∫ −x9−2x10+e2(625−x9) ______________ x8 (10000+4e4x8+2x9)+e625−x9 __________ x8 (−10000x+2x9−8e4x9−2x10)+e4(4x9+4x10)+(e2(625−x9) ______________ x8 x8+x9−2e625−x9 __________ x8 x9+x10) log(e2(625−x9) ______________ x8 +x−2e625−x9 __________ x8 x+x2) ___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 16e8+2(625−x9) x8 x8−32e8+625−x9 __________ x8 x9+e8(16x9+16x10)+(8e4+2(625−x9) x8 x8−16e4+625−x9 __________ x8 x9+e4(8x9+8x10)) log(e2(625−x9) ______________ x8 +x−2e625−x9 __________ x8 x+x2)+(e2(625−x9) ______________ x8 x8+x9−2e625−x9 __________ x8 x9+x10) log2(e2(625−x9) ______________ x8 +x−2e625−x9 _________

3.18.51 $\int \frac {-x^9-2 x^{10}+e^{\frac {2 (625-x^9)}{x^8}} (10000+4 e^4 x^8+2 x^9)+e^{\frac {625-x^9}{x^8}} (-10000 x+2 x^9-8 e^4 x^9-2 x^{10})+e^4 (4 x^9+4 x^{10})+(e^{\frac {2 (625-x^9)}{x^8}} x^8+x^9-2 e^{\frac {625-x^9}{x^8}} x^9+x^{10}) \log (e^{\frac {2 (625-x^9)}{x^8}}+x-2 e^{\frac {625-x^9}{x^8}} x+x^2)}{16 e^{8+\frac {2 (625-x^9)}{x^8}} x^8-32 e^{8+\frac {625-x^9}{x^8}} x^9+e^8 (16 x^9+16 x^{10})+(8 e^{4+\frac {2 (625-x^9)}{x^8}} x^8-16 e^{4+\frac {625-x^9}{x^8}} x^9+e^4 (8 x^9+8 x^{10})) \log (e^{\frac {2 (625-x^9)}{x^8}}+x-2 e^{\frac {625-x^9}{x^8}} x+x^2)+(e^{\frac {2 (625-x^9)}{x^8}} x^8+x^9-2 e^{\frac {625-x^9}{x^8}} x^9+x^{10}) \log ^2(e^{\frac {2 (625-x^9)}{x^8}}+x-2 e^{\frac {625-x^9}{x^8}} x+x^2)} \, dx$

Optimal. Leaf size=30 \[ \frac {x}{4 e^4+\log \left (\left (e^{\frac {625}{x^8}-x}-x\right )^2+x\right )} \]

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Rubi [F] time = 180.00, 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*} \text {\$Aborted} \end {gather*}

Veriﬁcation is not applicable to the result.

[In]

Int[(-x^9 - 2*x^10 + E^((2*(625 - x^9))/x^8)*(10000 + 4*E^4*x^8 + 2*x^9) + E^((625 - x^9)/x^8)*(-10000*x + 2*x

^9 - 8*E^4*x^9 - 2*x^10) + E^4*(4*x^9 + 4*x^10) + (E^((2*(625 - x^9))/x^8)*x^8 + x^9 - 2*E^((625 - x^9)/x^8)*x

^9 + x^10)*Log[E^((2*(625 - x^9))/x^8) + x - 2*E^((625 - x^9)/x^8)*x + x^2])/(16*E^(8 + (2*(625 - x^9))/x^8)*x

^8 - 32*E^(8 + (625 - x^9)/x^8)*x^9 + E^8*(16*x^9 + 16*x^10) + (8*E^(4 + (2*(625 - x^9))/x^8)*x^8 - 16*E^(4 +

(625 - x^9)/x^8)*x^9 + E^4*(8*x^9 + 8*x^10))*Log[E^((2*(625 - x^9))/x^8) + x - 2*E^((625 - x^9)/x^8)*x + x^2]

+ (E^((2*(625 - x^9))/x^8)*x^8 + x^9 - 2*E^((625 - x^9)/x^8)*x^9 + x^10)*Log[E^((2*(625 - x^9))/x^8) + x - 2*E

