3.35.48 \(\int \frac {-2400+160 x^2-2400 x^3-2 x^4+80 x^5+2 x^7-80 x^8+4 x^{10}+e^{-2 e^x+2 x} (-150+50 x-150 x^3+100 x^4+50 x^7+e^x (-50 x-100 x^4-50 x^7))+e^{-e^x+x} (1200-200 x-40 x^2+1210 x^3-400 x^4-20 x^5+20 x^6-200 x^7+20 x^8+10 x^9+e^x (200 x-10 x^3+400 x^4-20 x^6+200 x^7-10 x^9))}{x^7} \, dx\)

Optimal. Leaf size=28 \[ \left (\frac {1}{x^2}+x\right )^2 \left (\frac {5 \left (-4+e^{-e^x+x}\right )}{x}+x\right )^2 \]

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Rubi [F]  time = 18.69, 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 {-2400+160 x^2-2400 x^3-2 x^4+80 x^5+2 x^7-80 x^8+4 x^{10}+e^{-2 e^x+2 x} \left (-150+50 x-150 x^3+100 x^4+50 x^7+e^x \left (-50 x-100 x^4-50 x^7\right )\right )+e^{-e^x+x} \left (1200-200 x-40 x^2+1210 x^3-400 x^4-20 x^5+20 x^6-200 x^7+20 x^8+10 x^9+e^x \left (200 x-10 x^3+400 x^4-20 x^6+200 x^7-10 x^9\right )\right )}{x^7} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-2400 + 160*x^2 - 2400*x^3 - 2*x^4 + 80*x^5 + 2*x^7 - 80*x^8 + 4*x^10 + E^(-2*E^x + 2*x)*(-150 + 50*x - 1
50*x^3 + 100*x^4 + 50*x^7 + E^x*(-50*x - 100*x^4 - 50*x^7)) + E^(-E^x + x)*(1200 - 200*x - 40*x^2 + 1210*x^3 -
400*x^4 - 20*x^5 + 20*x^6 - 200*x^7 + 20*x^8 + 10*x^9 + E^x*(200*x - 10*x^3 + 400*x^4 - 20*x^6 + 200*x^7 - 10
*x^9)))/x^7,x]

[Out]

