3.8.2 \(\int \frac {3+x^2+e^4 x^2+(2 x+2 e^4 x) \log (3)+(1+e^4) \log ^2(3)+e^{2 x} (x^4+e^4 x^4) \log ^2(3)+e^x (3 x^2+3 x^3+(-2 x^3-2 e^4 x^3) \log (3)+(-2 x^2-2 e^4 x^2) \log ^2(3))}{-3 x-x^2+x^3+e^4 x^3+(-3-2 x+2 x^2+2 e^4 x^2) \log (3)+(-1+x+e^4 x) \log ^2(3)+e^x (3 x^3+(6 x^2+2 x^3-2 x^4-2 e^4 x^4) \log (3)+(2 x^2-2 x^3-2 e^4 x^3) \log ^2(3))+e^{2 x} (-3 x^4 \log (3)+(-x^4+x^5+e^4 x^5) \log ^2(3))} \, dx\)

Optimal. Leaf size=35 \[ 1+\log \left (1-x-e^4 x+\frac {3}{\frac {x}{1-e^x x^2}+\log (3)}\right ) \]

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Rubi [F]  time = 12.42, 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 {3+x^2+e^4 x^2+\left (2 x+2 e^4 x\right ) \log (3)+\left (1+e^4\right ) \log ^2(3)+e^{2 x} \left (x^4+e^4 x^4\right ) \log ^2(3)+e^x \left (3 x^2+3 x^3+\left (-2 x^3-2 e^4 x^3\right ) \log (3)+\left (-2 x^2-2 e^4 x^2\right ) \log ^2(3)\right )}{-3 x-x^2+x^3+e^4 x^3+\left (-3-2 x+2 x^2+2 e^4 x^2\right ) \log (3)+\left (-1+x+e^4 x\right ) \log ^2(3)+e^x \left (3 x^3+\left (6 x^2+2 x^3-2 x^4-2 e^4 x^4\right ) \log (3)+\left (2 x^2-2 x^3-2 e^4 x^3\right ) \log ^2(3)\right )+e^{2 x} \left (-3 x^4 \log (3)+\left (-x^4+x^5+e^4 x^5\right ) \log ^2(3)\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(3 + x^2 + E^4*x^2 + (2*x + 2*E^4*x)*Log[3] + (1 + E^4)*Log[3]^2 + E^(2*x)*(x^4 + E^4*x^4)*Log[3]^2 + E^x*
(3*x^2 + 3*x^3 + (-2*x^3 - 2*E^4*x^3)*Log[3] + (-2*x^2 - 2*E^4*x^2)*Log[3]^2))/(-3*x - x^2 + x^3 + E^4*x^3 + (
-3 - 2*x + 2*x^2 + 2*E^4*x^2)*Log[3] + (-1 + x + E^4*x)*Log[3]^2 + E^x*(3*x^3 + (6*x^2 + 2*x^3 - 2*x^4 - 2*E^4
*x^4)*Log[3] + (2*x^2 - 2*x^3 - 2*E^4*x^3)*Log[3]^2) + E^(2*x)*(-3*x^4*Log[3] + (-x^4 + x^5 + E^4*x^5)*Log[3]^
2)),x]

[Out]

