3.10.4 \(\int \frac {1985-2010 x+575 x^2-30 x^3-5 x^4+e^6 (125+5 x^2)+e^3 (1000-500 x+70 x^2)}{1-32 x+272 x^2+e^{12} x^2-258 x^3+96 x^4-16 x^5+x^6+e^9 (16 x^2-4 x^3)+e^6 (-2 x+96 x^2-48 x^3+6 x^4)+e^3 (-16 x+260 x^2-192 x^3+48 x^4-4 x^5)} \, dx\)

Optimal. Leaf size=29 \[ \frac {25 \left (5-\frac {1}{5} x (3+x)\right )}{1-\left (4+e^3-x\right )^2 x} \]

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Rubi [F]  time = 180.02, 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[(1985 - 2010*x + 575*x^2 - 30*x^3 - 5*x^4 + E^6*(125 + 5*x^2) + E^3*(1000 - 500*x + 70*x^2))/(1 - 32*x + 2
72*x^2 + E^12*x^2 - 258*x^3 + 96*x^4 - 16*x^5 + x^6 + E^9*(16*x^2 - 4*x^3) + E^6*(-2*x + 96*x^2 - 48*x^3 + 6*x
^4) + E^3*(-16*x + 260*x^2 - 192*x^3 + 48*x^4 - 4*x^5)),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [A]  time = 0.04, size = 36, normalized size = 1.24 \begin {gather*} \frac {5 \left (-25+3 x+x^2\right )}{-1+\left (4+e^3\right )^2 x-2 \left (4+e^3\right ) x^2+x^3} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(1985 - 2010*x + 575*x^2 - 30*x^3 - 5*x^4 + E^6*(125 + 5*x^2) + E^3*(1000 - 500*x + 70*x^2))/(1 - 32
*x + 272*x^2 + E^12*x^2 - 258*x^3 + 96*x^4 - 16*x^5 + x^6 + E^9*(16*x^2 - 4*x^3) + E^6*(-2*x + 96*x^2 - 48*x^3
+ 6*x^4) + E^3*(-16*x + 260*x^2 - 192*x^3 + 48*x^4 - 4*x^5)),x]

[Out]

(5*(-25 + 3*x + x^2))/(-1 + (4 + E^3)^2*x - 2*(4 + E^3)*x^2 + x^3)

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fricas [A]  time = 0.61, size = 40, normalized size = 1.38 \begin {gather*} \frac {5 \, {\left (x^{2} + 3 \, x - 25\right )}}{x^{3} - 8 \, x^{2} + x e^{6} - 2 \, {\left (x^{2} - 4 \, x\right )} e^{3} + 16 \, x - 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((5*x^2+125)*exp(3)^2+(70*x^2-500*x+1000)*exp(3)-5*x^4-30*x^3+575*x^2-2010*x+1985)/(x^2*exp(3)^4+(-4
*x^3+16*x^2)*exp(3)^3+(6*x^4-48*x^3+96*x^2-2*x)*exp(3)^2+(-4*x^5+48*x^4-192*x^3+260*x^2-16*x)*exp(3)+x^6-16*x^
5+96*x^4-258*x^3+272*x^2-32*x+1),x, algorithm="fricas")

[Out]

5*(x^2 + 3*x - 25)/(x^3 - 8*x^2 + x*e^6 - 2*(x^2 - 4*x)*e^3 + 16*x - 1)

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giac [A]  time = 4.62, size = 31, normalized size = 1.07 \begin {gather*} 4.569118653734130163 \times 10^{16} \, \log \left (x - 0.001724048629546139142\right ) - 1.808434789016200504 \times 10^{6} \, \log \left (x - 23.88081680205305961\right ) + 1.808416357463456109 \times 10^{6} \, \log \left (x - 23.88099207781958486\right ) + 1.8261087744196467752 \times 10^{6} \, \log \left (x - 24.288357140090717098\right ) - 1.826090325252777360 \times 10^{6} \, \log \left (x - 24.28853357552813258\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((5*x^2+125)*exp(3)^2+(70*x^2-500*x+1000)*exp(3)-5*x^4-30*x^3+575*x^2-2010*x+1985)/(x^2*exp(3)^4+(-4
*x^3+16*x^2)*exp(3)^3+(6*x^4-48*x^3+96*x^2-2*x)*exp(3)^2+(-4*x^5+48*x^4-192*x^3+260*x^2-16*x)*exp(3)+x^6-16*x^
5+96*x^4-258*x^3+272*x^2-32*x+1),x, algorithm="giac")