25/(2*E^(2*E^x)) + 25*E^(-2*E^x + x) - 200*E^(-E^x + x) + 25*E^(-2*E^x + 2*x) + 400/x^6 - 40/x^4 + 800/x^3 + x
^(-2) - 80/x + 2*x - 40*x^2 + x^4 + 50*Defer[Int][E^(-2*(E^x - x)), x] - 150*Defer[Int][1/(E^(2*(E^x - x))*x^7
), x] + 1200*Defer[Int][E^(-E^x + x)/x^7, x] + 50*Defer[Int][1/(E^(2*(E^x - x))*x^6), x] - 200*Defer[Int][E^(-
E^x + x)/x^6, x] + 200*Defer[Int][E^(-E^x + 2*x)/x^6, x] - 50*Defer[Int][E^(-2*E^x + 3*x)/x^6, x] - 40*Defer[I
nt][E^(-E^x + x)/x^5, x] - 150*Defer[Int][1/(E^(2*(E^x - x))*x^4), x] + 1210*Defer[Int][E^(-E^x + x)/x^4, x] -
10*Defer[Int][E^(-E^x + 2*x)/x^4, x] + 100*Defer[Int][1/(E^(2*(E^x - x))*x^3), x] - 400*Defer[Int][E^(-E^x +
x)/x^3, x] + 400*Defer[Int][E^(-E^x + 2*x)/x^3, x] - 100*Defer[Int][E^(-2*E^x + 3*x)/x^3, x] - 20*Defer[Int][E
^(-E^x + x)/x^2, x] + 20*Defer[Int][E^(-E^x + x)/x, x] - 20*Defer[Int][E^(-E^x + 2*x)/x, x] + 20*Defer[Int][E^
(-E^x + x)*x, x] + 10*Defer[Int][E^(-E^x + x)*x^2, x] - 10*Defer[Int][E^(-E^x + 2*x)*x^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {50 e^{-2 e^x+3 x} \left (1+x^3\right )^2}{x^6}+\frac {10 e^{-2 \left (e^x-x\right )} \left (1+x^3\right ) \left (-15+5 x+20 e^{e^x} x-e^{e^x} x^3+5 x^4+20 e^{e^x} x^4-e^{e^x} x^6\right )}{x^7}+\frac {10 e^{-e^x+x} \left (120-20 x-4 x^2+121 x^3-40 x^4-2 x^5+2 x^6-20 x^7+2 x^8+x^9\right )}{x^7}+\frac {2 \left (-1200+80 x^2-1200 x^3-x^4+40 x^5+x^7-40 x^8+2 x^{10}\right )}{x^7}\right ) \, dx\\ &=2 \int \frac {-1200+80 x^2-1200 x^3-x^4+40 x^5+x^7-40 x^8+2 x^{10}}{x^7} \, dx+10 \int \frac {e^{-2 \left (e^x-x\right )} \left (1+x^3\right ) \left (-15+5 x+20 e^{e^x} x-e^{e^x} x^3+5 x^4+20 e^{e^x} x^4-e^{e^x} x^6\right )}{x^7} \, dx+10 \int \frac {e^{-e^x+x} \left (120-20 x-4 x^2+121 x^3-40 x^4-2 x^5+2 x^6-20 x^7+2 x^8+x^9\right )}{x^7} \, dx-50 \int \frac {e^{-2 e^x+3 x} \left (1+x^3\right )^2}{x^6} \, dx\\ &=2 \int \left (1-\frac {1200}{x^7}+\frac {80}{x^5}-\frac {1200}{x^4}-\frac {1}{x^3}+\frac {40}{x^2}-40 x+2 x^3\right ) \, dx+10 \int \left (-20 e^{-e^x+x}+\frac {120 e^{-e^x+x}}{x^7}-\frac {20 e^{-e^x+x}}{x^6}-\frac {4 e^{-e^x+x}}{x^5}+\frac {121 e^{-e^x+x}}{x^4}-\frac {40 e^{-e^x+x}}{x^3}-\frac {2 e^{-e^x+x}}{x^2}+\frac {2 e^{-e^x+x}}{x}+2 e^{-e^x+x} x+e^{-e^x+x} x^2\right ) \, dx+10 \int \left (-\frac {e^{e^x-2 \left (e^x-x\right )} \left (-20+x^2\right ) \left (1+x^3\right )^2}{x^6}+\frac {5 e^{-2 \left (e^x-x\right )} (1+x) \left (1-x+x^2\right ) \left (-3+x+x^4\right )}{x^7}\right ) \, dx-50 \int \left (e^{-2 e^x+3 x}+\frac {e^{-2 e^x+3 x}}{x^6}+\frac {2 e^{-2 e^x+3 x}}{x^3}\right ) \, dx\\ &=\frac {400}{x^6}-\frac {40}{x^4}+\frac {800}{x^3}+\frac {1}{x^2}-\frac {80}{x}+2 x-40 x^2+x^4+10 \int e^{-e^x+x} x^2 \, dx-10 \int \frac {e^{e^x-2 \left (e^x-x\right )} \left (-20+x^2\right ) \left (1+x^3\right )^2}{x^6} \, dx-20 \int \frac {e^{-e^x+x}}{x^2} \, dx+20 \int \frac {e^{-e^x+x}}{x} \, dx+20 \int e^{-e^x+x} x \, dx-40 \int \frac {e^{-e^x+x}}{x^5} \, dx-50 \int e^{-2 e^x+3 x} \, dx-50 \int \frac {e^{-2 e^x+3 x}}{x^6} \, dx+50 \int \frac {e^{-2 \left (e^x-x\right )} (1+x) \left (1-x+x^2\right ) \left (-3+x+x^4\right )}{x^7} \, dx-100 \int \frac {e^{-2 e^x+3 x}}{x^3} \, dx-200 \int e^{-e^x+x} \, dx-200 \int \frac {e^{-e^x+x}}{x^6} \, dx-400 \int \frac {e^{-e^x+x}}{x^3} \, dx+1200 \int \frac {e^{-e^x+x}}{x^7} \, dx+1210 \int \frac {e^{-e^x+x}}{x^4} \, dx\\ &=\frac {400}{x^6}-\frac {40}{x^4}+\frac {800}{x^3}+\frac {1}{x^2}-\frac {80}{x}+2 x-40 x^2+x^4+10 \int e^{-e^x+x} x^2 \, dx-10 \int \frac {e^{-e^x+2 x} \left (-20+x^2\right ) \left (1+x^3\right )^2}{x^6} \, dx-20 \int \frac {e^{-e^x+x}}{x^2} \, dx+20 \int \frac {e^{-e^x+x}}{x} \, dx+20 \int e^{-e^x+x} x \, dx-40 \int \frac {e^{-e^x+x}}{x^5} \, dx+50 \int \left (e^{-2 \left (e^x-x\right )}-\frac {3 e^{-2 \left (e^x-x\right )}}{x^7}+\frac {e^{-2 \left (e^x-x\right )}}{x^6}-\frac {3 e^{-2 \left (e^x-x\right )}}{x^4}+\frac {2 e^{-2 \left (e^x-x\right )}}{x^3}\right ) \, dx-50 \int \frac {e^{-2 e^x+3 x}}{x^6} \, dx-50 \operatorname {Subst}\left (\int e^{-2 x} x^2 \, dx,x,e^x\right )-100 \int \frac {e^{-2 e^x+3 x}}{x^3} \, dx-200 \int \frac {e^{-e^x+x}}{x^6} \, dx-200 \operatorname {Subst}\left (\int e^{-x} \, dx,x,e^x\right )-400 \int \frac {e^{-e^x+x}}{x^3} \, dx+1200 \int \frac {e^{-e^x+x}}{x^7} \, dx+1210 \int \frac {e^{-e^x+x}}{x^4} \, dx\\ &=200 e^{-e^x}+25 e^{-2 e^x+2 x}+\frac {400}{x^6}-\frac {40}{x^4}+\frac {800}{x^3}+\frac {1}{x^2}-\frac {80}{x}+2 x-40 x^2+x^4+10 \int e^{-e^x+x} x^2 \, dx-10 \int \left (-20 e^{-e^x+2 x}-\frac {20 e^{-e^x+2 x}}{x^6}+\frac {e^{-e^x+2 x}}{x^4}-\frac {40 e^{-e^x+2 x}}{x^3}+\frac {2 e^{-e^x+2 x}}{x}+e^{-e^x+2 x} x^2\right ) \, dx-20 \int \frac {e^{-e^x+x}}{x^2} \, dx+20 \int \frac {e^{-e^x+x}}{x} \, dx+20 \int e^{-e^x+x} x \, dx-40 \int \frac {e^{-e^x+x}}{x^5} \, dx+50 \int e^{-2 \left (e^x-x\right )} \, dx+50 \int \frac {e^{-2 \left (e^x-x\right )}}{x^6} \, dx-50 \int \frac {e^{-2 e^x+3 x}}{x^6} \, dx-50 \operatorname {Subst}\left (\int e^{-2 x} x \, dx,x,e^x\right )+100 \int \frac {e^{-2 \left (e^x-x\right )}}{x^3} \, dx-100 \int \frac {e^{-2 e^x+3 x}}{x^3} \, dx-150 \int \frac {e^{-2 \left (e^x-x\right )}}{x^7} \, dx-150 \int \frac {e^{-2 \left (e^x-x\right )}}{x^4} \, dx-200 \int \frac {e^{-e^x+x}}{x^6} \, dx-400 \int \frac {e^{-e^x+x}}{x^3} \, dx+1200 \int \frac {e^{-e^x+x}}{x^7} \, dx+1210 \int \frac {e^{-e^x+x}}{x^4} \, dx\\ &=200 e^{-e^x}+25 e^{-2 e^x+x}+25 e^{-2 e^x+2 x}+\frac {400}{x^6}-\frac {40}{x^4}+\frac {800}{x^3}+\frac {1}{x^2}-\frac {80}{x}+2 x-40 x^2+x^4-10 \int \frac {e^{-e^x+2 x}}{x^4} \, dx+10 \int e^{-e^x+x} x^2 \, dx-10 \int e^{-e^x+2 x} x^2 \, dx-20 \int \frac {e^{-e^x+x}}{x^2} \, dx+20 \int \frac {e^{-e^x+x}}{x} \, dx-20 \int \frac {e^{-e^x+2 x}}{x} \, dx+20 \int e^{-e^x+x} x \, dx-25 \operatorname {Subst}\left (\int e^{-2 x} \, dx,x,e^x\right )-40 \int \frac {e^{-e^x+x}}{x^5} \, dx+50 \int e^{-2 \left (e^x-x\right )} \, dx+50 \int \frac {e^{-2 \left (e^x-x\right )}}{x^6} \, dx-50 \int \frac {e^{-2 e^x+3 x}}{x^6} \, dx+100 \int \frac {e^{-2 \left (e^x-x\right )}}{x^3} \, dx-100 \int \frac {e^{-2 e^x+3 x}}{x^3} \, dx-150 \int \frac {e^{-2 \left (e^x-x\right )}}{x^7} \, dx-150 \int \frac {e^{-2 \left (e^x-x\right )}}{x^4} \, dx+200 \int e^{-e^x+2 x} \, dx-200 \int \frac {e^{-e^x+x}}{x^6} \, dx+200 \int \frac {e^{-e^x+2 x}}{x^6} \, dx-400 \int \frac {e^{-e^x+x}}{x^3} \, dx+400 \int \frac {e^{-e^x+2 x}}{x^3} \, dx+1200 \int \frac {e^{-e^x+x}}{x^7} \, dx+1210 \int \frac {e^{-e^x+x}}{x^4} \, dx\\ &=\frac {25}{2} e^{-2 e^x}+200 e^{-e^x}+25 e^{-2 e^x+x}+25 e^{-2 e^x+2 x}+\frac {400}{x^6}-\frac {40}{x^4}+\frac {800}{x^3}+\frac {1}{x^2}-\frac {80}{x}+2 x-40 x^2+x^4-10 \int \frac {e^{-e^x+2 x}}{x^4} \, dx+10 \int e^{-e^x+x} x^2 \, dx-10 \int e^{-e^x+2 x} x^2 \, dx-20 \int \frac {e^{-e^x+x}}{x^2} \, dx+20 \int \frac {e^{-e^x+x}}{x} \, dx-20 \int \frac {e^{-e^x+2 x}}{x} \, dx+20 \int e^{-e^x+x} x \, dx-40 \int \frac {e^{-e^x+x}}{x^5} \, dx+50 \int e^{-2 \left (e^x-x\right )} \, dx+50 \int \frac {e^{-2 \left (e^x-x\right )}}{x^6} \, dx-50 \int \frac {e^{-2 e^x+3 x}}{x^6} \, dx+100 \int \frac {e^{-2 \left (e^x-x\right )}}{x^3} \, dx-100 \int \frac {e^{-2 e^x+3 x}}{x^3} \, dx-150 \int \frac {e^{-2 \left (e^x-x\right )}}{x^7} \, dx-150 \int \frac {e^{-2 \left (e^x-x\right )}}{x^4} \, dx-200 \int \frac {e^{-e^x+x}}{x^6} \, dx+200 \int \frac {e^{-e^x+2 x}}{x^6} \, dx+200 \operatorname {Subst}\left (\int e^{-x} x \, dx,x,e^x\right )-400 \int \frac {e^{-e^x+x}}{x^3} \, dx+400 \int \frac {e^{-e^x+2 x}}{x^3} \, dx+1200 \int \frac {e^{-e^x+x}}{x^7} \, dx+1210 \int \frac {e^{-e^x+x}}{x^4} \, dx\\ &=\frac {25}{2} e^{-2 e^x}+200 e^{-e^x}+25 e^{-2 e^x+x}-200 e^{-e^x+x}+25 e^{-2 e^x+2 x}+\frac {400}{x^6}-\frac {40}{x^4}+\frac {800}{x^3}+\frac {1}{x^2}-\frac {80}{x}+2 x-40 x^2+x^4-10 \int \frac {e^{-e^x+2 x}}{x^4} \, dx+10 \int e^{-e^x+x} x^2 \, dx-10 \int e^{-e^x+2 x} x^2 \, dx-20 \int \frac {e^{-e^x+x}}{x^2} \, dx+20 \int \frac {e^{-e^x+x}}{x} \, dx-20 \int \frac {e^{-e^x+2 x}}{x} \, dx+20 \int e^{-e^x+x} x \, dx-40 \int \frac {e^{-e^x+x}}{x^5} \, dx+50 \int e^{-2 \left (e^x-x\right )} \, dx+50 \int \frac {e^{-2 \left (e^x-x\right )}}{x^6} \, dx-50 \int \frac {e^{-2 e^x+3 x}}{x^6} \, dx+100 \int \frac {e^{-2 \left (e^x-x\right )}}{x^3} \, dx-100 \int \frac {e^{-2 e^x+3 x}}{x^3} \, dx-150 \int \frac {e^{-2 \left (e^x-x\right )}}{x^7} \, dx-150 \int \frac {e^{-2 \left (e^x-x\right )}}{x^4} \, dx-200 \int \frac {e^{-e^x+x}}{x^6} \, dx+200 \int \frac {e^{-e^x+2 x}}{x^6} \, dx+200 \operatorname {Subst}\left (\int e^{-x} \, dx,x,e^x\right )-400 \int \frac {e^{-e^x+x}}{x^3} \, dx+400 \int \frac {e^{-e^x+2 x}}{x^3} \, dx+1200 \int \frac {e^{-e^x+x}}{x^7} \, dx+1210 \int \frac {e^{-e^x+x}}{x^4} \, dx\\ &=\frac {25}{2} e^{-2 e^x}+25 e^{-2 e^x+x}-200 e^{-e^x+x}+25 e^{-2 e^x+2 x}+\frac {400}{x^6}-\frac {40}{x^4}+\frac {800}{x^3}+\frac {1}{x^2}-\frac {80}{x}+2 x-40 x^2+x^4-10 \int \frac {e^{-e^x+2 x}}{x^4} \, dx+10 \int e^{-e^x+x} x^2 \, dx-10 \int e^{-e^x+2 x} x^2 \, dx-20 \int \frac {e^{-e^x+x}}{x^2} \, dx+20 \int \frac {e^{-e^x+x}}{x} \, dx-20 \int \frac {e^{-e^x+2 x}}{x} \, dx+20 \int e^{-e^x+x} x \, dx-40 \int \frac {e^{-e^x+x}}{x^5} \, dx+50 \int e^{-2 \left (e^x-x\right )} \, dx+50 \int \frac {e^{-2 \left (e^x-x\right )}}{x^6} \, dx-50 \int \frac {e^{-2 e^x+3 x}}{x^6} \, dx+100 \int \frac {e^{-2 \left (e^x-x\right )}}{x^3} \, dx-100 \int \frac {e^{-2 e^x+3 x}}{x^3} \, dx-150 \int \frac {e^{-2 \left (e^x-x\right )}}{x^7} \, dx-150 \int \frac {e^{-2 \left (e^x-x\right )}}{x^4} \, dx-200 \int \frac {e^{-e^x+x}}{x^6} \, dx+200 \int \frac {e^{-e^x+2 x}}{x^6} \, dx-400 \int \frac {e^{-e^x+x}}{x^3} \, dx+400 \int \frac {e^{-e^x+2 x}}{x^3} \, dx+1200 \int \frac {e^{-e^x+x}}{x^7} \, dx+1210 \int \frac {e^{-e^x+x}}{x^4} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.19, size = 96, normalized size = 3.43 \begin {gather*} -2 \left (-\frac {200}{x^6}+\frac {20}{x^4}-\frac {400}{x^3}-\frac {1}{2 x^2}+\frac {40}{x}-x+20 x^2-\frac {x^4}{2}-\frac {25 e^{-2 e^x+2 x} \left (1+x^3\right )^2}{2 x^6}-\frac {5 e^{-e^x+x} \left (-20+x^2\right ) \left (1+x^3\right )^2}{x^6}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-2400 + 160*x^2 - 2400*x^3 - 2*x^4 + 80*x^5 + 2*x^7 - 80*x^8 + 4*x^10 + E^(-2*E^x + 2*x)*(-150 + 50
*x - 150*x^3 + 100*x^4 + 50*x^7 + E^x*(-50*x - 100*x^4 - 50*x^7)) + E^(-E^x + x)*(1200 - 200*x - 40*x^2 + 1210
*x^3 - 400*x^4 - 20*x^5 + 20*x^6 - 200*x^7 + 20*x^8 + 10*x^9 + E^x*(200*x - 10*x^3 + 400*x^4 - 20*x^6 + 200*x^
7 - 10*x^9)))/x^7,x]

