3.70.80 \(\int \frac {x^2-2 x^3-\log (2)+e^{2+x} (9 x^2-6 x^3+7 x^4-2 x^5+x^6+(-6 x+2 x^2-2 x^3) \log (2)+\log ^2(2))}{9 x^2-6 x^3+7 x^4-2 x^5+x^6+(-6 x+2 x^2-2 x^3) \log (2)+\log ^2(2)} \, dx\)

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

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Rubi [F]  time = 180.01, 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^2 - 2*x^3 - Log[2] + E^(2 + x)*(9*x^2 - 6*x^3 + 7*x^4 - 2*x^5 + x^6 + (-6*x + 2*x^2 - 2*x^3)*Log[2] + L
og[2]^2))/(9*x^2 - 6*x^3 + 7*x^4 - 2*x^5 + x^6 + (-6*x + 2*x^2 - 2*x^3)*Log[2] + Log[2]^2),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [F]  time = 0.12, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x^2-2 x^3-\log (2)+e^{2+x} \left (9 x^2-6 x^3+7 x^4-2 x^5+x^6+\left (-6 x+2 x^2-2 x^3\right ) \log (2)+\log ^2(2)\right )}{9 x^2-6 x^3+7 x^4-2 x^5+x^6+\left (-6 x+2 x^2-2 x^3\right ) \log (2)+\log ^2(2)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(x^2 - 2*x^3 - Log[2] + E^(2 + x)*(9*x^2 - 6*x^3 + 7*x^4 - 2*x^5 + x^6 + (-6*x + 2*x^2 - 2*x^3)*Log[
2] + Log[2]^2))/(9*x^2 - 6*x^3 + 7*x^4 - 2*x^5 + x^6 + (-6*x + 2*x^2 - 2*x^3)*Log[2] + Log[2]^2),x]

[Out]

Integrate[(x^2 - 2*x^3 - Log[2] + E^(2 + x)*(9*x^2 - 6*x^3 + 7*x^4 - 2*x^5 + x^6 + (-6*x + 2*x^2 - 2*x^3)*Log[
2] + Log[2]^2))/(9*x^2 - 6*x^3 + 7*x^4 - 2*x^5 + x^6 + (-6*x + 2*x^2 - 2*x^3)*Log[2] + Log[2]^2), x]

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fricas [A]  time = 0.62, size = 42, normalized size = 1.50 \begin {gather*} \frac {{\left (x^{3} - x^{2} + 3 \, x - \log \relax (2)\right )} e^{\left (x + 2\right )} + x}{x^{3} - x^{2} + 3 \, x - \log \relax (2)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((log(2)^2+(-2*x^3+2*x^2-6*x)*log(2)+x^6-2*x^5+7*x^4-6*x^3+9*x^2)*exp(2+x)-log(2)-2*x^3+x^2)/(log(2)
^2+(-2*x^3+2*x^2-6*x)*log(2)+x^6-2*x^5+7*x^4-6*x^3+9*x^2),x, algorithm="fricas")

[Out]

((x^3 - x^2 + 3*x - log(2))*e^(x + 2) + x)/(x^3 - x^2 + 3*x - log(2))

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giac [B]  time = 0.19, size = 53, normalized size = 1.89 \begin {gather*} \frac {x^{3} e^{\left (x + 2\right )} - x^{2} e^{\left (x + 2\right )} + 3 \, x e^{\left (x + 2\right )} - e^{\left (x + 2\right )} \log \relax (2) + x}{x^{3} - x^{2} + 3 \, x - \log \relax (2)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((log(2)^2+(-2*x^3+2*x^2-6*x)*log(2)+x^6-2*x^5+7*x^4-6*x^3+9*x^2)*exp(2+x)-log(2)-2*x^3+x^2)/(log(2)
^2+(-2*x^3+2*x^2-6*x)*log(2)+x^6-2*x^5+7*x^4-6*x^3+9*x^2),x, algorithm="giac")

[Out]

(x^3*e^(x + 2) - x^2*e^(x + 2) + 3*x*e^(x + 2) - e^(x + 2)*log(2) + x)/(x^3 - x^2 + 3*x - log(2))

