*x^2-320*x+128)*exp(3)^4)/(x^7-10*x^6+40*x^5-80*x^4+80*x^3-32*x^2)/exp(3)
^4,x, algorithm="fricas")

[Out]

-(x^2 - e^(((x^6 - 10*x^5 + 33*x^4 - 40*x^3 + 16*x^2)*e^12 - 4*(x^4 - 5*x^3 + 4*x^2)*e^9 - 2*(x^3 - 7*x^2 + 4*
x)*e^6 + 4*x*e^3 + 1)*e^(-12)/(x^4 - 8*x^3 + 24*x^2 - 32*x + 16)) - 4)/x

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giac [B]  time = 12.57, size = 166, normalized size = 4.88 \begin {gather*} -\frac {{\left (x^{2} e^{12} - 4 \, e^{12} - e^{\left (\frac {1}{16} \, {\left (48 \, e^{12} + 1\right )} e^{\left (-12\right )} + \frac {16 \, x^{6} e^{12} - 160 \, x^{5} e^{12} + 528 \, x^{4} e^{12} - 64 \, x^{4} e^{9} - x^{4} - 640 \, x^{3} e^{12} + 320 \, x^{3} e^{9} - 32 \, x^{3} e^{6} + 8 \, x^{3} + 256 \, x^{2} e^{12} - 256 \, x^{2} e^{9} + 224 \, x^{2} e^{6} - 24 \, x^{2} - 128 \, x e^{6} + 64 \, x e^{3} + 32 \, x}{16 \, {\left (x^{4} e^{12} - 8 \, x^{3} e^{12} + 24 \, x^{2} e^{12} - 32 \, x e^{12} + 16 \, e^{12}\right )}} + 9\right )}\right )} e^{\left (-12\right )}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x^7-22*x^6+99*x^5-214*x^4+168*x^3+16*x^2-80*x+32)*exp(3)^4+(12*x^4-88*x^3+64*x^2)*exp(3)^3+(2*x
^4-16*x^3-32*x^2+16*x)*exp(3)^2+(-12*x^2-8*x)*exp(3)-4*x)*exp(((x^6-10*x^5+33*x^4-40*x^3+16*x^2)*exp(3)^4+(-4*
x^4+20*x^3-16*x^2)*exp(3)^3+(-2*x^3+14*x^2-8*x)*exp(3)^2+4*x*exp(3)+1)/(x^4-8*x^3+24*x^2-32*x+16)/exp(3)^4)+(-
x^7+10*x^6-44*x^5+120*x^4-240*x^3+352*x^2-320*x+128)*exp(3)^4)/(x^7-10*x^6+40*x^5-80*x^4+80*x^3-32*x^2)/exp(3)
^4,x, algorithm="giac")

[Out]

-(x^2*e^12 - 4*e^12 - e^(1/16*(48*e^12 + 1)*e^(-12) + 1/16*(16*x^6*e^12 - 160*x^5*e^12 + 528*x^4*e^12 - 64*x^4
*e^9 - x^4 - 640*x^3*e^12 + 320*x^3*e^9 - 32*x^3*e^6 + 8*x^3 + 256*x^2*e^12 - 256*x^2*e^9 + 224*x^2*e^6 - 24*x
^2 - 128*x*e^6 + 64*x*e^3 + 32*x)/(x^4*e^12 - 8*x^3*e^12 + 24*x^2*e^12 - 32*x*e^12 + 16*e^12) + 9))*e^(-12)/x