^((625 - x^9)/x^8)*x + x^2]^2),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [A] time = 0.44, size = 41, normalized size = 1.37 \begin {gather*} \frac {x}{4 e^4+\log \left (e^{\frac {1250}{x^8}-2 x}+x-2 e^{\frac {625}{x^8}-x} x+x^2\right )} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Integrate[(-x^9 - 2*x^10 + E^((2*(625 - x^9))/x^8)*(10000 + 4*E^4*x^8 + 2*x^9) + E^((625 - x^9)/x^8)*(-10000*x

+ 2*x^9 - 8*E^4*x^9 - 2*x^10) + E^4*(4*x^9 + 4*x^10) + (E^((2*(625 - x^9))/x^8)*x^8 + x^9 - 2*E^((625 - x^9)/

x^8)*x^9 + x^10)*Log[E^((2*(625 - x^9))/x^8) + x - 2*E^((625 - x^9)/x^8)*x + x^2])/(16*E^(8 + (2*(625 - x^9))/

x^8)*x^8 - 32*E^(8 + (625 - x^9)/x^8)*x^9 + E^8*(16*x^9 + 16*x^10) + (8*E^(4 + (2*(625 - x^9))/x^8)*x^8 - 16*E

^(4 + (625 - x^9)/x^8)*x^9 + E^4*(8*x^9 + 8*x^10))*Log[E^((2*(625 - x^9))/x^8) + x - 2*E^((625 - x^9)/x^8)*x +

x^2] + (E^((2*(625 - x^9))/x^8)*x^8 + x^9 - 2*E^((625 - x^9)/x^8)*x^9 + x^10)*Log[E^((2*(625 - x^9))/x^8) + x

- 2*E^((625 - x^9)/x^8)*x + x^2]^2),x]

[Out]

x/(4*E^4 + Log[E^(1250/x^8 - 2*x) + x - 2*E^(625/x^8 - x)*x + x^2])

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fricas [B] time = 0.74, size = 59, normalized size = 1.97 \begin {gather*} \frac {x}{4 \, e^{4} + \log \left ({\left ({\left (x^{2} + x\right )} e^{16} - 2 \, x e^{\left (-\frac {x^{9} - 8 \, x^{8} - 625}{x^{8}} + 8\right )} + e^{\left (-\frac {2 \, {\left (x^{9} - 8 \, x^{8} - 625\right )}}{x^{8}}\right )}\right )} e^{\left (-16\right )}\right )} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x^8*exp((-x^9+625)/x^8)^2-2*x^9*exp((-x^9+625)/x^8)+x^10+x^9)*log(exp((-x^9+625)/x^8)^2-2*x*exp((-

x^9+625)/x^8)+x^2+x)+(4*x^8*exp(4)+2*x^9+10000)*exp((-x^9+625)/x^8)^2+(-8*x^9*exp(4)-2*x^10+2*x^9-10000*x)*exp

((-x^9+625)/x^8)+(4*x^10+4*x^9)*exp(4)-2*x^10-x^9)/((x^8*exp((-x^9+625)/x^8)^2-2*x^9*exp((-x^9+625)/x^8)+x^10+

x^9)*log(exp((-x^9+625)/x^8)^2-2*x*exp((-x^9+625)/x^8)+x^2+x)^2+(8*x^8*exp(4)*exp((-x^9+625)/x^8)^2-16*x^9*exp

(4)*exp((-x^9+625)/x^8)+(8*x^10+8*x^9)*exp(4))*log(exp((-x^9+625)/x^8)^2-2*x*exp((-x^9+625)/x^8)+x^2+x)+16*x^8

*exp(4)^2*exp((-x^9+625)/x^8)^2-32*x^9*exp(4)^2*exp((-x^9+625)/x^8)+(16*x^10+16*x^9)*exp(4)^2),x, algorithm="f

ricas")

[Out]

x/(4*e^4 + log(((x^2 + x)*e^16 - 2*x*e^(-(x^9 - 8*x^8 - 625)/x^8 + 8) + e^(-2*(x^9 - 8*x^8 - 625)/x^8))*e^(-16

)))

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giac [A] time = 1.24, size = 48, normalized size = 1.60 \begin {gather*} -\frac {x}{2 \, x - 4 \, e^{4} - \log \left (x^{2} e^{\left (2 \, x\right )} + x e^{\left (2 \, x\right )} - 2 \, x e^{\left (x + \frac {625}{x^{8}}\right )} + e^{\left (\frac {1250}{x^{8}}\right )}\right )} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x^8*exp((-x^9+625)/x^8)^2-2*x^9*exp((-x^9+625)/x^8)+x^10+x^9)*log(exp((-x^9+625)/x^8)^2-2*x*exp((-

x^9+625)/x^8)+x^2+x)+(4*x^8*exp(4)+2*x^9+10000)*exp((-x^9+625)/x^8)^2+(-8*x^9*exp(4)-2*x^10+2*x^9-10000*x)*exp

