3.25.41 \(\int \frac {e^{-5 x} (-62500-68750 x+15625 x^2+e^{e^x x} (-50000-55000 x+12500 x^2+e^x (12500 x+10000 x^2-2500 x^3))+e^{2 e^x x} (-15000-16500 x+3750 x^2+e^x (7500 x+6000 x^2-1500 x^3))+e^{3 e^x x} (-2000-2200 x+500 x^2+e^x (1500 x+1200 x^2-300 x^3))+e^{4 e^x x} (-100-110 x+25 x^2+e^x (100 x+80 x^2-20 x^3)))}{x^5} \, dx\)

Optimal. Leaf size=26 \[ \frac {5 e^{-5 x} \left (5+e^{e^x x}\right )^4 (5-x)}{x^4} \]

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Rubi [F]  time = 12.78, 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^{-5 x} \left (-62500-68750 x+15625 x^2+e^{e^x x} \left (-50000-55000 x+12500 x^2+e^x \left (12500 x+10000 x^2-2500 x^3\right )\right )+e^{2 e^x x} \left (-15000-16500 x+3750 x^2+e^x \left (7500 x+6000 x^2-1500 x^3\right )\right )+e^{3 e^x x} \left (-2000-2200 x+500 x^2+e^x \left (1500 x+1200 x^2-300 x^3\right )\right )+e^{4 e^x x} \left (-100-110 x+25 x^2+e^x \left (100 x+80 x^2-20 x^3\right )\right )\right )}{x^5} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-62500 - 68750*x + 15625*x^2 + E^(E^x*x)*(-50000 - 55000*x + 12500*x^2 + E^x*(12500*x + 10000*x^2 - 2500*
x^3)) + E^(2*E^x*x)*(-15000 - 16500*x + 3750*x^2 + E^x*(7500*x + 6000*x^2 - 1500*x^3)) + E^(3*E^x*x)*(-2000 -
2200*x + 500*x^2 + E^x*(1500*x + 1200*x^2 - 300*x^3)) + E^(4*E^x*x)*(-100 - 110*x + 25*x^2 + E^x*(100*x + 80*x
^2 - 20*x^3)))/(E^(5*x)*x^5),x]

[Out]