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maple [F]  time = 180.00, size = 0, normalized size = 0.00 \[\int \frac {\left (\left (\left (2 x^{7}-22 x^{6}+99 x^{5}-214 x^{4}+168 x^{3}+16 x^{2}-80 x +32\right ) {\mathrm e}^{12}+\left (12 x^{4}-88 x^{3}+64 x^{2}\right ) {\mathrm e}^{9}+\left (2 x^{4}-16 x^{3}-32 x^{2}+16 x \right ) {\mathrm e}^{6}+\left (-12 x^{2}-8 x \right ) {\mathrm e}^{3}-4 x \right ) {\mathrm e}^{\frac {\left (\left (x^{6}-10 x^{5}+33 x^{4}-40 x^{3}+16 x^{2}\right ) {\mathrm e}^{12}+\left (-4 x^{4}+20 x^{3}-16 x^{2}\right ) {\mathrm e}^{9}+\left (-2 x^{3}+14 x^{2}-8 x \right ) {\mathrm e}^{6}+4 x \,{\mathrm e}^{3}+1\right ) {\mathrm e}^{-12}}{x^{4}-8 x^{3}+24 x^{2}-32 x +16}}+\left (-x^{7}+10 x^{6}-44 x^{5}+120 x^{4}-240 x^{3}+352 x^{2}-320 x +128\right ) {\mathrm e}^{12}\right ) {\mathrm e}^{-12}}{x^{7}-10 x^{6}+40 x^{5}-80 x^{4}+80 x^{3}-32 x^{2}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((2*x^7-22*x^6+99*x^5-214*x^4+168*x^3+16*x^2-80*x+32)*exp(3)^4+(12*x^4-88*x^3+64*x^2)*exp(3)^3+(2*x^4-16*
x^3-32*x^2+16*x)*exp(3)^2+(-12*x^2-8*x)*exp(3)-4*x)*exp(((x^6-10*x^5+33*x^4-40*x^3+16*x^2)*exp(3)^4+(-4*x^4+20
*x^3-16*x^2)*exp(3)^3+(-2*x^3+14*x^2-8*x)*exp(3)^2+4*x*exp(3)+1)/(x^4-8*x^3+24*x^2-32*x+16)/exp(3)^4)+(-x^7+10
*x^6-44*x^5+120*x^4-240*x^3+352*x^2-320*x+128)*exp(3)^4)/(x^7-10*x^6+40*x^5-80*x^4+80*x^3-32*x^2)/exp(3)^4,x)

[Out]

int((((2*x^7-22*x^6+99*x^5-214*x^4+168*x^3+16*x^2-80*x+32)*exp(3)^4+(12*x^4-88*x^3+64*x^2)*exp(3)^3+(2*x^4-16*
x^3-32*x^2+16*x)*exp(3)^2+(-12*x^2-8*x)*exp(3)-4*x)*exp(((x^6-10*x^5+33*x^4-40*x^3+16*x^2)*exp(3)^4+(-4*x^4+20
*x^3-16*x^2)*exp(3)^3+(-2*x^3+14*x^2-8*x)*exp(3)^2+4*x*exp(3)+1)/(x^4-8*x^3+24*x^2-32*x+16)/exp(3)^4)+(-x^7+10
*x^6-44*x^5+120*x^4-240*x^3+352*x^2-320*x+128)*exp(3)^4)/(x^7-10*x^6+40*x^5-80*x^4+80*x^3-32*x^2)/exp(3)^4,x)