Log[3 + Log[3] - (1 + E^4)*x*Log[3]] - (1 + Log[3])*Defer[Int][(-x - Log[3] + E^x*x^2*Log[3])^(-1), x] - Log[9
]*Defer[Int][1/(x*(-x - Log[3] + E^x*x^2*Log[3])), x] - Defer[Int][x/(-x - Log[3] + E^x*x^2*Log[3]), x] - ((3
- 4*Log[3] + Log[3]^2 + 2*E^4*Log[3]^2)*Defer[Int][((1 + E^4)*x^2 - 3*(1 + Log[3]/3) + 3*E^x*x^2*(1 + Log[3]/3
) - E^x*(1 + E^4)*x^3*Log[3] - x*(1 - (1 + E^4)*Log[3]))^(-1), x])/Log[3] + 2*(3 + Log[3])*Defer[Int][1/(x*((1
+ E^4)*x^2 - 3*(1 + Log[3]/3) + 3*E^x*x^2*(1 + Log[3]/3) - E^x*(1 + E^4)*x^3*Log[3] - x*(1 - (1 + E^4)*Log[3]
))), x] - (Log[3] + E^4*(1 + Log[3]))*Defer[Int][x/((1 + E^4)*x^2 - 3*(1 + Log[3]/3) + 3*E^x*x^2*(1 + Log[3]/3
) - E^x*(1 + E^4)*x^3*Log[3] - x*(1 - (1 + E^4)*Log[3])), x] - (1 + E^4)*Defer[Int][x^2/((1 + E^4)*x^2 - 3*(1
+ Log[3]/3) + 3*E^x*x^2*(1 + Log[3]/3) - E^x*(1 + E^4)*x^3*Log[3] - x*(1 - (1 + E^4)*Log[3])), x] + ((9 + 5*Lo
g[3]^2 + Log[27] - Log[3]*Log[243])*Defer[Int][1/((3 + Log[3] - (1 + E^4)*x*Log[3])*((1 + E^4)*x^2 - 3*(1 + Lo
g[3]/3) + 3*E^x*x^2*(1 + Log[3]/3) - E^x*(1 + E^4)*x^3*Log[3] - x*(1 - (1 + E^4)*Log[3]))), x])/Log[3]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {3+\left (1+e^4\right ) x^2+\left (2 x+2 e^4 x\right ) \log (3)+\left (1+e^4\right ) \log ^2(3)+e^{2 x} \left (x^4+e^4 x^4\right ) \log ^2(3)+e^x \left (3 x^2+3 x^3+\left (-2 x^3-2 e^4 x^3\right ) \log (3)+\left (-2 x^2-2 e^4 x^2\right ) \log ^2(3)\right )}{-3 x-x^2+x^3+e^4 x^3+\left (-3-2 x+2 x^2+2 e^4 x^2\right ) \log (3)+\left (-1+x+e^4 x\right ) \log ^2(3)+e^x \left (3 x^3+\left (6 x^2+2 x^3-2 x^4-2 e^4 x^4\right ) \log (3)+\left (2 x^2-2 x^3-2 e^4 x^3\right ) \log ^2(3)\right )+e^{2 x} \left (-3 x^4 \log (3)+\left (-x^4+x^5+e^4 x^5\right ) \log ^2(3)\right )} \, dx\\ &=\int \frac {3+\left (1+e^4\right ) x^2+\left (2 x+2 e^4 x\right ) \log (3)+\left (1+e^4\right ) \log ^2(3)+e^{2 x} \left (x^4+e^4 x^4\right ) \log ^2(3)+e^x \left (3 x^2+3 x^3+\left (-2 x^3-2 e^4 x^3\right ) \log (3)+\left (-2 x^2-2 e^4 x^2\right ) \log ^2(3)\right )}{-3 x-x^2+\left (1+e^4\right ) x^3+\left (-3-2 x+2 x^2+2 e^4 x^2\right ) \log (3)+\left (-1+x+e^4 x\right ) \log ^2(3)+e^x \left (3 x^3+\left (6 x^2+2 x^3-2 x^4-2 e^4 x^4\right ) \log (3)+\left (2 x^2-2 x^3-2 e^4 x^3\right ) \log ^2(3)\right )+e^{2 x} \left (-3 x^4 \log (3)+\left (-x^4+x^5+e^4 x^5\right ) \log ^2(3)\right )} \, dx\\ &=\int \frac {-\left (\left (1+e^4\right ) x^2\right )-\left (2 x+2 e^4 x\right ) \log (3)-e^{2 x} \left (x^4+e^4 x^4\right ) \log ^2(3)-3 \left (1+\frac {1}{3} \left (1+e^4\right ) \log ^2(3)\right )-e^x \left (3 x^2+3 x^3+\left (-2 x^3-2 e^4 x^3\right ) \log (3)+\left (-2 x^2-2 e^4 x^2\right ) \log ^2(3)\right )}{3 x+x^2-\left (1+e^4\right ) x^3-\left (-3-2 x+2 x^2+2 e^4 x^2\right ) \log (3)-\left (-1+x+e^4 x\right ) \log ^2(3)-e^x \left (3 x^3+\left (6 x^2+2 x^3-2 x^4-2 e^4 x^4\right ) \log (3)+\left (2 x^2-2 x^3-2 e^4 x^3\right ) \log ^2(3)\right )-e^{2 x} \left (-3 x^4 \log (3)+\left (-x^4+x^5+e^4 x^5\right ) \log ^2(3)\right )} \, dx\\ &=\int \left (\frac {\left (-1-e^4\right ) \log (3)}{3+\log (3)-\left (1+e^4\right ) x \log (3)}+\frac {x^2+x (1+\log (3))+\log (9)}{x \left (x+\log (3)-e^x x^2 \log (3)\right )}+\frac {\left (1+e^4\right )^2 x^4 \log (3)+2 (3+\log (3))^2+x^2 \left (3-7 \log (3)-2 e^4 (4-\log (3)) \log (3)+2 e^8 \log ^2(3)\right )-\left (1+e^4\right ) x^3 \left (3+\log (3)-\log ^2(3)-e^4 \log (3) (1+\log (3))\right )+x \left (12-3 \log ^2(3)-4 e^4 \log (3) (3+\log (3))-\log (243)\right )}{x \left (3+\log (3)-\left (1+e^4\right ) x \log (3)\right ) \left (\left (1+e^4\right ) x^2-3 \left (1+\frac {\log (3)}{3}\right )+3 e^x x^2 \left (1+\frac {\log (3)}{3}\right )-e^x \left (1+e^4\right ) x^3 \log (3)-x \left (1-\left (1+e^4\right ) \log (3)\right )\right )}\right ) \, dx\\ &=\log \left (3+\log (3)-\left (1+e^4\right ) x \log (3)\right )+\int \frac {x^2+x (1+\log (3))+\log (9)}{x \left (x+\log (3)-e^x x^2 \log (3)\right )} \, dx+\int \frac {\left (1+e^4\right )^2 x^4 \log (3)+2 (3+\log (3))^2+x^2 \left (3-7 \log (3)-2 e^4 (4-\log (3)) \log (3)+2 e^8 \log ^2(3)\right )-\left (1+e^4\right ) x^3 \left (3+\log (3)-\log ^2(3)-e^4 \log (3) (1+\log (3))\right )+x \left (12-3 \log ^2(3)-4 e^4 \log (3) (3+\log (3))-\log (243)\right )}{x \left (3+\log (3)-\left (1+e^4\right ) x \log (3)\right ) \left (\left (1+e^4\right ) x^2-3 \left (1+\frac {\log (3)}{3}\right )+3 e^x x^2 \left (1+\frac {\log (3)}{3}\right )-e^x \left (1+e^4\right ) x^3 \log (3)-x \left (1-\left (1+e^4\right ) \log (3)\right )\right )} \, dx\\ &=\log \left (3+\log (3)-\left (1+e^4\right ) x \log (3)\right )+\int \left (-\frac {x}{-x-\log (3)+e^x x^2 \log (3)}-\frac {1+\log (3)}{-x-\log (3)+e^x x^2 \log (3)}-\frac {\log (9)}{x \left (-x-\log (3)+e^x x^2 \log (3)\right )}\right ) \, dx+\int \left (\frac {\left (-1-e^4\right ) x^2}{\left (1+e^4\right ) x^2-3 \left (1+\frac {\log (3)}{3}\right )+3 e^x x^2 \left (1+\frac {\log (3)}{3}\right )-e^x \left (1+e^4\right ) x^3 \log (3)-x \left (1-\left (1+e^4\right ) \log (3)\right )}+\frac {2 (3+\log (3))}{x \left (\left (1+e^4\right ) x^2-3 \left (1+\frac {\log (3)}{3}\right )+3 e^x x^2 \left (1+\frac {\log (3)}{3}\right )-e^x \left (1+e^4\right ) x^3 \log (3)-x \left (1-\left (1+e^4\right ) \log (3)\right )\right )}+\frac {-3+4 \log (3)-\log ^2(3)-2 e^4 \log ^2(3)}{\log (3) \left (\left (1+e^4\right ) x^2-3 \left (1+\frac {\log (3)}{3}\right )+3 e^x x^2 \left (1+\frac {\log (3)}{3}\right )-e^x \left (1+e^4\right ) x^3 \log (3)-x \left (1-\left (1+e^4\right ) \log (3)\right )\right )}+\frac {x \left (-\log (3)-e^4 (1+\log (3))\right )}{\left (1+e^4\right ) x^2-3 \left (1+\frac {\log (3)}{3}\right )+3 e^x x^2 \left (1+\frac {\log (3)}{3}\right )-e^x \left (1+e^4\right ) x^3 \log (3)-x \left (1-\left (1+e^4\right ) \log (3)\right )}+\frac {2 \left (1+e^4\right ) \log (3) (3+\log (3)) \left (1-\frac {-9+\log ^2(3)+2 \log ^3(3)+2 e^4 \log ^2(3) (3+\log (3))-\log (27)+\log (3) \log (243)}{2 \left (1+e^4\right ) \log ^2(3) (3+\log (3))}\right )}{\left (3+\log (3)-\left (1+e^4\right ) x \log (3)\right ) \left (\left (1+e^4\right ) x^2-3 \left (1+\frac {\log (3)}{3}\right )+3 e^x x^2 \left (1+\frac {\log (3)}{3}\right )-e^x \left (1+e^4\right ) x^3 \log (3)-x \left (1-\left (1+e^4\right ) \log (3)\right )\right )}\right ) \, dx\\ &=\log \left (3+\log (3)-\left (1+e^4\right ) x \log (3)\right )+\left (-1-e^4\right ) \int \frac {x^2}{\left (1+e^4\right ) x^2-3 \left (1+\frac {\log (3)}{3}\right )+3 e^x x^2 \left (1+\frac {\log (3)}{3}\right )-e^x \left (1+e^4\right ) x^3 \log (3)-x \left (1-\left (1+e^4\right ) \log (3)\right )} \, dx+(-1-\log (3)) \int \frac {1}{-x-\log (3)+e^x x^2 \log (3)} \, dx+(2 (3+\log (3))) \int \frac {1}{x \left (\left (1+e^4\right ) x^2-3 \left (1+\frac {\log (3)}{3}\right )+3 e^x x^2 \left (1+\frac {\log (3)}{3}\right )-e^x \left (1+e^4\right ) x^3 \log (3)-x \left (1-\left (1+e^4\right ) \log (3)\right )\right )} \, dx+\frac {\left (-3+4 \log (3)-\log ^2(3)-2 e^4 \log ^2(3)\right ) \int \frac {1}{\left (1+e^4\right ) x^2-3 \left (1+\frac {\log (3)}{3}\right )+3 e^x x^2 \left (1+\frac {\log (3)}{3}\right )-e^x \left (1+e^4\right ) x^3 \log (3)-x \left (1-\left (1+e^4\right ) \log (3)\right )} \, dx}{\log (3)}+\left (-\log (3)-e^4 (1+\log (3))\right ) \int \frac {x}{\left (1+e^4\right ) x^2-3 \left (1+\frac {\log (3)}{3}\right )+3 e^x x^2 \left (1+\frac {\log (3)}{3}\right )-e^x \left (1+e^4\right ) x^3 \log (3)-x \left (1-\left (1+e^4\right ) \log (3)\right )} \, dx-\log (9) \int \frac {1}{x \left (-x-\log (3)+e^x x^2 \log (3)\right )} \, dx+\frac {\left (9+5 \log ^2(3)+\log (27)-\log (3) \log (243)\right ) \int \frac {1}{\left (3+\log (3)-\left (1+e^4\right ) x \log (3)\right ) \left (\left (1+e^4\right ) x^2-3 \left (1+\frac {\log (3)}{3}\right )+3 e^x x^2 \left (1+\frac {\log (3)}{3}\right )-e^x \left (1+e^4\right ) x^3 \log (3)-x \left (1-\left (1+e^4\right ) \log (3)\right )\right )} \, dx}{\log (3)}-\int \frac {x}{-x-\log (3)+e^x x^2 \log (3)} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [F]  time = 13.32, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {3+x^2+e^4 x^2+\left (2 x+2 e^4 x\right ) \log (3)+\left (1+e^4\right ) \log ^2(3)+e^{2 x} \left (x^4+e^4 x^4\right ) \log ^2(3)+e^x \left (3 x^2+3 x^3+\left (-2 x^3-2 e^4 x^3\right ) \log (3)+\left (-2 x^2-2 e^4 x^2\right ) \log ^2(3)\right )}{-3 x-x^2+x^3+e^4 x^3+\left (-3-2 x+2 x^2+2 e^4 x^2\right ) \log (3)+\left (-1+x+e^4 x\right ) \log ^2(3)+e^x \left (3 x^3+\left (6 x^2+2 x^3-2 x^4-2 e^4 x^4\right ) \log (3)+\left (2 x^2-2 x^3-2 e^4 x^3\right ) \log ^2(3)\right )+e^{2 x} \left (-3 x^4 \log (3)+\left (-x^4+x^5+e^4 x^5\right ) \log ^2(3)\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(3 + x^2 + E^4*x^2 + (2*x + 2*E^4*x)*Log[3] + (1 + E^4)*Log[3]^2 + E^(2*x)*(x^4 + E^4*x^4)*Log[3]^2
+ E^x*(3*x^2 + 3*x^3 + (-2*x^3 - 2*E^4*x^3)*Log[3] + (-2*x^2 - 2*E^4*x^2)*Log[3]^2))/(-3*x - x^2 + x^3 + E^4*x
^3 + (-3 - 2*x + 2*x^2 + 2*E^4*x^2)*Log[3] + (-1 + x + E^4*x)*Log[3]^2 + E^x*(3*x^3 + (6*x^2 + 2*x^3 - 2*x^4 -
2*E^4*x^4)*Log[3] + (2*x^2 - 2*x^3 - 2*E^4*x^3)*Log[3]^2) + E^(2*x)*(-3*x^4*Log[3] + (-x^4 + x^5 + E^4*x^5)*L
og[3]^2)),x]