15625/(E^(5*x)*x^4) - 3125/(E^(5*x)*x^3) - 50000*Defer[Int][E^(-5*x + E^x*x)/x^5, x] - 15000*Defer[Int][E^(-5*
x + 2*E^x*x)/x^5, x] - 2000*Defer[Int][E^(-5*x + 3*E^x*x)/x^5, x] - 100*Defer[Int][E^(-5*x + 4*E^x*x)/x^5, x]
+ 7500*Defer[Int][E^(2*(-2 + E^x)*x)/x^4, x] + 100*Defer[Int][E^(4*(-1 + E^x)*x)/x^4, x] - 55000*Defer[Int][E^
(-5*x + E^x*x)/x^4, x] + 12500*Defer[Int][E^(-4*x + E^x*x)/x^4, x] - 16500*Defer[Int][E^(-5*x + 2*E^x*x)/x^4,
x] - 2200*Defer[Int][E^(-5*x + 3*E^x*x)/x^4, x] + 1500*Defer[Int][E^(-4*x + 3*E^x*x)/x^4, x] - 110*Defer[Int][
E^(-5*x + 4*E^x*x)/x^4, x] + 6000*Defer[Int][E^(2*(-2 + E^x)*x)/x^3, x] + 80*Defer[Int][E^(4*(-1 + E^x)*x)/x^3
, x] + 12500*Defer[Int][E^(-5*x + E^x*x)/x^3, x] + 10000*Defer[Int][E^(-4*x + E^x*x)/x^3, x] + 3750*Defer[Int]
[E^(-5*x + 2*E^x*x)/x^3, x] + 500*Defer[Int][E^(-5*x + 3*E^x*x)/x^3, x] + 1200*Defer[Int][E^(-4*x + 3*E^x*x)/x
^3, x] + 25*Defer[Int][E^(-5*x + 4*E^x*x)/x^3, x] - 1500*Defer[Int][E^(2*(-2 + E^x)*x)/x^2, x] - 20*Defer[Int]
[E^(4*(-1 + E^x)*x)/x^2, x] - 2500*Defer[Int][E^(-4*x + E^x*x)/x^2, x] - 300*Defer[Int][E^(-4*x + 3*E^x*x)/x^2
, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {5 e^{-5 x} \left (5+e^{e^x x}\right )^3 \left (-5 \left (20+22 x-5 x^2\right )-e^{e^x x} \left (20+22 x-5 x^2\right )-4 e^{x+e^x x} x \left (-5-4 x+x^2\right )\right )}{x^5} \, dx\\ &=5 \int \frac {e^{-5 x} \left (5+e^{e^x x}\right )^3 \left (-5 \left (20+22 x-5 x^2\right )-e^{e^x x} \left (20+22 x-5 x^2\right )-4 e^{x+e^x x} x \left (-5-4 x+x^2\right )\right )}{x^5} \, dx\\ &=5 \int \left (\frac {625 e^{-5 x} \left (-20-22 x+5 x^2\right )}{x^5}-\frac {500 e^{-5 x+e^x x} \left (20+22 x-5 e^x x-5 x^2-4 e^x x^2+e^x x^3\right )}{x^5}-\frac {150 e^{-5 x+2 e^x x} \left (20+22 x-10 e^x x-5 x^2-8 e^x x^2+2 e^x x^3\right )}{x^5}-\frac {20 e^{-5 x+3 e^x x} \left (20+22 x-15 e^x x-5 x^2-12 e^x x^2+3 e^x x^3\right )}{x^5}-\frac {e^{-5 x+4 e^x x} \left (20+22 x-20 e^x x-5 x^2-16 e^x x^2+4 e^x x^3\right )}{x^5}\right ) \, dx\\ &=-\left (5 \int \frac {e^{-5 x+4 e^x x} \left (20+22 x-20 e^x x-5 x^2-16 e^x x^2+4 e^x x^3\right )}{x^5} \, dx\right )-100 \int \frac {e^{-5 x+3 e^x x} \left (20+22 x-15 e^x x-5 x^2-12 e^x x^2+3 e^x x^3\right )}{x^5} \, dx-750 \int \frac {e^{-5 x+2 e^x x} \left (20+22 x-10 e^x x-5 x^2-8 e^x x^2+2 e^x x^3\right )}{x^5} \, dx-2500 \int \frac {e^{-5 x+e^x x} \left (20+22 x-5 e^x x-5 x^2-4 e^x x^2+e^x x^3\right )}{x^5} \, dx+3125 \int \frac {e^{-5 x} \left (-20-22 x+5 x^2\right )}{x^5} \, dx\\ &=-\left (5 \int \left (\frac {e^{-5 x+4 e^x x} \left (20+22 x-5 x^2\right )}{x^5}+\frac {4 e^{-4 x+4 e^x x} \left (-5-4 x+x^2\right )}{x^4}\right ) \, dx\right )-100 \int \left (\frac {e^{-5 x+3 e^x x} \left (20+22 x-5 x^2\right )}{x^5}+\frac {3 e^{-4 x+3 