[Out]

-2*(-200/x^6 + 20/x^4 - 400/x^3 - 1/(2*x^2) + 40/x - x + 20*x^2 - x^4/2 - (25*E^(-2*E^x + 2*x)*(1 + x^3)^2)/(2
*x^6) - (5*E^(-E^x + x)*(-20 + x^2)*(1 + x^3)^2)/x^6)

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fricas [B]  time = 0.56, size = 90, normalized size = 3.21 \begin {gather*} \frac {x^{10} - 40 \, x^{8} + 2 \, x^{7} - 80 \, x^{5} + x^{4} + 800 \, x^{3} - 40 \, x^{2} + 25 \, {\left (x^{6} + 2 \, x^{3} + 1\right )} e^{\left (2 \, x - 2 \, e^{x}\right )} + 10 \, {\left (x^{8} - 20 \, x^{6} + 2 \, x^{5} - 40 \, x^{3} + x^{2} - 20\right )} e^{\left (x - e^{x}\right )} + 400}{x^{6}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-50*x^7-100*x^4-50*x)*exp(x)+50*x^7+100*x^4-150*x^3+50*x-150)*exp(x-exp(x))^2+((-10*x^9+200*x^7-2
0*x^6+400*x^4-10*x^3+200*x)*exp(x)+10*x^9+20*x^8-200*x^7+20*x^6-20*x^5-400*x^4+1210*x^3-40*x^2-200*x+1200)*exp
(x-exp(x))+4*x^10-80*x^8+2*x^7+80*x^5-2*x^4-2400*x^3+160*x^2-2400)/x^7,x, algorithm="fricas")

