3.23.1 \(\int \frac {-e^{3 x}+3375 x^6-10125 x^7+10125 x^8-3375 x^9+e^{\frac {16-2 e^{2 x}-450 x^4+900 x^5-450 x^6+e^x (60 x^2-60 x^3)}{e^{2 x}+225 x^4-450 x^5+225 x^6+e^x (-30 x^2+30 x^3)}} (32 e^x-960 x+1440 x^2)+e^{2 x} (45 x^2-45 x^3)+e^x (-675 x^4+1350 x^5-675 x^6)}{e^{3 x}-3375 x^6+10125 x^7-10125 x^8+3375 x^9+e^{2 x} (-45 x^2+45 x^3)+e^x (675 x^4-1350 x^5+675 x^6)} \, dx\)

Optimal. Leaf size=28 \[ -e^{-2+\frac {16}{\left (e^x+5 x^2 (-3+3 x)\right )^2}}-x \]

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Rubi [F]  time = 23.55, 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^{3 x}+3375 x^6-10125 x^7+10125 x^8-3375 x^9+\exp \left (\frac {16-2 e^{2 x}-450 x^4+900 x^5-450 x^6+e^x \left (60 x^2-60 x^3\right )}{e^{2 x}+225 x^4-450 x^5+225 x^6+e^x \left (-30 x^2+30 x^3\right )}\right ) \left (32 e^x-960 x+1440 x^2\right )+e^{2 x} \left (45 x^2-45 x^3\right )+e^x \left (-675 x^4+1350 x^5-675 x^6\right )}{e^{3 x}-3375 x^6+10125 x^7-10125 x^8+3375 x^9+e^{2 x} \left (-45 x^2+45 x^3\right )+e^x \left (675 x^4-1350 x^5+675 x^6\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-E^(3*x) + 3375*x^6 - 10125*x^7 + 10125*x^8 - 3375*x^9 + E^((16 - 2*E^(2*x) - 450*x^4 + 900*x^5 - 450*x^6
+ E^x*(60*x^2 - 60*x^3))/(E^(2*x) + 225*x^4 - 450*x^5 + 225*x^6 + E^x*(-30*x^2 + 30*x^3)))*(32*E^x - 960*x +
1440*x^2) + E^(2*x)*(45*x^2 - 45*x^3) + E^x*(-675*x^4 + 1350*x^5 - 675*x^6))/(E^(3*x) - 3375*x^6 + 10125*x^7 -
10125*x^8 + 3375*x^9 + E^(2*x)*(-45*x^2 + 45*x^3) + E^x*(675*x^4 - 1350*x^5 + 675*x^6)),x]

[Out]