[Out]

Integrate[(3 + x^2 + E^4*x^2 + (2*x + 2*E^4*x)*Log[3] + (1 + E^4)*Log[3]^2 + E^(2*x)*(x^4 + E^4*x^4)*Log[3]^2
+ E^x*(3*x^2 + 3*x^3 + (-2*x^3 - 2*E^4*x^3)*Log[3] + (-2*x^2 - 2*E^4*x^2)*Log[3]^2))/(-3*x - x^2 + x^3 + E^4*x
^3 + (-3 - 2*x + 2*x^2 + 2*E^4*x^2)*Log[3] + (-1 + x + E^4*x)*Log[3]^2 + E^x*(3*x^3 + (6*x^2 + 2*x^3 - 2*x^4 -
2*E^4*x^4)*Log[3] + (2*x^2 - 2*x^3 - 2*E^4*x^3)*Log[3]^2) + E^(2*x)*(-3*x^4*Log[3] + (-x^4 + x^5 + E^4*x^5)*L
og[3]^2)), x]

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fricas [B]  time = 0.85, size = 118, normalized size = 3.37 \begin {gather*} \log \left ({\left (x e^{4} + x - 1\right )} \log \relax (3) - 3\right ) + \log \left (\frac {x^{2} e^{4} + x^{2} + {\left (3 \, x^{2} - {\left (x^{3} e^{4} + x^{3} - x^{2}\right )} \log \relax (3)\right )} e^{x} + {\left (x e^{4} + x - 1\right )} \log \relax (3) - x - 3}{3 \, x^{2} - {\left (x^{3} e^{4} + x^{3} - x^{2}\right )} \log \relax (3)}\right ) - \log \left (\frac {x^{2} e^{x} \log \relax (3) - x - \log \relax (3)}{x^{2}}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x^4*exp(4)+x^4)*log(3)^2*exp(x)^2+((-2*x^2*exp(4)-2*x^2)*log(3)^2+(-2*x^3*exp(4)-2*x^3)*log(3)+3*x
^3+3*x^2)*exp(x)+(exp(4)+1)*log(3)^2+(2*x*exp(4)+2*x)*log(3)+x^2*exp(4)+x^2+3)/(((x^5*exp(4)+x^5-x^4)*log(3)^2
-3*x^4*log(3))*exp(x)^2+((-2*x^3*exp(4)-2*x^3+2*x^2)*log(3)^2+(-2*x^4*exp(4)-2*x^4+2*x^3+6*x^2)*log(3)+3*x^3)*
exp(x)+(x*exp(4)+x-1)*log(3)^2+(2*x^2*exp(4)+2*x^2-2*x-3)*log(3)+x^3*exp(4)+x^3-x^2-3*x),x, algorithm="fricas"
)