[Out]

(x^10 - 40*x^8 + 2*x^7 - 80*x^5 + x^4 + 800*x^3 - 40*x^2 + 25*(x^6 + 2*x^3 + 1)*e^(2*x - 2*e^x) + 10*(x^8 - 20
*x^6 + 2*x^5 - 40*x^3 + x^2 - 20)*e^(x - e^x) + 400)/x^6

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {2 \, {\left (2 \, x^{10} - 40 \, x^{8} + x^{7} + 40 \, x^{5} - x^{4} - 1200 \, x^{3} + 80 \, x^{2} + 25 \, {\left (x^{7} + 2 \, x^{4} - 3 \, x^{3} - {\left (x^{7} + 2 \, x^{4} + x\right )} e^{x} + x - 3\right )} e^{\left (2 \, x - 2 \, e^{x}\right )} + 5 \, {\left (x^{9} + 2 \, x^{8} - 20 \, x^{7} + 2 \, x^{6} - 2 \, x^{5} - 40 \, x^{4} + 121 \, x^{3} - 4 \, x^{2} - {\left (x^{9} - 20 \, x^{7} + 2 \, x^{6} - 40 \, x^{4} + x^{3} - 20 \, x\right )} e^{x} - 20 \, x + 120\right )} e^{\left (x - e^{x}\right )} - 1200\right )}}{x^{7}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-50*x^7-100*x^4-50*x)*exp(x)+50*x^7+100*x^4-150*x^3+50*x-150)*exp(x-exp(x))^2+((-10*x^9+200*x^7-2
0*x^6+400*x^4-10*x^3+200*x)*exp(x)+10*x^9+20*x^8-200*x^7+20*x^6-20*x^5-400*x^4+1210*x^3-40*x^2-200*x+1200)*exp
(x-exp(x))+4*x^10-80*x^8+2*x^7+80*x^5-2*x^4-2400*x^3+160*x^2-2400)/x^7,x, algorithm="giac")