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maxima [B]  time = 1.78, size = 697, normalized size = 20.50 \begin {gather*} -\frac {1}{3} \, {\left ({\left (3 \, x - \frac {8 \, {\left (15 \, x^{3} - 75 \, x^{2} + 130 \, x - 77\right )}}{x^{4} - 8 \, x^{3} + 24 \, x^{2} - 32 \, x + 16} + 30 \, \log \left (x - 2\right )\right )} e^{12} - 2 \, {\left (\frac {2 \, {\left (15 \, x^{4} - 105 \, x^{3} + 260 \, x^{2} - 250 \, x + 48\right )}}{x^{5} - 8 \, x^{4} + 24 \, x^{3} - 32 \, x^{2} + 16 \, x} + 15 \, \log \left (x - 2\right ) - 15 \, \log \relax (x)\right )} e^{12} + 10 \, {\left (\frac {4 \, {\left (6 \, x^{3} - 27 \, x^{2} + 44 \, x - 25\right )}}{x^{4} - 8 \, x^{3} + 24 \, x^{2} - 32 \, x + 16} - 3 \, \log \left (x - 2\right )\right )} e^{12} + 10 \, {\left (\frac {2 \, {\left (3 \, x^{3} - 21 \, x^{2} + 52 \, x - 50\right )}}{x^{4} - 8 \, x^{3} + 24 \, x^{2} - 32 \, x + 16} + 3 \, \log \left (x - 2\right ) - 3 \, \log \relax (x)\right )} e^{12} - \frac {132 \, {\left (x^{3} - 3 \, x^{2} + 4 \, x - 2\right )} e^{12}}{x^{4} - 8 \, x^{3} + 24 \, x^{2} - 32 \, x + 16} + \frac {60 \, {\left (3 \, x^{2} - 4 \, x + 2\right )} e^{12}}{x^{4} - 8 \, x^{3} + 24 \, x^{2} - 32 \, x + 16} - \frac {120 \, {\left (2 \, x - 1\right )} e^{12}}{x^{4} - 8 \, x^{3} + 24 \, x^{2} - 32 \, x + 16} + \frac {264 \, e^{12}}{x^{4} - 8 \, x^{3} + 24 \, x^{2} - 32 \, x + 16} - \frac {3 \, e^{\left (x^{2} - 2 \, x + \frac {1}{x^{4} e^{12} - 8 \, x^{3} e^{12} + 24 \, x^{2} e^{12} - 32 \, x e^{12} + 16 \, e^{12}} + \frac {8}{x^{4} e^{9} - 8 \, x^{3} e^{9} + 24 \, x^{2} e^{9} - 32 \, x e^{9} + 16 \, e^{9}} + \frac {24}{x^{4} e^{6} - 8 \, x^{3} e^{6} + 24 \, x^{2} e^{6} - 32 \, x e^{6} + 16 \, e^{6}} + \frac {32}{x^{4} e^{3} - 8 \, x^{3} e^{3} + 24 \, x^{2} e^{3} - 32 \, x e^{3} + 16 \, e^{3}} + \frac {16}{x^{4} - 8 \, x^{3} + 24 \, x^{2} - 32 \, x + 16} + \frac {4}{x^{3} e^{9} - 6 \, x^{2} e^{9} + 12 \, x e^{9} - 8 \, e^{9}} + \frac {24}{x^{3} e^{6} - 6 \, x^{2} e^{6} + 12 \, x e^{6} - 8 \, e^{6}} + \frac {48}{x^{3} e^{3} - 6 \, x^{2} e^{3} + 12 \, x e^{3} - 8 \, e^{3}} + \frac {32}{x^{3} - 6 \, x^{2} + 12 \, x - 8} + \frac {2}{x^{2} e^{6} - 4 \, x e^{6} + 4 \, e^{6}} + \frac {8}{x^{2} e^{3} - 4 \, x e^{3} + 4 \, e^{3}} + \frac {8}{x^{2} - 4 \, x + 4} - \frac {2}{x e^{6} - 2 \, e^{6}} - \frac {12}{x e^{3} - 2 \, e^{3}} - \frac {16}{x - 2} - 4 \, e^{\left (-3\right )} + 5\right )}}{x}\right )} e^{\left (-12\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x^7-22*x^6+99*x^5-214*x^4+168*x^3+16*x^2-80*x+32)*exp(3)^4+(12*x^4-88*x^3+64*x^2)*exp(3)^3+(2*x
^4-16*x^3-32*x^2+16*x)*exp(3)^2+(-12*x^2-8*x)*exp(3)-4*x)*exp(((x^6-10*x^5+33*x^4-40*x^3+16*x^2)*exp(3)^4+(-4*
x^4+20*x^3-16*x^2)*exp(3)^3+(-2*x^3+14*x^2-8*x)*exp(3)^2+4*x*exp(3)+1)/(x^4-8*x^3+24*x^2-32*x+16)/exp(3)^4)+(-
x^7+10*x^6-44*x^5+120*x^4-240*x^3+352*x^2-320*x+128)*exp(3)^4)/(x^7-10*x^6+40*x^5-80*x^4+80*x^3-32*x^2)/exp(3)
^4,x, algorithm="maxima")

[Out]