((-x^9+625)/x^8)+(4*x^10+4*x^9)*exp(4)-2*x^10-x^9)/((x^8*exp((-x^9+625)/x^8)^2-2*x^9*exp((-x^9+625)/x^8)+x^10+

x^9)*log(exp((-x^9+625)/x^8)^2-2*x*exp((-x^9+625)/x^8)+x^2+x)^2+(8*x^8*exp(4)*exp((-x^9+625)/x^8)^2-16*x^9*exp

(4)*exp((-x^9+625)/x^8)+(8*x^10+8*x^9)*exp(4))*log(exp((-x^9+625)/x^8)^2-2*x*exp((-x^9+625)/x^8)+x^2+x)+16*x^8

*exp(4)^2*exp((-x^9+625)/x^8)^2-32*x^9*exp(4)^2*exp((-x^9+625)/x^8)+(16*x^10+16*x^9)*exp(4)^2),x, algorithm="g

iac")

[Out]

-x/(2*x - 4*e^4 - log(x^2*e^(2*x) + x*e^(2*x) - 2*x*e^(x + 625/x^8) + e^(1250/x^8)))

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maple [A] time = 0.08, size = 41, normalized size = 1.37


method	result	size

risch	$\frac {x}{4 \,{\mathrm e}^{4}+\ln \left ({\mathrm e}^{-\frac {2 \left (x^{9}-625\right )}{x^{8}}}-2 x \,{\mathrm e}^{-\frac {x^{9}-625}{x^{8}}}+x^{2}+x \right )}$	$41$

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(((x^8*exp((-x^9+625)/x^8)^2-2*x^9*exp((-x^9+625)/x^8)+x^10+x^9)*ln(exp((-x^9+625)/x^8)^2-2*x*exp((-x^9+625

)/x^8)+x^2+x)+(4*x^8*exp(4)+2*x^9+10000)*exp((-x^9+625)/x^8)^2+(-8*x^9*exp(4)-2*x^10+2*x^9-10000*x)*exp((-x^9+

625)/x^8)+(4*x^10+4*x^9)*exp(4)-2*x^10-x^9)/((x^8*exp((-x^9+625)/x^8)^2-2*x^9*exp((-x^9+625)/x^8)+x^10+x^9)*ln

(exp((-x^9+625)/x^8)^2-2*x*exp((-x^9+625)/x^8)+x^2+x)^2+(8*x^8*exp(4)*exp((-x^9+625)/x^8)^2-16*x^9*exp(4)*exp(

(-x^9+625)/x^8)+(8*x^10+8*x^9)*exp(4))*ln(exp((-x^9+625)/x^8)^2-2*x*exp((-x^9+625)/x^8)+x^2+x)+16*x^8*exp(4)^2

*exp((-x^9+625)/x^8)^2-32*x^9*exp(4)^2*exp((-x^9+625)/x^8)+(16*x^10+16*x^9)*exp(4)^2),x,method=_RETURNVERBOSE)

[Out]

x/(4*exp(4)+ln(exp(-2*(x^9-625)/x^8)-2*x*exp(-(x^9-625)/x^8)+x^2+x))

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maxima [A] time = 0.82, size = 44, normalized size = 1.47 \begin {gather*} -\frac {x}{2 \, x - 4 \, e^{4} - \log \left ({\left (x^{2} + x\right )} e^{\left (2 \, x\right )} - 2 \, x e^{\left (x + \frac {625}{x^{8}}\right )} + e^{\left (\frac {1250}{x^{8}}\right )}\right )} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x^8*exp((-x^9+625)/x^8)^2-2*x^9*exp((-x^9+625)/x^8)+x^10+x^9)*log(exp((-x^9+625)/x^8)^2-2*x*exp((-

x^9+625)/x^8)+x^2+x)+(4*x^8*exp(4)+2*x^9+10000)*exp((-x^9+625)/x^8)^2+(-8*x^9*exp(4)-2*x^10+2*x^9-10000*x)*exp