[Out]

integrate(2*(2*x^10 - 40*x^8 + x^7 + 40*x^5 - x^4 - 1200*x^3 + 80*x^2 + 25*(x^7 + 2*x^4 - 3*x^3 - (x^7 + 2*x^4
+ x)*e^x + x - 3)*e^(2*x - 2*e^x) + 5*(x^9 + 2*x^8 - 20*x^7 + 2*x^6 - 2*x^5 - 40*x^4 + 121*x^3 - 4*x^2 - (x^9
- 20*x^7 + 2*x^6 - 40*x^4 + x^3 - 20*x)*e^x - 20*x + 120)*e^(x - e^x) - 1200)/x^7, x)

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maple [B]  time = 0.10, size = 96, normalized size = 3.43

method	result	size
risch	\(x^{4}-40 x^{2}+2 x +\frac {-80 x^{5}+x^{4}+800 x^{3}-40 x^{2}+400}{x^{6}}+\frac {25 \left (x^{6}+2 x^{3}+1\right ) {\mathrm e}^{-2 \,{\mathrm e}^{x}+2 x}}{x^{6}}+\frac {10 \left (x^{8}-20 x^{6}+2 x^{5}-40 x^{3}+x^{2}-20\right ) {\mathrm e}^{x -{\mathrm e}^{x}}}{x^{6}}\)	\(96\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-50*x^7-100*x^4-50*x)*exp(x)+50*x^7+100*x^4-150*x^3+50*x-150)*exp(x-exp(x))^2+((-10*x^9+200*x^7-20*x^6+
400*x^4-10*x^3+200*x)*exp(x)+10*x^9+20*x^8-200*x^7+20*x^6-20*x^5-400*x^4+1210*x^3-40*x^2-200*x+1200)*exp(x-exp
(x))+4*x^10-80*x^8+2*x^7+80*x^5-2*x^4-2400*x^3+160*x^2-2400)/x^7,x,method=_RETURNVERBOSE)

[Out]

x^4-40*x^2+2*x+(-80*x^5+x^4+800*x^3-40*x^2+400)/x^6+25/x^6*(x^6+2*x^3+1)*exp(-2*exp(x)+2*x)+10/x^6*(x^8-20*x^6
+2*x^5-40*x^3+x^2-20)*exp(x-exp(x))

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maxima [B]  time = 0.85, size = 120, normalized size = 4.29 \begin {gather*} x^{4} - 40 \, x^{2} - \frac {25}{2} \, {\left (2 \, e^{x} + 1\right )} e^{\left (-2 \, e^{x}\right )} + 2 \, x - \frac {80}{x} + \frac {1}{x^{2}} + \frac {800}{x^{3}} - \frac {40}{x^{4}} + \frac {5 \, {\left (4 \, {\left (x^{8} - 20 \, x^{6} + 2 \, x^{5} - 40 \, x^{3} + x^{2} - 20\right )} e^{\left (x - e^{x}\right )} + 5 \, {\left (2 \, x^{6} e^{x} + x^{6} + 2 \, {\left (x^{6} + 2 \, x^{3} + 1\right )} e^{\left (2 \, x\right )}\right )} e^{\left (-2 \, e^{x}\right )}\right )}}{2 \, x^{6}} + \frac {400}{x^{6}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-50*x^7-100*x^4-50*x)*exp(x)+50*x^7+100*x^4-150*x^3+50*x-150)*exp(x-exp(x))^2+((-10*x^9+200*x^7-2
0*x^6+400*x^4-10*x^3+200*x)*exp(x)+10*x^9+20*x^8-200*x^7+20*x^6-20*x^5-400*x^4+1210*x^3-40*x^2-200*x+1200)*exp
(x-exp(x))+4*x^10-80*x^8+2*x^7+80*x^5-2*x^4-2400*x^3+160*x^2-2400)/x^7,x, algorithm="maxima")