-1/3*((3*x - 8*(15*x^3 - 75*x^2 + 130*x - 77)/(x^4 - 8*x^3 + 24*x^2 - 32*x + 16) + 30*log(x - 2))*e^12 - 2*(2*
(15*x^4 - 105*x^3 + 260*x^2 - 250*x + 48)/(x^5 - 8*x^4 + 24*x^3 - 32*x^2 + 16*x) + 15*log(x - 2) - 15*log(x))*
e^12 + 10*(4*(6*x^3 - 27*x^2 + 44*x - 25)/(x^4 - 8*x^3 + 24*x^2 - 32*x + 16) - 3*log(x - 2))*e^12 + 10*(2*(3*x
^3 - 21*x^2 + 52*x - 50)/(x^4 - 8*x^3 + 24*x^2 - 32*x + 16) + 3*log(x - 2) - 3*log(x))*e^12 - 132*(x^3 - 3*x^2
+ 4*x - 2)*e^12/(x^4 - 8*x^3 + 24*x^2 - 32*x + 16) + 60*(3*x^2 - 4*x + 2)*e^12/(x^4 - 8*x^3 + 24*x^2 - 32*x +
16) - 120*(2*x - 1)*e^12/(x^4 - 8*x^3 + 24*x^2 - 32*x + 16) + 264*e^12/(x^4 - 8*x^3 + 24*x^2 - 32*x + 16) - 3
*e^(x^2 - 2*x + 1/(x^4*e^12 - 8*x^3*e^12 + 24*x^2*e^12 - 32*x*e^12 + 16*e^12) + 8/(x^4*e^9 - 8*x^3*e^9 + 24*x^
2*e^9 - 32*x*e^9 + 16*e^9) + 24/(x^4*e^6 - 8*x^3*e^6 + 24*x^2*e^6 - 32*x*e^6 + 16*e^6) + 32/(x^4*e^3 - 8*x^3*e
^3 + 24*x^2*e^3 - 32*x*e^3 + 16*e^3) + 16/(x^4 - 8*x^3 + 24*x^2 - 32*x + 16) + 4/(x^3*e^9 - 6*x^2*e^9 + 12*x*e
^9 - 8*e^9) + 24/(x^3*e^6 - 6*x^2*e^6 + 12*x*e^6 - 8*e^6) + 48/(x^3*e^3 - 6*x^2*e^3 + 12*x*e^3 - 8*e^3) + 32/(
x^3 - 6*x^2 + 12*x - 8) + 2/(x^2*e^6 - 4*x*e^6 + 4*e^6) + 8/(x^2*e^3 - 4*x*e^3 + 4*e^3) + 8/(x^2 - 4*x + 4) -
2/(x*e^6 - 2*e^6) - 12/(x*e^3 - 2*e^3) - 16/(x - 2) - 4*e^(-3) + 5)/x)*e^(-12)

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mupad [B]  time = 9.43, size = 358, normalized size = 10.53 \begin {gather*} \frac {4}{x}-x+\frac {{\mathrm {e}}^{\frac {{\mathrm {e}}^{-12}}{x^4-8\,x^3+24\,x^2-32\,x+16}}\,{\mathrm {e}}^{\frac {x^6}{x^4-8\,x^3+24\,x^2-32\,x+16}}\,{\mathrm {e}}^{-\frac {10\,x^5}{x^4-8\,x^3+24\,x^2-32\,x+16}}\,{\mathrm {e}}^{\frac {16\,x^2}{x^4-8\,x^3+24\,x^2-32\,x+16}}\,{\mathrm {e}}^{\frac {33\,x^4}{x^4-8\,x^3+24\,x^2-32\,x+16}}\,{\mathrm {e}}^{-\frac {40\,x^3}{x^4-8\,x^3+24\,x^2-32\,x+16}}\,{\mathrm {e}}^{\frac {4\,x\,{\mathrm {e}}^{-9}}{x^4-8\,x^3+24\,x^2-32\,x+16}}\,{\mathrm {e}}^{-\frac {8\,x\,{\mathrm {e}}^{-6}}{x^4-8\,x^3+24\,x^2-32\,x+16}}\,{\mathrm {e}}^{-\frac {2\,x^3\,{\mathrm {e}}^{-6}}{x^4-8\,x^3+24\,x^2-32\,x+16}}\,{\mathrm {e}}^{-\frac {4\,x^4\,{\mathrm {e}}^{-3}}{x^4-8\,x^3+24\,x^2-32\,x+16}}\,{\mathrm {e}}^{-\frac {16\,x^2\,{\mathrm {e}}^{-3}}{x^4-8\,x^3+24\,x^2-32\,x+16}}\,{\mathrm {e}}^{\frac {14\,x^2\,{\mathrm {e}}^{-6}}{x^4-8\,x^3+24\,x^2-32\,x+16}}\,{\mathrm {e}}^{\frac {20\,x^3\,{\mathrm {e}}^{-3}}{x^4-8\,x^3+24\,x^2-32\,x+16}}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(-12)*(exp((exp(-12)*(4*x*exp(3) - exp(6)*(8*x - 14*x^2 + 2*x^3) - exp(9)*(16*x^2 - 20*x^3 + 4*x^4) +
exp(12)*(16*x^2 - 40*x^3 + 33*x^4 - 10*x^5 + x^6) + 1))/(24*x^2 - 32*x - 8*x^3 + x^4 + 16))*(exp(12)*(16*x^2
- 80*x + 168*x^3 - 214*x^4 + 99*x^5 - 22*x^6 + 2*x^7 + 32) - exp(3)*(8*x + 12*x^2) - 4*x + exp(6)*(16*x - 32*x
^2 - 16*x^3 + 2*x^4) + exp(9)*(64*x^2 - 88*x^3 + 12*x^4)) - exp(12)*(320*x - 352*x^2 + 240*x^3 - 120*x^4 + 44*
x^5 - 10*x^6 + x^7 - 128)))/(32*x^2 - 80*x^3 + 80*x^4 - 40*x^5 + 10*x^6 - x^7),x)