-Defer[Int][E^(3*x)/(E^x - 15*x^2 + 15*x^3)^3, x] - 960*Defer[Int][x/(E^((2*(-8 + E^(2*x) - 30*E^x*x^2 + 30*E^
x*x^3 + 225*x^4 - 450*x^5 + 225*x^6))/(E^x - 15*x^2 + 15*x^3)^2)*(E^x - 15*x^2 + 15*x^3)^3), x] + 45*Defer[Int
][(E^(2*x)*x^2)/(E^x - 15*x^2 + 15*x^3)^3, x] + 1920*Defer[Int][x^2/(E^((2*(-8 + E^(2*x) - 30*E^x*x^2 + 30*E^x
*x^3 + 225*x^4 - 450*x^5 + 225*x^6))/(E^x - 15*x^2 + 15*x^3)^2)*(E^x - 15*x^2 + 15*x^3)^3), x] - 45*Defer[Int]
[(E^(2*x)*x^3)/(E^x - 15*x^2 + 15*x^3)^3, x] - 480*Defer[Int][x^3/(E^((2*(-8 + E^(2*x) - 30*E^x*x^2 + 30*E^x*x
^3 + 225*x^4 - 450*x^5 + 225*x^6))/(E^x - 15*x^2 + 15*x^3)^2)*(E^x - 15*x^2 + 15*x^3)^3), x] - 675*Defer[Int][
(E^x*x^4)/(E^x - 15*x^2 + 15*x^3)^3, x] + 1350*Defer[Int][(E^x*x^5)/(E^x - 15*x^2 + 15*x^3)^3, x] + 3375*Defer
[Int][x^6/(E^x - 15*x^2 + 15*x^3)^3, x] - 675*Defer[Int][(E^x*x^6)/(E^x - 15*x^2 + 15*x^3)^3, x] - 10125*Defer
[Int][x^7/(E^x - 15*x^2 + 15*x^3)^3, x] + 10125*Defer[Int][x^8/(E^x - 15*x^2 + 15*x^3)^3, x] - 3375*Defer[Int]
[x^9/(E^x - 15*x^2 + 15*x^3)^3, x] + 32*Defer[Int][1/(E^((2*(-8 + E^(2*x) - 30*E^x*x^2 + 30*E^x*x^3 + 225*x^4
- 450*x^5 + 225*x^6))/(E^x - 15*x^2 + 15*x^3)^2)*(E^x - 15*x^2 + 15*x^3)^2), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-e^{3 x}-45 e^{2 x} (-1+x) x^2-675 e^x (-1+x)^2 x^4+3375 x^6-10125 x^7+10125 x^8-3375 x^9+32 \exp \left (-\frac {2 \left (-8+e^{2 x}+30 e^x (-1+x) x^2+225 x^4-450 x^5+225 x^6\right )}{\left (e^x+15 (-1+x) x^2\right )^2}\right ) \left (e^x+15 x (-2+3 x)\right )}{\left (e^x+15 (-1+x) x^2\right )^3} \, dx\\ &=\int \left (-\frac {e^{3 x}}{\left (e^x-15 x^2+15 x^3\right )^3}-\frac {45 e^{2 x} (-1+x) x^2}{\left (e^x-15 x^2+15 x^3\right )^3}-\frac {675 e^x (-1+x)^2 x^4}{\left (e^x-15 x^2+15 x^3\right )^3}+\frac {3375 x^6}{\left (e^x-15 x^2+15 x^3\right )^3}-\frac {10125 x^7}{\left (e^x-15 x^2+15 x^3\right )^3}+\frac {10125 x^8}{\left (e^x-15 x^2+15 x^3\right )^3}-\frac {3375 x^9}{\left (e^x-15 x^2+15 x^3\right )^3}+\frac {32 \exp \left (-\frac {2 \left (-8+e^{2 x}-30 e^x x^2+30 e^x x^3+225 x^4-450 x^5+225 x^6\right )}{\left (e^x-15 x^2+15 x^3\right )^2}\right ) \left (e^x-30 x+45 x^2\right )}{\left (e^x-15 x^2+15 x^3\right )^3}\right ) \, dx\\ &=32 \int \frac {\exp \left (-\frac {2 \left (-8+e^{2 x}-30 e^x x^2+30 e^x x^3+225 x^4-450 x^5+225 x^6\right )}{\left (e^x-15 x^2+15 x^3\right )^2}\right ) \left (e^x-30 x+45 x^2\right )}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx-45 \int \frac {e^{2 x} (-1+x) x^2}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx-675 \int \frac {e^x (-1+x)^2 x^4}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx+3375 \int \frac {x^6}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx-3375 \int \frac {x^9}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx-10125 \int \frac {x^7}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx+10125 \int \frac {x^8}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx-\int \frac {e^{3 x}}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx\\ &=32 \int \left (-\frac {15 \exp \left (-\frac {2 \left (-8+e^{2 x}-30 e^x x^2+30 e^x x^3+225 x^4-450 x^5+225 x^6\right )}{\left (e^x-15 x^2+15 x^3\right )^2}\right ) x \left (2-4 x+x^2\right )}{\left (e^x-15 x^2+15 x^3\right )^3}+\frac {\exp \left (-\frac {2 \left (-8+e^{2 x}-30 e^x x^2+30 e^x x^3+225 x^4-450 x^5+225 x^6\right )}{\left (e^x-15 x^2+15 x^3\right )^2}\right )}{\left (e^x-15 x^2+15 x^3\right )^2}\right ) \, dx-45 \int \left (-\frac {e^{2 x} x^2}{\left (e^x-15 x^2+15 x^3\right )^3}+\frac {e^{2 x} x^3}{\left (e^x-15 x^2+15 x^3\right )^3}\right ) \, dx-675 \int \left (\frac {e^x x^4}{\left (e^x-15 x^2+15 x^3\right )^3}-\frac {2 e^x x^5}{\left (e^x-15 x^2+15 x^3\right )^3}+\frac {e^x x^6}{\left (e^x-15 x^2+15 x^3\right )^3}\right ) \, dx+3375 \int \frac {x^6}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx-3375 \int \frac {x^9}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx-10125 \int \frac {x^7}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx+10125 \int \frac {x^8}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx-\int \frac {e^{3 x}}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx\\ &=32 \int \frac {\exp \left (-\frac {2 \left (-8+e^{2 x}-30 e^x x^2+30 e^x x^3+225 x^4-450 x^5+225 x^6\right )}{\left (e^x-15 x^2+15 x^3\right )^2}\right )}{\left (e^x-15 x^2+15 x^3\right )^2} \, dx+45 \int \frac {e^{2 x} x^2}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx-45 \int \frac {e^{2 x} x^3}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx-480 \int \frac {\exp \left (-\frac {2 \left (-8+e^{2 x}-30 e^x x^2+30 e^x x^3+225 x^4-450 