((-x^9+625)/x^8)+(4*x^10+4*x^9)*exp(4)-2*x^10-x^9)/((x^8*exp((-x^9+625)/x^8)^2-2*x^9*exp((-x^9+625)/x^8)+x^10+

x^9)*log(exp((-x^9+625)/x^8)^2-2*x*exp((-x^9+625)/x^8)+x^2+x)^2+(8*x^8*exp(4)*exp((-x^9+625)/x^8)^2-16*x^9*exp

(4)*exp((-x^9+625)/x^8)+(8*x^10+8*x^9)*exp(4))*log(exp((-x^9+625)/x^8)^2-2*x*exp((-x^9+625)/x^8)+x^2+x)+16*x^8

*exp(4)^2*exp((-x^9+625)/x^8)^2-32*x^9*exp(4)^2*exp((-x^9+625)/x^8)+(16*x^10+16*x^9)*exp(4)^2),x, algorithm="m

axima")

[Out]

-x/(2*x - 4*e^4 - log((x^2 + x)*e^(2*x) - 2*x*e^(x + 625/x^8) + e^(1250/x^8)))

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mupad [F] time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {\ln \left (x+{\mathrm {e}}^{-\frac {2\,\left (x^9-625\right )}{x^8}}-2\,x\,{\mathrm {e}}^{-\frac {x^9-625}{x^8}}+x^2\right )\,\left (x^8\,{\mathrm {e}}^{-\frac {2\,\left (x^9-625\right )}{x^8}}-2\,x^9\,{\mathrm {e}}^{-\frac {x^9-625}{x^8}}+x^9+x^{10}\right )+{\mathrm {e}}^{-\frac {2\,\left (x^9-625\right )}{x^8}}\,\left (2\,x^9+4\,{\mathrm {e}}^4\,x^8+10000\right )-{\mathrm {e}}^{-\frac {x^9-625}{x^8}}\,\left (10000\,x+8\,x^9\,{\mathrm {e}}^4-2\,x^9+2\,x^{10}\right )+{\mathrm {e}}^4\,\left (4\,x^{10}+4\,x^9\right )-x^9-2\,x^{10}}{{\ln \left (x+{\mathrm {e}}^{-\frac {2\,\left (x^9-625\right )}{x^8}}-2\,x\,{\mathrm {e}}^{-\frac {x^9-625}{x^8}}+x^2\right )}^2\,\left (x^8\,{\mathrm {e}}^{-\frac {2\,\left (x^9-625\right )}{x^8}}-2\,x^9\,{\mathrm {e}}^{-\frac {x^9-625}{x^8}}+x^9+x^{10}\right )+{\mathrm {e}}^8\,\left (16\,x^{10}+16\,x^9\right )+\ln \left (x+{\mathrm {e}}^{-\frac {2\,\left (x^9-625\right )}{x^8}}-2\,x\,{\mathrm {e}}^{-\frac {x^9-625}{x^8}}+x^2\right )\,\left ({\mathrm {e}}^4\,\left (8\,x^{10}+8\,x^9\right )+8\,x^8\,{\mathrm {e}}^4\,{\mathrm {e}}^{-\frac {2\,\left (x^9-625\right )}{x^8}}-16\,x^9\,{\mathrm {e}}^4\,{\mathrm {e}}^{-\frac {x^9-625}{x^8}}\right )+16\,x^8\,{\mathrm {e}}^8\,{\mathrm {e}}^{-\frac {2\,\left (x^9-625\right )}{x^8}}-32\,x^9\,{\mathrm {e}}^8\,{\mathrm {e}}^{-\frac {x^9-625}{x^8}}} \,d x \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((log(x + exp(-(2*(x^9 - 625))/x^8) - 2*x*exp(-(x^9 - 625)/x^8) + x^2)*(x^8*exp(-(2*(x^9 - 625))/x^8) - 2*x

^9*exp(-(x^9 - 625)/x^8) + x^9 + x^10) + exp(-(2*(x^9 - 625))/x^8)*(4*x^8*exp(4) + 2*x^9 + 10000) - exp(-(x^9

- 625)/x^8)*(10000*x + 8*x^9*exp(4) - 2*x^9 + 2*x^10) + exp(4)*(4*x^9 + 4*x^10) - x^9 - 2*x^10)/(log(x + exp(-