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maple [A]  time = 0.26, size = 25, normalized size = 0.89

method	result	size
risch	\(-\frac {x}{-x^{3}+x^{2}+\ln \relax (2)-3 x}+{\mathrm e}^{2+x}\)	\(25\)
norman	\(\frac {x^{2} {\mathrm e}^{2+x}-x +\ln \relax (2) {\mathrm e}^{2+x}-3 x \,{\mathrm e}^{2+x}-{\mathrm e}^{2+x} x^{3}}{-x^{3}+x^{2}+\ln \relax (2)-3 x}\)	\(53\)
derivativedivides	\(\text {Expression too large to display}\)	\(3011\)
default	\(\text {Expression too large to display}\)	\(3011\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((ln(2)^2+(-2*x^3+2*x^2-6*x)*ln(2)+x^6-2*x^5+7*x^4-6*x^3+9*x^2)*exp(2+x)-ln(2)-2*x^3+x^2)/(ln(2)^2+(-2*x^3
+2*x^2-6*x)*ln(2)+x^6-2*x^5+7*x^4-6*x^3+9*x^2),x,method=_RETURNVERBOSE)

[Out]

-x/(-x^3+x^2+ln(2)-3*x)+exp(2+x)

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maxima [A]  time = 0.46, size = 49, normalized size = 1.75 \begin {gather*} \frac {{\left (x^{3} e^{2} - x^{2} e^{2} + 3 \, x e^{2} - e^{2} \log \relax (2)\right )} e^{x} + x}{x^{3} - x^{2} + 3 \, x - \log \relax (2)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((log(2)^2+(-2*x^3+2*x^2-6*x)*log(2)+x^6-2*x^5+7*x^4-6*x^3+9*x^2)*exp(2+x)-log(2)-2*x^3+x^2)/(log(2)
^2+(-2*x^3+2*x^2-6*x)*log(2)+x^6-2*x^5+7*x^4-6*x^3+9*x^2),x, algorithm="maxima")

[Out]

((x^3*e^2 - x^2*e^2 + 3*x*e^2 - e^2*log(2))*e^x + x)/(x^3 - x^2 + 3*x - log(2))

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mupad [B]  time = 5.06, size = 368, normalized size = 13.14 \begin {gather*} {\mathrm {e}}^{x+2}+\left (\sum _{k=1}^6\ln \left (-1089\,\ln \relax (2)+\mathrm {root}\left (9900\,\ln \relax (2)-7846\,{\ln \relax (2)}^2+2700\,{\ln \relax (2)}^3-729\,{\ln \relax (2)}^4-9801,z,k\right )\,\ln \relax (2)\,6534-\mathrm {root}\left (9900\,\ln \relax (2)-7846\,{\ln \relax (2)}^2+2700\,{\ln \relax (2)}^3-729\,{\ln \relax (2)}^4-9801,z,k\right )\,x\,19602+1452\,x\,\ln \relax (2)-\mathrm {root}\left (9900\,\ln \relax (2)-7846\,{\ln \relax (2)}^2+2700\,{\ln \relax (2)}^3-729\,{\ln \relax (2)}^4-9801,z,k\right )\,{\ln \relax (2)}^2\,3894+\mathrm {root}\left (9900\,\ln \relax (2)-7846\,{\ln \relax (2)}^2+2700\,{\ln \relax (2)}^3-729\,{\ln \relax (2)}^4-9801,z,k\right )\,{\ln \relax (2)}^3\,2082-\mathrm {root}\left (9900\,\ln \relax (2)-7846\,{\ln \relax (2)}^2+2700\,{\ln \relax (2)}^3-729\,{\ln \relax (2)}^4-9801,z,k\right )\,{\ln \relax (2)}^4\,162-1832\,x\,{\ln \relax (2)}^2+108\,x\,{\ln \relax (2)}^3-250\,{\ln \relax (2)}^2+567\,{\ln \relax (2)}^3+\mathrm {root}\left (9900\,\ln \relax (2)-7846\,{\ln \relax (2)}^2+2700\,{\ln \relax (2)}^3-729\,{\ln \relax (2)}^4-9801,z,k\right )\,x\,\ln \relax (2)\,15444-\mathrm {root}\left (9900\,\ln \relax (2)-7846\,{\ln \relax (2)}^2+2700\,{\ln \relax (2)}^3-729\,{\ln \relax (2)}^4-9801,z,k\right )\,x\,{\ln \relax (2)}^2\,9928+\mathrm {root}\left (9900\,\ln \relax (2)-7846\,{\ln \relax (2)}^2+2700\,{\ln \relax (2)}^3-729\,{\ln \relax (2)}^4-9801,z,k\right )\,x\,{\ln \relax (2)}^3\,2412-\mathrm {root}\left (9900\,\ln \relax (2)-7846\,{\ln \relax (2)}^2+2700\,{\ln \relax (2)}^3-729\,{\ln \relax (2)}^4-9801,z,k\right )\,x\,{\ln \relax (2)}^4\,486\right )\,\mathrm {root}\left (9900\,\ln \relax (2)-7846\,{\ln \relax (2)}^2+2700\,{\ln \relax (2)}^3-729\,{\ln \relax (2)}^4-9801,z,k\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log(2) - x^2 + 2*x^3 - exp(x + 2)*(log(2)^2 - log(2)*(6*x - 2*x^2 + 2*x^3) + 9*x^2 - 6*x^3 + 7*x^4 - 2*x
^5 + x^6))/(log(2)^2 - log(2)*(6*x - 2*x^2 + 2*x^3) + 9*x^2 - 6*x^3 + 7*x^4 - 2*x^5 + x^6),x)