e^x x} \left (-5-4 x+x^2\right )}{x^4}\right ) \, dx-750 \int \left (\frac {e^{-5 x+2 e^x x} \left (20+22 x-5 x^2\right )}{x^5}+\frac {2 e^{-4 x+2 e^x x} \left (-5-4 x+x^2\right )}{x^4}\right ) \, dx-2500 \int \left (\frac {e^{-5 x+e^x x} \left (20+22 x-5 x^2\right )}{x^5}+\frac {e^{-4 x+e^x x} \left (-5-4 x+x^2\right )}{x^4}\right ) \, dx+3125 \int \left (-\frac {20 e^{-5 x}}{x^5}-\frac {22 e^{-5 x}}{x^4}+\frac {5 e^{-5 x}}{x^3}\right ) \, dx\\ &=-\left (5 \int \frac {e^{-5 x+4 e^x x} \left (20+22 x-5 x^2\right )}{x^5} \, dx\right )-20 \int \frac {e^{-4 x+4 e^x x} \left (-5-4 x+x^2\right )}{x^4} \, dx-100 \int \frac {e^{-5 x+3 e^x x} \left (20+22 x-5 x^2\right )}{x^5} \, dx-300 \int \frac {e^{-4 x+3 e^x x} \left (-5-4 x+x^2\right )}{x^4} \, dx-750 \int \frac {e^{-5 x+2 e^x x} \left (20+22 x-5 x^2\right )}{x^5} \, dx-1500 \int \frac {e^{-4 x+2 e^x x} \left (-5-4 x+x^2\right )}{x^4} \, dx-2500 \int \frac {e^{-5 x+e^x x} \left (20+22 x-5 x^2\right )}{x^5} \, dx-2500 \int \frac {e^{-4 x+e^x x} \left (-5-4 x+x^2\right )}{x^4} \, dx+15625 \int \frac {e^{-5 x}}{x^3} \, dx-62500 \int \frac {e^{-5 x}}{x^5} \, dx-68750 \int \frac {e^{-5 x}}{x^4} \, dx\\ &=\frac {15625 e^{-5 x}}{x^4}+\frac {68750 e^{-5 x}}{3 x^3}-\frac {15625 e^{-5 x}}{2 x^2}-5 \int \left (\frac {20 e^{-5 x+4 e^x x}}{x^5}+\frac {22 e^{-5 x+4 e^x x}}{x^4}-\frac {5 e^{-5 x+4 e^x x}}{x^3}\right ) \, dx-20 \int \frac {e^{4 \left (-1+e^x\right ) x} \left (-5-4 x+x^2\right )}{x^4} \, dx-100 \int \left (\frac {20 e^{-5 x+3 e^x x}}{x^5}+\frac {22 e^{-5 x+3 e^x x}}{x^4}-\frac {5 e^{-5 x+3 e^x x}}{x^3}\right ) \, dx-300 \int \left (-\frac {5 e^{-4 x+3 e^x x}}{x^4}-\frac {4 e^{-4 x+3 e^x x}}{x^3}+\frac {e^{-4 x+3 e^x x}}{x^2}\right ) \, dx-750 \int \left (\frac {20 e^{-5 x+2 e^x x}}{x^5}+\frac {22 e^{-5 x+2 e^x x}}{x^4}-\frac {5 e^{-5 x+2 e^x x}}{x^3}\right ) \, dx-1500 \int \frac {e^{2 \left (-2+e^x\right ) x} \left (-5-4 x+x^2\right )}{x^4} \, dx-2500 \int \left (\frac {20 e^{-5 x+e^x x}}{x^5}+\frac {22 e^{-5 x+e^x x}}{x^4}-\frac {5 e^{-5 x+e^x x}}{x^3}\right ) \, dx-2500 \int \left (-\frac {5 e^{-4 x+e^x x}}{x^4}-\frac {4 e^{-4 x+e^x x}}{x^3}+\frac {e^{-4 x+e^x x}}{x^2}\right ) \, dx-\frac {78125}{2} \int \frac {e^{-5 x}}{x^2} \, dx+78125 \int \frac {e^{-5 x}}{x^4} \, dx+\frac {343750}{3} \int \frac {e^{-5 x}}{x^3} \, dx\\ &=\frac {15625 e^{-5 x}}{x^4}-\frac {3125 e^{-5 x}}{x^3}-\frac {390625 e^{-5 x}}{6 x^2}+\frac {78125 e^{-5 x}}{2 x}-20 \int \left (-\frac {5 e^{4 \left (-1+e^x\right ) x}}{x^4}-\frac {4 e^{4 \left (-1+e^x\right ) x}}{x^3}+\frac {e^{4 \left (-1+e^x\right ) x}}{x^2}\right ) \, dx+25 \int \frac {e^{-5 x+4 e^x x}}{x^3} \, dx-100 \int \frac {e^{-5 x+4 e^x x}}{x^5} \, dx-110 \int \frac {e^{-5 x+4 e^x x}}{x^4} \, dx-300 \int \frac {e^{-4 x+3 e^x x}}{x^2} \, dx+500 \int \frac {e^{-5 x+3 e^x x}}{x^3} \, dx+1200 \int \frac {e^{-4 x+3 e^x x}}{x^3} \, dx-1500 \int \left (-\frac {5 e^{2 \left (-2+e^x\right ) x}}{x^4}-\frac {4 e^{2 \left (-2+e^x\right ) x}}{x^3}+\frac {e^{2 \left (-2+e^x\right ) x}}{x^2}\right ) \, dx+1500 \int \frac {e^{-4 x+3 e^x x}}{x^4} \, dx-2000 \int \frac {e^{-5 x+3 e^x x}}{x^5} \, dx-2200 \int \frac {e^{-5 x+3 e^x x}}{x^4} \, dx-2500 \int \frac {e^{-4 x+e^x x}}{x^2} \, dx+3750 \int \frac {e^{-5 x+2 e^x x}}{x^3} \, dx+10000 \int \frac {e^{-4 x+e^x x}}{x^3} \, dx+12500 \int \frac {e^{-4 x+e^x x}}{x^4} \, dx+12500 \int \frac {e^{-5 x+e^x x}}{x^3} \, dx-15000 \int \frac {e^{-5 x+2 e^x x}}{x^5} \, dx-16500 \int \frac {e^{-5 x+2 e^x x}}{x^4} \, dx-50000 \int \frac {e^{-5 x+e^x x}}{x^5} \, dx-55000 \int \frac {e^{-5 x+e^x x}}{x^4} \, dx-\frac {390625}{3} \int \frac {e^{-5 x}}{x^3} \, dx+\frac {390625}{2} \int \frac {e^{-5 x}}{x} \, dx-\frac {859375}{3} \int \frac {e^{-5 x}}{x^2} \, dx\\ &=\frac {15625 e^{-5 x}}{x^4}-\frac {3125 e^{-5 x}}{x^3}+\frac {1953125 e^{-5 x}}{6 x}+\frac {390625 \text {Ei}(-5 x)}{2}-20 \int \frac {e^{4 \left (-1+e^x\right ) x}}{x^2} \, dx+25 \int \frac {e^{-5 x+4 e^x x}}{x^3} \, dx+80 \int \frac {e^{4 \left (-1+e^x\right ) x}}{x^3} \, dx-100 \int \frac {e^{-5 x+4 e^x x}}{x^5} \, dx+100 \int \frac {e^{4 \left (-1+e^x\right ) x}}{x^4} \, dx-110 \int \frac {e^{-5 x+4 e^x x}}{x^4} \, dx-300 \int \frac {e^{-4 x+3 e^x x}}{x^2} \, dx+500 \int \frac {e^{-5 x+3 e^x x}}{x^3} \, dx+1200 \int \frac {e^{-4 x+3 e^x x}}{x^3} \, dx+1500 \int \frac {e^{-4 x+3 e^x x}}{x^4} \, dx-1500 \int \frac {e^{2 \left (-2+e^x\right ) x}}{x^2} \, dx-2000 \int \frac {e^{-5 x+3 e^x x}}{x^5} \, dx-2200 \int \frac {e^{-5 x+3 e^x x}}{x^4} \, dx-2500 \int \frac {e^{-4 x+e^x x}}{x^2} \, dx+3750 \int \frac {e^{-5 x+2 e^x x}}{x^3} \, dx+6000 \int \frac {e^{2 \left (-2+e^x\right ) x}}{x^3} \, dx+7500 \int \frac {e^{2 \left (-2+e^x\right ) x}}{x^4} \, dx+10000 \int \frac {e^{-4 x+e^x x}}{x^3} \, dx+12500 \int \frac {e^{-4 x+e^x x}}{x^4} \, dx+12500 \int \frac {e^{-5 x+e^x x}}{x^3} \, dx-15000 \int \frac {e^{-5 x+2 e^x x}}{x^5} \, dx-16500 \int \frac {e^{-5 x+2 e^x x}}{x^4} \, dx-50000 \int \frac {e^{-5 x+e^x x}}{x^5} \, dx-55000 \int \frac {e^{-5 x+e^x x}}{x^4} \, dx+\frac {1953125}{6} \int \frac {e^{-5 x}}{x^2} \, dx+\frac {4296875}{3} \int \frac {e^{-5 x}}{x} \, dx\\ &=\frac {15625 e^{-5 x}}{x^4}-\frac {3125 e^{-5 x}}{x^3}+\frac {9765625 \text {Ei}(-5 x)}{6}-20 \int \frac {e^{4 \left (-1+e^x\right ) x}}{x^2} \, dx+25 \int \frac {e^{-5 x+4 e^x x}}{x^3} \, dx+80 \int \frac {e^{4 \left (-1+e^x\right ) x}}{x^3} \, dx-100 \int \frac {e^{-5 x+4 e^x x}}{x^5} \, dx+100 \int \frac {e^{4 \left (-1+e^x\right ) x}}{x^4} \, dx-110 \int \frac {e^{-5 x+4 e^x x}}{x^4} \, dx-300 \int \frac {e^{-4 x+3 e^x x}}{x^2} \, dx+500 \int \frac {e^{-5 x+3 e^x x}}{x^3} \, dx+1200 \int \frac {e^{-4 x+3 e^x x}}{x^3} \, dx+1500 \int \frac {e^{-4 x+3 e^x x}}{x^4} \, dx-1500 \int \frac {e^{2 \left (-2+e^x\right ) x}}{x^2} \, dx-2000 \int \frac {e^{-5 x+3 e^x x}}{x^5} \, dx-2200 \int \frac {e^{-5 x+3 e^x x}}{x^4} \, dx-2500 \int \frac {e^{-4 x+e^x x}}{x^2} \, dx+3750 \int \frac {e^{-5 x+2 e^x x}}{x^3} \, dx+6000 \int \frac {e^{2 \left (-2+e^x\right ) x}}{x^3} \, dx+7500 \int \frac {e^{2 \left (-2+e^x\right ) x}}{x^4} \, dx+10000 \int \frac {e^{-4 x+e^x x}}{x^3} \, dx+12500 \int \frac {e^{-4 x+e^x x}}{x^4} \, dx+12500 \int \frac {e^{-5 x+e^x x}}{x^3} \, dx-15000 \int \frac {e^{-5 x+2 e^x x}}{x^5} \, dx-16500 \int \frac {e^{-5 x+2 e^x x}}{x^4} \, dx-50000 \int \frac {e^{-5 x+e^x x}}{x^5} \, dx-55000 \int \frac {e^{-5 x+e^x x}}{x^4} \, dx-\frac {9765625}{6} \int \frac {e^{-5 x}}{x} \, dx\\ &=\frac {15625 e^{-5 x}}{x^4}-\frac {3125 e^{-5 x}}{x^3}-20 \int \frac {e^{4 \left (-1+e^x\right ) x}}{x^2} \, dx+25 \int \frac {e^{-5 x+4 e^x x}}{x^3} \, dx+80 \int \frac {e^{4 \left (-1+e^x\right ) x}}{x^3} \, dx-100 \int \frac {e^{-5 x+4 e^x x}}{x^5} \, dx+100 \int \frac {e^{4 \left (-1+e^x\right ) x}}{x^4} \, dx-110 \int \frac {e^{-5 x+4 e^x x}}{x^4} \, dx-300 \int \frac {e^{-4 x+3 e^x x}}{x^2} \, dx+500 \int \frac {e^{-5 x+3 e^x x}}{x^3} \, dx+1200 \int \frac {e^{-4 x+3 e^x x}}{x^3} \, dx+1500 \int \frac {e^{-4 x+3 e^x x}}{x^4} \, dx-1500 \int \frac {e^{2 \left (-2+e^x\right ) x}}{x^2} \, dx-2000 \int \frac {e^{-5 x+3 e^x x}}{x^5} \, dx-2200 \int \frac {e^{-5 x+3 e^x x}}{x^4} \, dx-2500 \int \frac {e^{-4 x+e^x x}}{x^2} \, dx+3750 \int \frac {e^{-5 x+2 e^x x}}{x^3} \, dx+6000 \int \frac {e^{2 \left (-2+e^x\right ) x}}{x^3} \, dx+7500 \int \frac {e^{2 \left (-2+e^x\right ) x}}{x^4} \, dx+10000 \int \frac {e^{-4 x+e^x x}}{x^3} \, dx+12500 \int \frac {e^{-4 x+e^x x}}{x^4} \, dx+12500 \int \frac {e^{-5 x+e^x x}}{x^3} \, dx-15000 \int \frac {e^{-5 x+2 e^x x}}{x^5} \, dx-16500 \int \frac {e^{-5 x+2 e^x x}}{x^4} \, dx-50000 \int \frac {e^{-5 x+e^x x}}{x^5} \, dx-55000 \int \frac {e^{-5 x+e^x x}}{x^4} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 4.75, size = 24, normalized size = 0.92 \begin {gather*} -\frac {5 e^{-5 x} \left (5+e^{e^x x}\right )^4 (-5+x)}{x^4} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-62500 - 68750*x + 15625*x^2 + E^(E^x*x)*(-50000 - 55000*x + 12500*x^2 + E^x*(12500*x + 10000*x^2 -
2500*x^3)) + E^(2*E^x*x)*(-15000 - 16500*x + 3750*x^2 + E^x*(7500*x + 6000*x^2 - 1500*x^3)) + E^(3*E^x*x)*(-2
000 - 2200*x + 500*x^2 + E^x*(1500*x + 1200*x^2 - 300*x^3)) + E^(4*E^x*x)*(-100 - 110*x + 25*x^2 + E^x*(100*x
+ 80*x^2 - 20*x^3)))/(E^(5*x)*x^5),x]