x^5+225 x^6\right )}{\left (e^x-15 x^2+15 x^3\right )^2}\right ) x \left (2-4 x+x^2\right )}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx-675 \int \frac {e^x x^4}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx-675 \int \frac {e^x x^6}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx+1350 \int \frac {e^x x^5}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx+3375 \int \frac {x^6}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx-3375 \int \frac {x^9}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx-10125 \int \frac {x^7}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx+10125 \int \frac {x^8}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx-\int \frac {e^{3 x}}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx\\ &=32 \int \frac {\exp \left (-\frac {2 \left (-8+e^{2 x}-30 e^x x^2+30 e^x x^3+225 x^4-450 x^5+225 x^6\right )}{\left (e^x-15 x^2+15 x^3\right )^2}\right )}{\left (e^x-15 x^2+15 x^3\right )^2} \, dx+45 \int \frac {e^{2 x} x^2}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx-45 \int \frac {e^{2 x} x^3}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx-480 \int \left (\frac {2 \exp \left (-\frac {2 \left (-8+e^{2 x}-30 e^x x^2+30 e^x x^3+225 x^4-450 x^5+225 x^6\right )}{\left (e^x-15 x^2+15 x^3\right )^2}\right ) x}{\left (e^x-15 x^2+15 x^3\right )^3}-\frac {4 \exp \left (-\frac {2 \left (-8+e^{2 x}-30 e^x x^2+30 e^x x^3+225 x^4-450 x^5+225 x^6\right )}{\left (e^x-15 x^2+15 x^3\right )^2}\right ) x^2}{\left (e^x-15 x^2+15 x^3\right )^3}+\frac {\exp \left (-\frac {2 \left (-8+e^{2 x}-30 e^x x^2+30 e^x x^3+225 x^4-450 x^5+225 x^6\right )}{\left (e^x-15 x^2+15 x^3\right )^2}\right ) x^3}{\left (e^x-15 x^2+15 x^3\right )^3}\right ) \, dx-675 \int \frac {e^x x^4}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx-675 \int \frac {e^x x^6}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx+1350 \int \frac {e^x x^5}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx+3375 \int \frac {x^6}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx-3375 \int \frac {x^9}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx-10125 \int \frac {x^7}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx+10125 \int \frac {x^8}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx-\int \frac {e^{3 x}}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx\\ &=32 \int \frac {\exp \left (-\frac {2 \left (-8+e^{2 x}-30 e^x x^2+30 e^x x^3+225 x^4-450 x^5+225 x^6\right )}{\left (e^x-15 x^2+15 x^3\right )^2}\right )}{\left (e^x-15 x^2+15 x^3\right )^2} \, dx+45 \int \frac {e^{2 x} x^2}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx-45 \int \frac {e^{2 x} x^3}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx-480 \int \frac {\exp \left (-\frac {2 \left (-8+e^{2 x}-30 e^x x^2+30 e^x x^3+225 x^4-450 x^5+225 x^6\right )}{\left (e^x-15 x^2+15 x^3\right )^2}\right ) x^3}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx-675 \int \frac {e^x x^4}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx-675 \int \frac {e^x x^6}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx-960 \int \frac {\exp \left (-\frac {2 \left (-8+e^{2 x}-30 e^x x^2+30 e^x x^3+225 x^4-450 x^5+225 x^6\right )}{\left (e^x-15 x^2+15 x^3\right )^2}\right ) x}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx+1350 \int \frac {e^x x^5}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx+1920 \int \frac {\exp \left (-\frac {2 \left (-8+e^{2 x}-30 e^x x^2+30 e^x x^3+225 x^4-450 x^5+225 x^6\right )}{\left (e^x-15 x^2+15 x^3\right )^2}\right ) x^2}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx+3375 \int \frac {x^6}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx-3375 \int \frac {x^9}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx-10125 \int \frac {x^7}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx+10125 \int \frac {x^8}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx-\int \frac {e^{3 x}}{\left (e^x-15 x^2+15 x^3\right )^3} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.66, size = 28, normalized size = 1.00 \begin {gather*} -e^{-2+\frac {16}{\left (e^x-15 x^2+15 x^3\right )^2}}-x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-E^(3*x) + 3375*x^6 - 10125*x^7 + 10125*x^8 - 3375*x^9 + E^((16 - 2*E^(2*x) - 450*x^4 + 900*x^5 - 4
50*x^6 + E^x*(60*x^2 - 60*x^3))/(E^(2*x) + 225*x^4 - 450*x^5 + 225*x^6 + E^x*(-30*x^2 + 30*x^3)))*(32*E^x - 96
0*x + 1440*x^2) + E^(2*x)*(45*x^2 - 45*x^3) + E^x*(-675*x^4 + 1350*x^5 - 675*x^6))/(E^(3*x) - 3375*x^6 + 10125
*x^7 - 10125*x^8 + 3375*x^9 + E^(2*x)*(-45*x^2 + 45*x^3) + E^x*(675*x^4 - 1350*x^5 + 675*x^6)),x]