[Out]

log((x*e^4 + x - 1)*log(3) - 3) + log((x^2*e^4 + x^2 + (3*x^2 - (x^3*e^4 + x^3 - x^2)*log(3))*e^x + (x*e^4 + x
- 1)*log(3) - x - 3)/(3*x^2 - (x^3*e^4 + x^3 - x^2)*log(3))) - log((x^2*e^x*log(3) - x - log(3))/x^2)

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \mathit {sage}_{0} x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x^4*exp(4)+x^4)*log(3)^2*exp(x)^2+((-2*x^2*exp(4)-2*x^2)*log(3)^2+(-2*x^3*exp(4)-2*x^3)*log(3)+3*x
^3+3*x^2)*exp(x)+(exp(4)+1)*log(3)^2+(2*x*exp(4)+2*x)*log(3)+x^2*exp(4)+x^2+3)/(((x^5*exp(4)+x^5-x^4)*log(3)^2
-3*x^4*log(3))*exp(x)^2+((-2*x^3*exp(4)-2*x^3+2*x^2)*log(3)^2+(-2*x^4*exp(4)-2*x^4+2*x^3+6*x^2)*log(3)+3*x^3)*
exp(x)+(x*exp(4)+x-1)*log(3)^2+(2*x^2*exp(4)+2*x^2-2*x-3)*log(3)+x^3*exp(4)+x^3-x^2-3*x),x, algorithm="giac")

[Out]

sage0*x

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maple [B]  time = 0.89, size = 85, normalized size = 2.43

method	result	size
norman	\(-\ln \left (x^{2} \ln \relax (3) {\mathrm e}^{x}-\ln \relax (3)-x \right )+\ln \left ({\mathrm e}^{4} {\mathrm e}^{x} \ln \relax (3) x^{3}+{\mathrm e}^{x} \ln \relax (3) x^{3}-x^{2} \ln \relax (3) {\mathrm e}^{x}-{\mathrm e}^{4} x \ln \relax (3)-x^{2} {\mathrm e}^{4}-3 \,{\mathrm e}^{x} x^{2}-x \ln \relax (3)-x^{2}+\ln \relax (3)+x +3\right )\)	\(85\)
risch	\(\ln \left (\left ({\mathrm e}^{4} \ln \relax (3)+\ln \relax (3)\right ) x -\ln \relax (3)-3\right )+\ln \left ({\mathrm e}^{x}-\frac {{\mathrm e}^{4} x \ln \relax (3)+x^{2} {\mathrm e}^{4}+x \ln \relax (3)+x^{2}-\ln \relax (3)-x -3}{x^{2} \left ({\mathrm e}^{4} x \ln \relax (3)+x \ln \relax (3)-\ln \relax (3)-3\right )}\right )-\ln \left ({\mathrm e}^{x}-\frac {\ln \relax (3)+x}{\ln \relax (3) x^{2}}\right )\)	\(93\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((x^4*exp(4)+x^4)*ln(3)^2*exp(x)^2+((-2*x^2*exp(4)-2*x^2)*ln(3)^2+(-2*x^3*exp(4)-2*x^3)*ln(3)+3*x^3+3*x^2)
*exp(x)+(exp(4)+1)*ln(3)^2+(2*x*exp(4)+2*x)*ln(3)+x^2*exp(4)+x^2+3)/(((x^5*exp(4)+x^5-x^4)*ln(3)^2-3*x^4*ln(3)
)*exp(x)^2+((-2*x^3*exp(4)-2*x^3+2*x^2)*ln(3)^2+(-2*x^4*exp(4)-2*x^4+2*x^3+6*x^2)*ln(3)+3*x^3)*exp(x)+(x*exp(4
)+x-1)*ln(3)^2+(2*x^2*exp(4)+2*x^2-2*x-3)*ln(3)+x^3*exp(4)+x^3-x^2-3*x),x,method=_RETURNVERBOSE)