[Out]

(-5*(5 + E^(E^x*x))^4*(-5 + x))/(E^(5*x)*x^4)

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fricas [B]  time = 0.55, size = 56, normalized size = 2.15 \begin {gather*} -\frac {5 \, {\left ({\left (x - 5\right )} e^{\left (4 \, x e^{x}\right )} + 20 \, {\left (x - 5\right )} e^{\left (3 \, x e^{x}\right )} + 150 \, {\left (x - 5\right )} e^{\left (2 \, x e^{x}\right )} + 500 \, {\left (x - 5\right )} e^{\left (x e^{x}\right )} + 625 \, x - 3125\right )} e^{\left (-5 \, x\right )}}{x^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-20*x^3+80*x^2+100*x)*exp(x)+25*x^2-110*x-100)*exp(exp(x)*x)^4+((-300*x^3+1200*x^2+1500*x)*exp(x)
+500*x^2-2200*x-2000)*exp(exp(x)*x)^3+((-1500*x^3+6000*x^2+7500*x)*exp(x)+3750*x^2-16500*x-15000)*exp(exp(x)*x
)^2+((-2500*x^3+10000*x^2+12500*x)*exp(x)+12500*x^2-55000*x-50000)*exp(exp(x)*x)+15625*x^2-68750*x-62500)/x^5/
exp(5*x),x, algorithm="fricas")