[Out]

-E^(-2 + 16/(E^x - 15*x^2 + 15*x^3)^2) - x

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fricas [B]  time = 1.02, size = 78, normalized size = 2.79 \begin {gather*} -x - e^{\left (-\frac {2 \, {\left (225 \, x^{6} - 450 \, x^{5} + 225 \, x^{4} + 30 \, {\left (x^{3} - x^{2}\right )} e^{x} + e^{\left (2 \, x\right )} - 8\right )}}{225 \, x^{6} - 450 \, x^{5} + 225 \, x^{4} + 30 \, {\left (x^{3} - x^{2}\right )} e^{x} + e^{\left (2 \, x\right )}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((32*exp(x)+1440*x^2-960*x)*exp((-2*exp(x)^2+(-60*x^3+60*x^2)*exp(x)-450*x^6+900*x^5-450*x^4+16)/(ex
p(x)^2+(30*x^3-30*x^2)*exp(x)+225*x^6-450*x^5+225*x^4))-exp(x)^3+(-45*x^3+45*x^2)*exp(x)^2+(-675*x^6+1350*x^5-
675*x^4)*exp(x)-3375*x^9+10125*x^8-10125*x^7+3375*x^6)/(exp(x)^3+(45*x^3-45*x^2)*exp(x)^2+(675*x^6-1350*x^5+67
5*x^4)*exp(x)+3375*x^9-10125*x^8+10125*x^7-3375*x^6),x, algorithm="fricas")

[Out]