[Out]

4/x - x + (exp(exp(-12)/(24*x^2 - 32*x - 8*x^3 + x^4 + 16))*exp(x^6/(24*x^2 - 32*x - 8*x^3 + x^4 + 16))*exp(-(
10*x^5)/(24*x^2 - 32*x - 8*x^3 + x^4 + 16))*exp((16*x^2)/(24*x^2 - 32*x - 8*x^3 + x^4 + 16))*exp((33*x^4)/(24*
x^2 - 32*x - 8*x^3 + x^4 + 16))*exp(-(40*x^3)/(24*x^2 - 32*x - 8*x^3 + x^4 + 16))*exp((4*x*exp(-9))/(24*x^2 -
32*x - 8*x^3 + x^4 + 16))*exp(-(8*x*exp(-6))/(24*x^2 - 32*x - 8*x^3 + x^4 + 16))*exp(-(2*x^3*exp(-6))/(24*x^2
- 32*x - 8*x^3 + x^4 + 16))*exp(-(4*x^4*exp(-3))/(24*x^2 - 32*x - 8*x^3 + x^4 + 16))*exp(-(16*x^2*exp(-3))/(24
*x^2 - 32*x - 8*x^3 + x^4 + 16))*exp((14*x^2*exp(-6))/(24*x^2 - 32*x - 8*x^3 + x^4 + 16))*exp((20*x^3*exp(-3))
/(24*x^2 - 32*x - 8*x^3 + x^4 + 16)))/x

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sympy [B]  time = 1.67, size = 100, normalized size = 2.94 \begin {gather*} - x + \frac {e^{\frac {4 x e^{3} + \left (- 2 x^{3} + 14 x^{2} - 8 x\right ) e^{6} + \left (- 4 x^{4} + 20 x^{3} - 16 x^{2}\right ) e^{9} + \left (x^{6} - 10 x^{5} + 33 x^{4} - 40 x^{3} + 16 x^{2}\right ) e^{12} + 1}{\left (x^{4} - 8 x^{3} + 24 x^{2} - 32 x + 16\right ) e^{12}}}}{x} + \frac {4}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x**7-22*x**6+99*x**5-214*x**4+168*x**3+16*x**2-80*x+32)*exp(3)**4+(12*x**4-88*x**3+64*x**2)*exp
(3)**3+(2*x**4-16*x**3-32*x**2+16*x)*exp(3)**2+(-12*x**2-8*x)*exp(3)-4*x)*exp(((x**6-10*x**5+33*x**4-40*x**3+1
6*x**2)*exp(3)**4+(-4*x**4+20*x**3-16*x**2)*exp(3)**3+(-2*x**3+14*x**2-8*x)*exp(3)**2+4*x*exp(3)+1)/(x**4-8*x*
*3+24*x**2-32*x+16)/exp(3)**4)+(-x**7+10*x**6-44*x**5+120*x**4-240*x**3+352*x**2-320*x+128)*exp(3)**4)/(x**7-1
0*x**6+40*x**5-80*x**4+80*x**3-32*x**2)/exp(3)**4,x)

[Out]

-x + exp((4*x*exp(3) + (-2*x**3 + 14*x**2 - 8*x)*exp(6) + (-4*x**4 + 20*x**3 - 16*x**2)*exp(9) + (x**6 - 10*x*
*5 + 33*x**4 - 40*x**3 + 16*x**2)*exp(12) + 1)*exp(-12)/(x**4 - 8*x**3 + 24*x**2 - 32*x + 16))/x + 4/x

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