[Out]

x^4 - 40*x^2 - 25/2*(2*e^x + 1)*e^(-2*e^x) + 2*x - 80/x + 1/x^2 + 800/x^3 - 40/x^4 + 5/2*(4*(x^8 - 20*x^6 + 2*
x^5 - 40*x^3 + x^2 - 20)*e^(x - e^x) + 5*(2*x^6*e^x + x^6 + 2*(x^6 + 2*x^3 + 1)*e^(2*x))*e^(-2*e^x))/x^6 + 400
/x^6

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mupad [B]  time = 2.30, size = 99, normalized size = 3.54 \begin {gather*} 2\,x+\frac {-80\,x^5+x^4+800\,x^3-40\,x^2+400}{x^6}-40\,x^2+x^4+\frac {{\mathrm {e}}^{x-{\mathrm {e}}^x}\,\left (10\,x^8-200\,x^6+20\,x^5-400\,x^3+10\,x^2-200\right )}{x^6}+\frac {{\mathrm {e}}^{2\,x-2\,{\mathrm {e}}^x}\,\left (25\,x^6+50\,x^3+25\right )}{x^6} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(x - exp(x))*(exp(x)*(200*x - 10*x^3 + 400*x^4 - 20*x^6 + 200*x^7 - 10*x^9) - 200*x - 40*x^2 + 1210*x^
3 - 400*x^4 - 20*x^5 + 20*x^6 - 200*x^7 + 20*x^8 + 10*x^9 + 1200) + 160*x^2 - 2400*x^3 - 2*x^4 + 80*x^5 + 2*x^
7 - 80*x^8 + 4*x^10 + exp(2*x - 2*exp(x))*(50*x - 150*x^3 + 100*x^4 + 50*x^7 - exp(x)*(50*x + 100*x^4 + 50*x^7
) - 150) - 2400)/x^7,x)

[Out]

2*x + (800*x^3 - 40*x^2 + x^4 - 80*x^5 + 400)/x^6 - 40*x^2 + x^4 + (exp(x - exp(x))*(10*x^2 - 400*x^3 + 20*x^5
- 200*x^6 + 10*x^8 - 200))/x^6 + (exp(2*x - 2*exp(x))*(50*x^3 + 25*x^6 + 25))/x^6

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sympy [B]  time = 0.37, size = 100, normalized size = 3.57 \begin {gather*} x^{4} - 40 x^{2} + 2 x + \frac {- 80 x^{5} + x^{4} + 800 x^{3} - 40 x^{2} + 400}{x^{6}} + \frac {\left (25 x^{12} + 50 x^{9} + 25 x^{6}\right ) e^{2 x - 2 e^{x}} + \left (10 x^{14} - 200 x^{12} + 20 x^{11} - 400 x^{9} + 10 x^{8} - 200 x^{6}\right ) e^{x - e^{x}}}{x^{12}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-50*x**7-100*x**4-50*x)*exp(x)+50*x**7+100*x**4-150*x**3+50*x-150)*exp(x-exp(x))**2+((-10*x**9+20
0*x**7-20*x**6+400*x**4-10*x**3+200*x)*exp(x)+10*x**9+20*x**8-200*x**7+20*x**6-20*x**5-400*x**4+1210*x**3-40*x
**2-200*x+1200)*exp(x-exp(x))+4*x**10-80*x**8+2*x**7+80*x**5-2*x**4-2400*x**3+160*x**2-2400)/x**7,x)

[Out]

x**4 - 40*x**2 + 2*x + (-80*x**5 + x**4 + 800*x**3 - 40*x**2 + 400)/x**6 + ((25*x**12 + 50*x**9 + 25*x**6)*exp
(2*x - 2*exp(x)) + (10*x**14 - 200*x**12 + 20*x**11 - 400*x**9 + 10*x**8 - 200*x**6)*exp(x - exp(x)))/x**12

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