-x - e^(-2*(225*x^6 - 450*x^5 + 225*x^4 + 30*(x^3 - x^2)*e^x + e^(2*x) - 8)/(225*x^6 - 450*x^5 + 225*x^4 + 30*
(x^3 - x^2)*e^x + e^(2*x)))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -\frac {3375 \, x^{9} - 10125 \, x^{8} + 10125 \, x^{7} - 3375 \, x^{6} + 45 \, {\left (x^{3} - x^{2}\right )} e^{\left (2 \, x\right )} + 675 \, {\left (x^{6} - 2 \, x^{5} + x^{4}\right )} e^{x} - 32 \, {\left (45 \, x^{2} - 30 \, x + e^{x}\right )} e^{\left (-\frac {2 \, {\left (225 \, x^{6} - 450 \, x^{5} + 225 \, x^{4} + 30 \, {\left (x^{3} - x^{2}\right )} e^{x} + e^{\left (2 \, x\right )} - 8\right )}}{225 \, x^{6} - 450 \, x^{5} + 225 \, x^{4} + 30 \, {\left (x^{3} - x^{2}\right )} e^{x} + e^{\left (2 \, x\right )}}\right )} + e^{\left (3 \, x\right )}}{3375 \, x^{9} - 10125 \, x^{8} + 10125 \, x^{7} - 3375 \, x^{6} + 45 \, {\left (x^{3} - x^{2}\right )} e^{\left (2 \, x\right )} + 675 \, {\left (x^{6} - 2 \, x^{5} + x^{4}\right )} e^{x} + e^{\left (3 \, x\right )}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((32*exp(x)+1440*x^2-960*x)*exp((-2*exp(x)^2+(-60*x^3+60*x^2)*exp(x)-450*x^6+900*x^5-450*x^4+16)/(ex
p(x)^2+(30*x^3-30*x^2)*exp(x)+225*x^6-450*x^5+225*x^4))-exp(x)^3+(-45*x^3+45*x^2)*exp(x)^2+(-675*x^6+1350*x^5-
675*x^4)*exp(x)-3375*x^9+10125*x^8-10125*x^7+3375*x^6)/(exp(x)^3+(45*x^3-45*x^2)*exp(x)^2+(675*x^6-1350*x^5+67
5*x^4)*exp(x)+3375*x^9-10125*x^8+10125*x^7-3375*x^6),x, algorithm="giac")

[Out]

integrate(-(3375*x^9 - 10125*x^8 + 10125*x^7 - 3375*x^6 + 45*(x^3 - x^2)*e^(2*x) + 675*(x^6 - 2*x^5 + x^4)*e^x
- 32*(45*x^2 - 30*x + e^x)*e^(-2*(225*x^6 - 450*x^5 + 225*x^4 + 30*(x^3 - x^2)*e^x + e^(2*x) - 8)/(225*x^6 -
450*x^5 + 225*x^4 + 30*(x^3 - x^2)*e^x + e^(2*x))) + e^(3*x))/(3375*x^9 - 10125*x^8 + 10125*x^7 - 3375*x^6 + 4
5*(x^3 - x^2)*e^(2*x) + 675*(x^6 - 2*x^5 + x^4)*e^x + e^(3*x)), x)

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maple [B]  time = 0.16, size = 81, normalized size = 2.89

method	result	size
risch	\(-x -{\mathrm e}^{-\frac {2 \left (225 x^{6}-450 x^{5}+30 \,{\mathrm e}^{x} x^{3}+225 x^{4}-30 \,{\mathrm e}^{x} x^{2}+{\mathrm e}^{2 x}-8\right )}{225 x^{6}-450 x^{5}+30 \,{\mathrm e}^{x} x^{3}+225 x^{4}-30 \,{\mathrm e}^{x} x^{2}+{\mathrm e}^{2 x}}}\)	\(81\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((32*exp(x)+1440*x^2-960*x)*exp((-2*exp(x)^2+(-60*x^3+60*x^2)*exp(x)-450*x^6+900*x^5-450*x^4+16)/(exp(x)^2
+(30*x^3-30*x^2)*exp(x)+225*x^6-450*x^5+225*x^4))-exp(x)^3+(-45*x^3+45*x^2)*exp(x)^2+(-675*x^6+1350*x^5-675*x^
4)*exp(x)-3375*x^9+10125*x^8-10125*x^7+3375*x^6)/(exp(x)^3+(45*x^3-45*x^2)*exp(x)^2+(675*x^6-1350*x^5+675*x^4)
*exp(x)+3375*x^9-10125*x^8+10125*x^7-3375*x^6),x,method=_RETURNVERBOSE)

[Out]

-x-exp(-2*(225*x^6-450*x^5+30*exp(x)*x^3+225*x^4-30*exp(x)*x^2+exp(2*x)-8)/(225*x^6-450*x^5+30*exp(x)*x^3+225*
x^4-30*exp(x)*x^2+exp(2*x)))