(2*(x^9 - 625))/x^8) - 2*x*exp(-(x^9 - 625)/x^8) + x^2)^2*(x^8*exp(-(2*(x^9 - 625))/x^8) - 2*x^9*exp(-(x^9 - 6

25)/x^8) + x^9 + x^10) + exp(8)*(16*x^9 + 16*x^10) + log(x + exp(-(2*(x^9 - 625))/x^8) - 2*x*exp(-(x^9 - 625)/

x^8) + x^2)*(exp(4)*(8*x^9 + 8*x^10) + 8*x^8*exp(4)*exp(-(2*(x^9 - 625))/x^8) - 16*x^9*exp(4)*exp(-(x^9 - 625)

/x^8)) + 16*x^8*exp(8)*exp(-(2*(x^9 - 625))/x^8) - 32*x^9*exp(8)*exp(-(x^9 - 625)/x^8)),x)

[Out]

int((log(x + exp(-(2*(x^9 - 625))/x^8) - 2*x*exp(-(x^9 - 625)/x^8) + x^2)*(x^8*exp(-(2*(x^9 - 625))/x^8) - 2*x

^9*exp(-(x^9 - 625)/x^8) + x^9 + x^10) + exp(-(2*(x^9 - 625))/x^8)*(4*x^8*exp(4) + 2*x^9 + 10000) - exp(-(x^9

- 625)/x^8)*(10000*x + 8*x^9*exp(4) - 2*x^9 + 2*x^10) + exp(4)*(4*x^9 + 4*x^10) - x^9 - 2*x^10)/(log(x + exp(-

(2*(x^9 - 625))/x^8) - 2*x*exp(-(x^9 - 625)/x^8) + x^2)^2*(x^8*exp(-(2*(x^9 - 625))/x^8) - 2*x^9*exp(-(x^9 - 6

25)/x^8) + x^9 + x^10) + exp(8)*(16*x^9 + 16*x^10) + log(x + exp(-(2*(x^9 - 625))/x^8) - 2*x*exp(-(x^9 - 625)/

x^8) + x^2)*(exp(4)*(8*x^9 + 8*x^10) + 8*x^8*exp(4)*exp(-(2*(x^9 - 625))/x^8) - 16*x^9*exp(4)*exp(-(x^9 - 625)

/x^8)) + 16*x^8*exp(8)*exp(-(2*(x^9 - 625))/x^8) - 32*x^9*exp(8)*exp(-(x^9 - 625)/x^8)), x)

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sympy [A] time = 1.05, size = 37, normalized size = 1.23 \begin {gather*} \frac {x}{\log {\left (x^{2} - 2 x e^{\frac {625 - x^{9}}{x^{8}}} + x + e^{\frac {2 \left (625 - x^{9}\right )}{x^{8}}} \right )} + 4 e^{4}} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x**8*exp((-x**9+625)/x**8)**2-2*x**9*exp((-x**9+625)/x**8)+x**10+x**9)*ln(exp((-x**9+625)/x**8)**2

-2*x*exp((-x**9+625)/x**8)+x**2+x)+(4*x**8*exp(4)+2*x**9+10000)*exp((-x**9+625)/x**8)**2+(-8*x**9*exp(4)-2*x**

10+2*x**9-10000*x)*exp((-x**9+625)/x**8)+(4*x**10+4*x**9)*exp(4)-2*x**10-x**9)/((x**8*exp((-x**9+625)/x**8)**2

-2*x**9*exp((-x**9+625)/x**8)+x**10+x**9)*ln(exp((-x**9+625)/x**8)**2-2*x*exp((-x**9+625)/x**8)+x**2+x)**2+(8*

x**8*exp(4)*exp((-x**9+625)/x**8)**2-16*x**9*exp(4)*exp((-x**9+625)/x**8)+(8*x**10+8*x**9)*exp(4))*ln(exp((-x*

*9+625)/x**8)**2-2*x*exp((-x**9+625)/x**8)+x**2+x)+16*x**8*exp(4)**2*exp((-x**9+625)/x**8)**2-32*x**9*exp(4)**

2*exp((-x**9+625)/x**8)+(16*x**10+16*x**9)*exp(4)**2),x)

[Out]

x/(log(x**2 - 2*x*exp((625 - x**9)/x**8) + x + exp(2*(625 - x**9)/x**8)) + 4*exp(4))

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