[Out]

-5*((x - 5)*e^(4*x*e^x) + 20*(x - 5)*e^(3*x*e^x) + 150*(x - 5)*e^(2*x*e^x) + 500*(x - 5)*e^(x*e^x) + 625*x - 3
125)*e^(-5*x)/x^4

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giac [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-20*x^3+80*x^2+100*x)*exp(x)+25*x^2-110*x-100)*exp(exp(x)*x)^4+((-300*x^3+1200*x^2+1500*x)*exp(x)
+500*x^2-2200*x-2000)*exp(exp(x)*x)^3+((-1500*x^3+6000*x^2+7500*x)*exp(x)+3750*x^2-16500*x-15000)*exp(exp(x)*x
)^2+((-2500*x^3+10000*x^2+12500*x)*exp(x)+12500*x^2-55000*x-50000)*exp(exp(x)*x)+15625*x^2-68750*x-62500)/x^5/
exp(5*x),x, algorithm="giac")

[Out]

Timed out

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maple [B]  time = 0.12, size = 80, normalized size = 3.08

method	result	size
risch	\(-\frac {3125 \left (x -5\right ) {\mathrm e}^{-5 x}}{x^{4}}-\frac {5 \left (x -5\right ) {\mathrm e}^{x \left (4 \,{\mathrm e}^{x}-5\right )}}{x^{4}}-\frac {100 \left (x -5\right ) {\mathrm e}^{x \left (3 \,{\mathrm e}^{x}-5\right )}}{x^{4}}-\frac {750 \left (x -5\right ) {\mathrm e}^{x \left (2 \,{\mathrm e}^{x}-5\right )}}{x^{4}}-\frac {2500 \left (x -5\right ) {\mathrm e}^{x \left ({\mathrm e}^{x}-5\right )}}{x^{4}}\)	\(80\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-20*x^3+80*x^2+100*x)*exp(x)+25*x^2-110*x-100)*exp(exp(x)*x)^4+((-300*x^3+1200*x^2+1500*x)*exp(x)+500*x
^2-2200*x-2000)*exp(exp(x)*x)^3+((-1500*x^3+6000*x^2+7500*x)*exp(x)+3750*x^2-16500*x-15000)*exp(exp(x)*x)^2+((
-2500*x^3+10000*x^2+12500*x)*exp(x)+12500*x^2-55000*x-50000)*exp(exp(x)*x)+15625*x^2-68750*x-62500)/x^5/exp(5*
x),x,method=_RETURNVERBOSE)

[Out]

-3125*(x-5)/x^4*exp(-5*x)-5*(x-5)/x^4*exp(x*(4*exp(x)-5))-100*(x-5)/x^4*exp(x*(3*exp(x)-5))-750*(x-5)/x^4*exp(
x*(2*exp(x)-5))-2500*(x-5)/x^4*exp(x*(exp(x)-5))

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maxima [C]  time = 0.57, size = 74, normalized size = 2.85 \begin {gather*} -\frac {5 \, {\left ({\left (x - 5\right )} e^{\left (4 \, x e^{x}\right )} + 20 \, {\left (x - 5\right )} e^{\left (3 \, x e^{x}\right )} + 150 \, {\left (x - 5\right )} e^{\left (2 \, x e^{x}\right )} + 500 \, {\left (x - 5\right )} e^{\left (x e^{x}\right )}\right )} e^{\left (-5 \, x\right )}}{x^{4}} - 390625 \, \Gamma \left (-2, 5 \, x\right ) + 8593750 \, \Gamma \left (-3, 5 \, x\right ) + 39062500 \, \Gamma \left (-4, 5 \, x\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-20*x^3+80*x^2+100*x)*exp(x)+25*x^2-110*x-100)*exp(exp(x)*x)^4+((-300*x^3+1200*x^2+1500*x)*exp(x)
+500*x^2-2200*x-2000)*exp(exp(x)*x)^3+((-1500*x^3+6000*x^2+7500*x)*exp(x)+3750*x^2-16500*x-15000)*exp(exp(x)*x
)^2+((-2500*x^3+10000*x^2+12500*x)*exp(x)+12500*x^2-55000*x-50000)*exp(exp(x)*x)+15625*x^2-68750*x-62500)/x^5/
exp(5*x),x, algorithm="maxima")

[Out]

-5*((x - 5)*e^(4*x*e^x) + 20*(x - 5)*e^(3*x*e^x) + 150*(x - 5)*e^(2*x*e^x) + 500*(x - 5)*e^(x*e^x))*e^(-5*x)/x
^4 - 390625*gamma(-2, 5*x) + 8593750*gamma(-3, 5*x) + 39062500*gamma(-4, 5*x)