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maxima [B]  time = 1.45, size = 173, normalized size = 6.18 \begin {gather*} -{\left (x e^{\left (\frac {2 \, e^{\left (2 \, x\right )}}{225 \, x^{6} - 450 \, x^{5} + 225 \, x^{4} + 30 \, {\left (x^{3} - x^{2}\right )} e^{x} + e^{\left (2 \, x\right )}} + 2\right )} + e^{\left (\frac {2 \, e^{\left (2 \, x\right )}}{225 \, x^{6} - 450 \, x^{5} + 225 \, x^{4} + 30 \, {\left (x^{3} - x^{2}\right )} e^{x} + e^{\left (2 \, x\right )}} + \frac {16}{225 \, x^{6} - 450 \, x^{5} + 225 \, x^{4} + 30 \, {\left (x^{3} - x^{2}\right )} e^{x} + e^{\left (2 \, x\right )}}\right )}\right )} e^{\left (-\frac {2 \, e^{\left (2 \, x\right )}}{225 \, x^{6} - 450 \, x^{5} + 225 \, x^{4} + 30 \, {\left (x^{3} - x^{2}\right )} e^{x} + e^{\left (2 \, x\right )}} - 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((32*exp(x)+1440*x^2-960*x)*exp((-2*exp(x)^2+(-60*x^3+60*x^2)*exp(x)-450*x^6+900*x^5-450*x^4+16)/(ex
p(x)^2+(30*x^3-30*x^2)*exp(x)+225*x^6-450*x^5+225*x^4))-exp(x)^3+(-45*x^3+45*x^2)*exp(x)^2+(-675*x^6+1350*x^5-
675*x^4)*exp(x)-3375*x^9+10125*x^8-10125*x^7+3375*x^6)/(exp(x)^3+(45*x^3-45*x^2)*exp(x)^2+(675*x^6-1350*x^5+67
5*x^4)*exp(x)+3375*x^9-10125*x^8+10125*x^7-3375*x^6),x, algorithm="maxima")

[Out]

-(x*e^(2*e^(2*x)/(225*x^6 - 450*x^5 + 225*x^4 + 30*(x^3 - x^2)*e^x + e^(2*x)) + 2) + e^(2*e^(2*x)/(225*x^6 - 4
50*x^5 + 225*x^4 + 30*(x^3 - x^2)*e^x + e^(2*x)) + 16/(225*x^6 - 450*x^5 + 225*x^4 + 30*(x^3 - x^2)*e^x + e^(2
*x))))*e^(-2*e^(2*x)/(225*x^6 - 450*x^5 + 225*x^4 + 30*(x^3 - x^2)*e^x + e^(2*x)) - 2)

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mupad [B]  time = 1.55, size = 302, normalized size = 10.79 \begin {gather*} -x-{\mathrm {e}}^{\frac {60\,x^2\,{\mathrm {e}}^x}{{\mathrm {e}}^{2\,x}-30\,x^2\,{\mathrm {e}}^x+30\,x^3\,{\mathrm {e}}^x+225\,x^4-450\,x^5+225\,x^6}}\,{\mathrm {e}}^{-\frac {60\,x^3\,{\mathrm {e}}^x}{{\mathrm {e}}^{2\,x}-30\,x^2\,{\mathrm {e}}^x+30\,x^3\,{\mathrm {e}}^x+225\,x^4-450\,x^5+225\,x^6}}\,{\mathrm {e}}^{-\frac {450\,x^4}{{\mathrm {e}}^{2\,x}-30\,x^2\,{\mathrm {e}}^x+30\,x^3\,{\mathrm {e}}^x+225\,x^4-450\,x^5+225\,x^6}}\,{\mathrm {e}}^{-\frac {450\,x^6}{{\mathrm {e}}^{2\,x}-30\,x^2\,{\mathrm {e}}^x+30\,x^3\,{\mathrm {e}}^x+225\,x^4-450\,x^5+225\,x^6}}\,{\mathrm {e}}^{\frac {900\,x^5}{{\mathrm {e}}^{2\,x}-30\,x^2\,{\mathrm {e}}^x+30\,x^3\,{\mathrm {e}}^x+225\,x^4-450\,x^5+225\,x^6}}\,{\mathrm {e}}^{\frac {16}{{\mathrm {e}}^{2\,x}-30\,x^2\,{\mathrm {e}}^x+30\,x^3\,{\mathrm {e}}^x+225\,x^4-450\,x^5+225\,x^6}}\,{\mathrm {e}}^{-\frac {2\,{\mathrm {e}}^{2\,x}}{{\mathrm {e}}^{2\,x}-30\,x^2\,{\mathrm {e}}^x+30\,x^3\,{\mathrm {e}}^x+225\,x^4-450\,x^5+225\,x^6}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(3*x) - exp(-(2*exp(2*x) - exp(x)*(60*x^2 - 60*x^3) + 450*x^4 - 900*x^5 + 450*x^6 - 16)/(exp(2*x) - e
xp(x)*(30*x^2 - 30*x^3) + 225*x^4 - 450*x^5 + 225*x^6))*(32*exp(x) - 960*x + 1440*x^2) + exp(x)*(675*x^4 - 135
0*x^5 + 675*x^6) - exp(2*x)*(45*x^2 - 45*x^3) - 3375*x^6 + 10125*x^7 - 10125*x^8 + 3375*x^9)/(exp(3*x) + exp(x
)*(675*x^4 - 1350*x^5 + 675*x^6) - exp(2*x)*(45*x^2 - 45*x^3) - 3375*x^6 + 10125*x^7 - 10125*x^8 + 3375*x^9),x
)