[Out]

4.569118653734130163e16*log(x - 0.001724048629546139142) - 1.808434789016200504e6*log(x - 23.88081680205305961
) + 1.808416357463456109e6*log(x - 23.88099207781958486) + 1.8261087744196467752e6*log(x - 24.2883571400907170
98) - 1.826090325252777360e6*log(x - 24.28853357552813258)

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maple [A]  time = 0.32, size = 43, normalized size = 1.48

method	result	size
risch	\(\frac {5 x^{2}+15 x -125}{x \,{\mathrm e}^{6}-2 x^{2} {\mathrm e}^{3}+x^{3}+8 x \,{\mathrm e}^{3}-8 x^{2}+16 x -1}\)	\(43\)
gosper	\(\frac {5 x^{2}+15 x -125}{x \,{\mathrm e}^{6}-2 x^{2} {\mathrm e}^{3}+x^{3}+8 x \,{\mathrm e}^{3}-8 x^{2}+16 x -1}\)	\(44\)
norman	\(\frac {5 x^{2}+15 x -125}{x \,{\mathrm e}^{6}-2 x^{2} {\mathrm e}^{3}+x^{3}+8 x \,{\mathrm e}^{3}-8 x^{2}+16 x -1}\)	\(45\)
default	\(\frac {5 \left (\munderset {\textit {\_R} =\RootOf \left (1+\textit {\_Z}^{6}+\left (-4 \,{\mathrm e}^{3}-16\right ) \textit {\_Z}^{5}+\left (48 \,{\mathrm e}^{3}+6 \,{\mathrm e}^{6}+96\right ) \textit {\_Z}^{4}+\left (-192 \,{\mathrm e}^{3}-4 \,{\mathrm e}^{9}-48 \,{\mathrm e}^{6}-258\right ) \textit {\_Z}^{3}+\left ({\mathrm e}^{12}+260 \,{\mathrm e}^{3}+16 \,{\mathrm e}^{9}+96 \,{\mathrm e}^{6}+272\right ) \textit {\_Z}^{2}+\left (-16 \,{\mathrm e}^{3}-2 \,{\mathrm e}^{6}-32\right ) \textit {\_Z} \right )}{\sum }\frac {\left (397-\textit {\_R}^{4}-6 \textit {\_R}^{3}+\left (14 \,{\mathrm e}^{3}+{\mathrm e}^{6}+115\right ) \textit {\_R}^{2}+2 \left (-201-50 \,{\mathrm e}^{3}\right ) \textit {\_R} +25 \,{\mathrm e}^{6}+200 \,{\mathrm e}^{3}\right ) \ln \left (x -\textit {\_R} \right )}{-16+\textit {\_R} \,{\mathrm e}^{12}-6 \textit {\_R}^{2} {\mathrm e}^{9}+12 \textit {\_R}^{3} {\mathrm e}^{6}-10 \textit {\_R}^{4} {\mathrm e}^{3}+3 \textit {\_R}^{5}+16 \textit {\_R} \,{\mathrm e}^{9}-72 \textit {\_R}^{2} {\mathrm e}^{6}+96 \textit {\_R}^{3} {\mathrm e}^{3}-40 \textit {\_R}^{4}+96 \textit {\_R} \,{\mathrm e}^{6}-288 \textit {\_R}^{2} {\mathrm e}^{3}+192 \textit {\_R}^{3}-{\mathrm e}^{6}+260 \textit {\_R} \,{\mathrm e}^{3}-387 \textit {\_R}^{2}-8 \,{\mathrm e}^{3}+272 \textit {\_R}}\right )}{2}\)	\(230\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((5*x^2+125)*exp(3)^2+(70*x^2-500*x+1000)*exp(3)-5*x^4-30*x^3+575*x^2-2010*x+1985)/(x^2*exp(3)^4+(-4*x^3+1
6*x^2)*exp(3)^3+(6*x^4-48*x^3+96*x^2-2*x)*exp(3)^2+(-4*x^5+48*x^4-192*x^3+260*x^2-16*x)*exp(3)+x^6-16*x^5+96*x
^4-258*x^3+272*x^2-32*x+1),x,method=_RETURNVERBOSE)