[Out]

exp(x + 2) + symsum(log(6534*root(9900*log(2) - 7846*log(2)^2 + 2700*log(2)^3 - 729*log(2)^4 - 9801, z, k)*log
(2) - 1089*log(2) - 19602*root(9900*log(2) - 7846*log(2)^2 + 2700*log(2)^3 - 729*log(2)^4 - 9801, z, k)*x + 14
52*x*log(2) - 3894*root(9900*log(2) - 7846*log(2)^2 + 2700*log(2)^3 - 729*log(2)^4 - 9801, z, k)*log(2)^2 + 20
82*root(9900*log(2) - 7846*log(2)^2 + 2700*log(2)^3 - 729*log(2)^4 - 9801, z, k)*log(2)^3 - 162*root(9900*log(
2) - 7846*log(2)^2 + 2700*log(2)^3 - 729*log(2)^4 - 9801, z, k)*log(2)^4 - 1832*x*log(2)^2 + 108*x*log(2)^3 -
250*log(2)^2 + 567*log(2)^3 + 15444*root(9900*log(2) - 7846*log(2)^2 + 2700*log(2)^3 - 729*log(2)^4 - 9801, z,
k)*x*log(2) - 9928*root(9900*log(2) - 7846*log(2)^2 + 2700*log(2)^3 - 729*log(2)^4 - 9801, z, k)*x*log(2)^2 +
2412*root(9900*log(2) - 7846*log(2)^2 + 2700*log(2)^3 - 729*log(2)^4 - 9801, z, k)*x*log(2)^3 - 486*root(9900
*log(2) - 7846*log(2)^2 + 2700*log(2)^3 - 729*log(2)^4 - 9801, z, k)*x*log(2)^4)*root(9900*log(2) - 7846*log(2
)^2 + 2700*log(2)^3 - 729*log(2)^4 - 9801, z, k), k, 1, 6)

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sympy [A]  time = 0.62, size = 19, normalized size = 0.68 \begin {gather*} \frac {x}{x^{3} - x^{2} + 3 x - \log {\relax (2 )}} + e^{x + 2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((ln(2)**2+(-2*x**3+2*x**2-6*x)*ln(2)+x**6-2*x**5+7*x**4-6*x**3+9*x**2)*exp(2+x)-ln(2)-2*x**3+x**2)/
(ln(2)**2+(-2*x**3+2*x**2-6*x)*ln(2)+x**6-2*x**5+7*x**4-6*x**3+9*x**2),x)

[Out]

x/(x**3 - x**2 + 3*x - log(2)) + exp(x + 2)

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