[Out]

- x - exp((60*x^2*exp(x))/(exp(2*x) - 30*x^2*exp(x) + 30*x^3*exp(x) + 225*x^4 - 450*x^5 + 225*x^6))*exp(-(60*x
^3*exp(x))/(exp(2*x) - 30*x^2*exp(x) + 30*x^3*exp(x) + 225*x^4 - 450*x^5 + 225*x^6))*exp(-(450*x^4)/(exp(2*x)
- 30*x^2*exp(x) + 30*x^3*exp(x) + 225*x^4 - 450*x^5 + 225*x^6))*exp(-(450*x^6)/(exp(2*x) - 30*x^2*exp(x) + 30*
x^3*exp(x) + 225*x^4 - 450*x^5 + 225*x^6))*exp((900*x^5)/(exp(2*x) - 30*x^2*exp(x) + 30*x^3*exp(x) + 225*x^4 -
450*x^5 + 225*x^6))*exp(16/(exp(2*x) - 30*x^2*exp(x) + 30*x^3*exp(x) + 225*x^4 - 450*x^5 + 225*x^6))*exp(-(2*
exp(2*x))/(exp(2*x) - 30*x^2*exp(x) + 30*x^3*exp(x) + 225*x^4 - 450*x^5 + 225*x^6))

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sympy [B]  time = 0.64, size = 75, normalized size = 2.68 \begin {gather*} - x - e^{\frac {- 450 x^{6} + 900 x^{5} - 450 x^{4} + \left (- 60 x^{3} + 60 x^{2}\right ) e^{x} - 2 e^{2 x} + 16}{225 x^{6} - 450 x^{5} + 225 x^{4} + \left (30 x^{3} - 30 x^{2}\right ) e^{x} + e^{2 x}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((32*exp(x)+1440*x**2-960*x)*exp((-2*exp(x)**2+(-60*x**3+60*x**2)*exp(x)-450*x**6+900*x**5-450*x**4+
16)/(exp(x)**2+(30*x**3-30*x**2)*exp(x)+225*x**6-450*x**5+225*x**4))-exp(x)**3+(-45*x**3+45*x**2)*exp(x)**2+(-
675*x**6+1350*x**5-675*x**4)*exp(x)-3375*x**9+10125*x**8-10125*x**7+3375*x**6)/(exp(x)**3+(45*x**3-45*x**2)*ex
p(x)**2+(675*x**6-1350*x**5+675*x**4)*exp(x)+3375*x**9-10125*x**8+10125*x**7-3375*x**6),x)

[Out]

-x - exp((-450*x**6 + 900*x**5 - 450*x**4 + (-60*x**3 + 60*x**2)*exp(x) - 2*exp(2*x) + 16)/(225*x**6 - 450*x**
5 + 225*x**4 + (30*x**3 - 30*x**2)*exp(x) + exp(2*x)))

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