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mupad [B]  time = 1.79, size = 94, normalized size = 3.62 \begin {gather*} -\frac {{\mathrm {e}}^{-5\,x}\,\left (3125\,x-15625\right )}{x^4}-\frac {{\mathrm {e}}^{4\,x\,{\mathrm {e}}^x-5\,x}\,\left (5\,x-25\right )}{x^4}-\frac {{\mathrm {e}}^{3\,x\,{\mathrm {e}}^x-5\,x}\,\left (100\,x-500\right )}{x^4}-\frac {{\mathrm {e}}^{2\,x\,{\mathrm {e}}^x-5\,x}\,\left (750\,x-3750\right )}{x^4}-\frac {{\mathrm {e}}^{x\,{\mathrm {e}}^x-5\,x}\,\left (2500\,x-12500\right )}{x^4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(-5*x)*(68750*x + exp(4*x*exp(x))*(110*x - 25*x^2 - exp(x)*(100*x + 80*x^2 - 20*x^3) + 100) + exp(3*x
*exp(x))*(2200*x - 500*x^2 - exp(x)*(1500*x + 1200*x^2 - 300*x^3) + 2000) + exp(2*x*exp(x))*(16500*x - 3750*x^
2 - exp(x)*(7500*x + 6000*x^2 - 1500*x^3) + 15000) + exp(x*exp(x))*(55000*x - 12500*x^2 - exp(x)*(12500*x + 10
000*x^2 - 2500*x^3) + 50000) - 15625*x^2 + 62500))/x^5,x)

[Out]

- (exp(-5*x)*(3125*x - 15625))/x^4 - (exp(4*x*exp(x) - 5*x)*(5*x - 25))/x^4 - (exp(3*x*exp(x) - 5*x)*(100*x -
500))/x^4 - (exp(2*x*exp(x) - 5*x)*(750*x - 3750))/x^4 - (exp(x*exp(x) - 5*x)*(2500*x - 12500))/x^4

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sympy [B]  time = 0.67, size = 129, normalized size = 4.96 \begin {gather*} \frac {\left (15625 - 3125 x\right ) e^{- 5 x}}{x^{4}} + \frac {\left (- 2500 x^{13} e^{- 5 x} + 12500 x^{12} e^{- 5 x}\right ) e^{x e^{x}} + \left (- 750 x^{13} e^{- 5 x} + 3750 x^{12} e^{- 5 x}\right ) e^{2 x e^{x}} + \left (- 100 x^{13} e^{- 5 x} + 500 x^{12} e^{- 5 x}\right ) e^{3 x e^{x}} + \left (- 5 x^{13} e^{- 5 x} + 25 x^{12} e^{- 5 x}\right ) e^{4 x e^{x}}}{x^{16}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-20*x**3+80*x**2+100*x)*exp(x)+25*x**2-110*x-100)*exp(exp(x)*x)**4+((-300*x**3+1200*x**2+1500*x)*
exp(x)+500*x**2-2200*x-2000)*exp(exp(x)*x)**3+((-1500*x**3+6000*x**2+7500*x)*exp(x)+3750*x**2-16500*x-15000)*e
xp(exp(x)*x)**2+((-2500*x**3+10000*x**2+12500*x)*exp(x)+12500*x**2-55000*x-50000)*exp(exp(x)*x)+15625*x**2-687
50*x-62500)/x**5/exp(5*x),x)

[Out]

(15625 - 3125*x)*exp(-5*x)/x**4 + ((-2500*x**13*exp(-5*x) + 12500*x**12*exp(-5*x))*exp(x*exp(x)) + (-750*x**13
*exp(-5*x) + 3750*x**12*exp(-5*x))*exp(2*x*exp(x)) + (-100*x**13*exp(-5*x) + 500*x**12*exp(-5*x))*exp(3*x*exp(
x)) + (-5*x**13*exp(-5*x) + 25*x**12*exp(-5*x))*exp(4*x*exp(x)))/x**16

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