[Out]

-ln(x^2*ln(3)*exp(x)-ln(3)-x)+ln(exp(4)*exp(x)*ln(3)*x^3+exp(x)*ln(3)*x^3-x^2*ln(3)*exp(x)-exp(4)*x*ln(3)-x^2*
exp(4)-3*exp(x)*x^2-x*ln(3)-x^2+ln(3)+x+3)

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maxima [B]  time = 0.79, size = 123, normalized size = 3.51 \begin {gather*} \log \left ({\left (e^{4} \log \relax (3) + \log \relax (3)\right )} x - \log \relax (3) - 3\right ) + \log \left (-\frac {x^{2} {\left (e^{4} + 1\right )} + {\left (e^{4} \log \relax (3) + \log \relax (3) - 1\right )} x - {\left ({\left (e^{4} \log \relax (3) + \log \relax (3)\right )} x^{3} - x^{2} {\left (\log \relax (3) + 3\right )}\right )} e^{x} - \log \relax (3) - 3}{{\left (e^{4} \log \relax (3) + \log \relax (3)\right )} x^{3} - x^{2} {\left (\log \relax (3) + 3\right )}}\right ) - \log \left (\frac {x^{2} e^{x} \log \relax (3) - x - \log \relax (3)}{x^{2} \log \relax (3)}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x^4*exp(4)+x^4)*log(3)^2*exp(x)^2+((-2*x^2*exp(4)-2*x^2)*log(3)^2+(-2*x^3*exp(4)-2*x^3)*log(3)+3*x
^3+3*x^2)*exp(x)+(exp(4)+1)*log(3)^2+(2*x*exp(4)+2*x)*log(3)+x^2*exp(4)+x^2+3)/(((x^5*exp(4)+x^5-x^4)*log(3)^2
-3*x^4*log(3))*exp(x)^2+((-2*x^3*exp(4)-2*x^3+2*x^2)*log(3)^2+(-2*x^4*exp(4)-2*x^4+2*x^3+6*x^2)*log(3)+3*x^3)*
exp(x)+(x*exp(4)+x-1)*log(3)^2+(2*x^2*exp(4)+2*x^2-2*x-3)*log(3)+x^3*exp(4)+x^3-x^2-3*x),x, algorithm="maxima"
)

[Out]

log((e^4*log(3) + log(3))*x - log(3) - 3) + log(-(x^2*(e^4 + 1) + (e^4*log(3) + log(3) - 1)*x - ((e^4*log(3) +
log(3))*x^3 - x^2*(log(3) + 3))*e^x - log(3) - 3)/((e^4*log(3) + log(3))*x^3 - x^2*(log(3) + 3))) - log((x^2*
e^x*log(3) - x - log(3))/(x^2*log(3)))