[Out]

(5*x^2+15*x-125)/(x*exp(6)-2*x^2*exp(3)+x^3+8*x*exp(3)-8*x^2+16*x-1)

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maxima [A]  time = 0.59, size = 36, normalized size = 1.24 \begin {gather*} \frac {5 \, {\left (x^{2} + 3 \, x - 25\right )}}{x^{3} - 2 \, x^{2} {\left (e^{3} + 4\right )} + x {\left (e^{6} + 8 \, e^{3} + 16\right )} - 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((5*x^2+125)*exp(3)^2+(70*x^2-500*x+1000)*exp(3)-5*x^4-30*x^3+575*x^2-2010*x+1985)/(x^2*exp(3)^4+(-4
*x^3+16*x^2)*exp(3)^3+(6*x^4-48*x^3+96*x^2-2*x)*exp(3)^2+(-4*x^5+48*x^4-192*x^3+260*x^2-16*x)*exp(3)+x^6-16*x^
5+96*x^4-258*x^3+272*x^2-32*x+1),x, algorithm="maxima")

[Out]

5*(x^2 + 3*x - 25)/(x^3 - 2*x^2*(e^3 + 4) + x*(e^6 + 8*e^3 + 16) - 1)

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mupad [B]  time = 0.81, size = 42, normalized size = 1.45 \begin {gather*} -\frac {5\,x^2+15\,x-125}{-x^3+\left (2\,{\mathrm {e}}^3+8\right )\,x^2+\left (-8\,{\mathrm {e}}^3-{\mathrm {e}}^6-16\right )\,x+1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(3)*(70*x^2 - 500*x + 1000) - 2010*x + exp(6)*(5*x^2 + 125) + 575*x^2 - 30*x^3 - 5*x^4 + 1985)/(exp(9)
*(16*x^2 - 4*x^3) - 32*x + x^2*exp(12) - exp(6)*(2*x - 96*x^2 + 48*x^3 - 6*x^4) - exp(3)*(16*x - 260*x^2 + 192
*x^3 - 48*x^4 + 4*x^5) + 272*x^2 - 258*x^3 + 96*x^4 - 16*x^5 + x^6 + 1),x)

[Out]

-(15*x + 5*x^2 - 125)/(x^2*(2*exp(3) + 8) - x*(8*exp(3) + exp(6) + 16) - x^3 + 1)

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sympy [A]  time = 2.13, size = 39, normalized size = 1.34 \begin {gather*} - \frac {- 5 x^{2} - 15 x + 125}{x^{3} + x^{2} \left (- 2 e^{3} - 8\right ) + x \left (16 + 8 e^{3} + e^{6}\right ) - 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((5*x**2+125)*exp(3)**2+(70*x**2-500*x+1000)*exp(3)-5*x**4-30*x**3+575*x**2-2010*x+1985)/(x**2*exp(3
)**4+(-4*x**3+16*x**2)*exp(3)**3+(6*x**4-48*x**3+96*x**2-2*x)*exp(3)**2+(-4*x**5+48*x**4-192*x**3+260*x**2-16*
x)*exp(3)+x**6-16*x**5+96*x**4-258*x**3+272*x**2-32*x+1),x)

[Out]

-(-5*x**2 - 15*x + 125)/(x**3 + x**2*(-2*exp(3) - 8) + x*(16 + 8*exp(3) + exp(6)) - 1)

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