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} -\int \frac {\ln \relax (3)\,\left (2\,x+2\,x\,{\mathrm {e}}^4\right )-{\mathrm {e}}^x\,\left ({\ln \relax (3)}^2\,\left (2\,x^2\,{\mathrm {e}}^4+2\,x^2\right )-3\,x^2-3\,x^3+\ln \relax (3)\,\left (2\,x^3\,{\mathrm {e}}^4+2\,x^3\right )\right )+x^2\,{\mathrm {e}}^4+x^2+{\ln \relax (3)}^2\,\left ({\mathrm {e}}^4+1\right )+{\mathrm {e}}^{2\,x}\,{\ln \relax (3)}^2\,\left (x^4\,{\mathrm {e}}^4+x^4\right )+3}{3\,x-{\ln \relax (3)}^2\,\left (x+x\,{\mathrm {e}}^4-1\right )-x^3\,{\mathrm {e}}^4+{\mathrm {e}}^x\,\left (\ln \relax (3)\,\left (2\,x^4\,{\mathrm {e}}^4-6\,x^2-2\,x^3+2\,x^4\right )+{\ln \relax (3)}^2\,\left (2\,x^3\,{\mathrm {e}}^4-2\,x^2+2\,x^3\right )-3\,x^3\right )-{\mathrm {e}}^{2\,x}\,\left ({\ln \relax (3)}^2\,\left (x^5\,{\mathrm {e}}^4-x^4+x^5\right )-3\,x^4\,\ln \relax (3)\right )+\ln \relax (3)\,\left (2\,x-2\,x^2\,{\mathrm {e}}^4-2\,x^2+3\right )+x^2-x^3} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log(3)*(2*x + 2*x*exp(4)) - exp(x)*(log(3)^2*(2*x^2*exp(4) + 2*x^2) - 3*x^2 - 3*x^3 + log(3)*(2*x^3*exp(
4) + 2*x^3)) + x^2*exp(4) + x^2 + log(3)^2*(exp(4) + 1) + exp(2*x)*log(3)^2*(x^4*exp(4) + x^4) + 3)/(3*x - log
(3)^2*(x + x*exp(4) - 1) - x^3*exp(4) + exp(x)*(log(3)*(2*x^4*exp(4) - 6*x^2 - 2*x^3 + 2*x^4) + log(3)^2*(2*x^
3*exp(4) - 2*x^2 + 2*x^3) - 3*x^3) - exp(2*x)*(log(3)^2*(x^5*exp(4) - x^4 + x^5) - 3*x^4*log(3)) + log(3)*(2*x
- 2*x^2*exp(4) - 2*x^2 + 3) + x^2 - x^3),x)

[Out]

-int((log(3)*(2*x + 2*x*exp(4)) - exp(x)*(log(3)^2*(2*x^2*exp(4) + 2*x^2) - 3*x^2 - 3*x^3 + log(3)*(2*x^3*exp(
4) + 2*x^3)) + x^2*exp(4) + x^2 + log(3)^2*(exp(4) + 1) + exp(2*x)*log(3)^2*(x^4*exp(4) + x^4) + 3)/(3*x - log
(3)^2*(x + x*exp(4) - 1) - x^3*exp(4) + exp(x)*(log(3)*(2*x^4*exp(4) - 6*x^2 - 2*x^3 + 2*x^4) + log(3)^2*(2*x^
3*exp(4) - 2*x^2 + 2*x^3) - 3*x^3) - exp(2*x)*(log(3)^2*(x^5*exp(4) - x^4 + x^5) - 3*x^4*log(3)) + log(3)*(2*x
- 2*x^2*exp(4) - 2*x^2 + 3) + x^2 - x^3), x)

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sympy [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: PolynomialError} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x**4*exp(4)+x**4)*ln(3)**2*exp(x)**2+((-2*x**2*exp(4)-2*x**2)*ln(3)**2+(-2*x**3*exp(4)-2*x**3)*ln(
3)+3*x**3+3*x**2)*exp(x)+(exp(4)+1)*ln(3)**2+(2*x*exp(4)+2*x)*ln(3)+x**2*exp(4)+x**2+3)/(((x**5*exp(4)+x**5-x*
*4)*ln(3)**2-3*x**4*ln(3))*exp(x)**2+((-2*x**3*exp(4)-2*x**3+2*x**2)*ln(3)**2+(-2*x**4*exp(4)-2*x**4+2*x**3+6*
x**2)*ln(3)+3*x**3)*exp(x)+(x*exp(4)+x-1)*ln(3)**2+(2*x**2*exp(4)+2*x**2-2*x-3)*ln(3)+x**3*exp(4)+x**3-x**2-3*
x),x)

[Out]

Exception raised: PolynomialError

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