3.13.14 \(\int \frac {-12+4 x^2+e^{25-9 e^{2 x}+2 x} (216 x-72 x^3)+(e^{25-9 e^{2 x}} (6+2 x^2)+(6+2 x^2) \log (x)) \log (e^{50-18 e^{2 x}}+2 e^{25-9 e^{2 x}} \log (x)+\log ^2(x))}{e^{25-9 e^{2 x}} x^2+x^2 \log (x)} \, dx\)

Optimal. Leaf size=26 \[ 2 \left (-\frac {3}{x}+x\right ) \log \left (\left (e^{25-9 e^{2 x}}+\log (x)\right )^2\right ) \]

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Rubi [F]  time = 4.04, 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 {-12+4 x^2+e^{25-9 e^{2 x}+2 x} \left (216 x-72 x^3\right )+\left (e^{25-9 e^{2 x}} \left (6+2 x^2\right )+\left (6+2 x^2\right ) \log (x)\right ) \log \left (e^{50-18 e^{2 x}}+2 e^{25-9 e^{2 x}} \log (x)+\log ^2(x)\right )}{e^{25-9 e^{2 x}} x^2+x^2 \log (x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-12 + 4*x^2 + E^(25 - 9*E^(2*x) + 2*x)*(216*x - 72*x^3) + (E^(25 - 9*E^(2*x))*(6 + 2*x^2) + (6 + 2*x^2)*L
og[x])*Log[E^(50 - 18*E^(2*x)) + 2*E^(25 - 9*E^(2*x))*Log[x] + Log[x]^2])/(E^(25 - 9*E^(2*x))*x^2 + x^2*Log[x]
),x]

[Out]

-12*ExpIntegralEi[-Log[x]] - (6*Log[(E^25 + E^(9*E^(2*x))*Log[x])^2/E^(18*E^(2*x))])/x + 2*x*Log[(E^25 + E^(9*
E^(2*x))*Log[x])^2/E^(18*E^(2*x))] + 4*LogIntegral[x] - 4*Defer[Int][E^(9*E^(2*x))/(E^25 + E^(9*E^(2*x))*Log[x
]), x] + 12*Defer[Int][E^(9*E^(2*x))/(x^2*(E^25 + E^(9*E^(2*x))*Log[x])), x] - 4*E^25*Defer[Int][1/(Log[x]*(E^
25 + E^(9*E^(2*x))*Log[x])), x] + 12*E^25*Defer[Int][1/(x^2*Log[x]*(E^25 + E^(9*E^(2*x))*Log[x])), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 \left (\frac {2 \left (e^{9 e^{2 x}}-18 e^{25+2 x} x\right ) \left (-3+x^2\right )}{e^{25}+e^{9 e^{2 x}} \log (x)}+\left (3+x^2\right ) \log \left (e^{-18 e^{2 x}} \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )^2\right )\right )}{x^2} \, dx\\ &=2 \int \frac {\frac {2 \left (e^{9 e^{2 x}}-18 e^{25+2 x} x\right ) \left (-3+x^2\right )}{e^{25}+e^{9 e^{2 x}} \log (x)}+\left (3+x^2\right ) \log \left (e^{-18 e^{2 x}} \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )^2\right )}{x^2} \, dx\\ &=2 \int \left (-\frac {36 e^{25+2 x} \left (-3+x^2\right )}{x \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )}+\frac {-6 e^{9 e^{2 x}}+2 e^{9 e^{2 x}} x^2+3 e^{25} \log \left (e^{-18 e^{2 x}} \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )^2\right )+e^{25} x^2 \log \left (e^{-18 e^{2 x}} \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )^2\right )+3 e^{9 e^{2 x}} \log (x) \log \left (e^{-18 e^{2 x}} \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )^2\right )+e^{9 e^{2 x}} x^2 \log (x) \log \left (e^{-18 e^{2 x}} \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )^2\right )}{x^2 \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )}\right ) \, dx\\ &=2 \int \frac {-6 e^{9 e^{2 x}}+2 e^{9 e^{2 x}} x^2+3 e^{25} \log \left (e^{-18 e^{2 x}} \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )^2\right )+e^{25} x^2 \log \left (e^{-18 e^{2 x}} \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )^2\right )+3 e^{9 e^{2 x}} \log (x) \log \left (e^{-18 e^{2 x}} \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )^2\right )+e^{9 e^{2 x}} x^2 \log (x) \log \left (e^{-18 e^{2 x}} \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )^2\right )}{x^2 \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )} \, dx-72 \int \frac {e^{25+2 x} \left (-3+x^2\right )}{x \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )} \, dx\\ &=2 \int \frac {\frac {2 e^{9 e^{2 x}} \left (-3+x^2\right )}{e^{25}+e^{9 e^{2 x}} \log (x)}+\left (3+x^2\right ) \log \left (e^{-18 e^{2 x}} \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )^2\right )}{x^2} \, dx-72 \int \left (\frac {e^{25+2 x} x}{e^{25}+e^{9 e^{2 x}} \log (x)}-\frac {3 e^{25+2 x}}{e^{25} x+e^{9 e^{2 x}} x \log (x)}\right ) \, dx\\ &=2 \int \left (-\frac {2 e^{25} \left (-3+x^2\right )}{x^2 \log (x) \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )}+\frac {-6+2 x^2+3 \log (x) \log \left (e^{-18 e^{2 x}} \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )^2\right )+x^2 \log (x) \log \left (e^{-18 e^{2 x}} \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )^2\right )}{x^2 \log (x)}\right ) \, dx-72 \int \frac {e^{25+2 x} x}{e^{25}+e^{9 e^{2 x}} \log (x)} \, dx+216 \int \frac {e^{25+2 x}}{e^{25} x+e^{9 e^{2 x}} x \log (x)} \, dx\\ &=2 \int \frac {-6+2 x^2+3 \log (x) \log \left (e^{-18 e^{2 x}} \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )^2\right )+x^2 \log (x) \log \left (e^{-18 e^{2 x}} \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )^2\right )}{x^2 \log (x)} \, dx-72 \int \frac {e^{25+2 x} x}{e^{25}+e^{9 e^{2 x}} \log (x)} \, dx+216 \int \frac {e^{25+2 x}}{e^{25} x+e^{9 e^{2 x}} x \log (x)} \, dx-\left (4 e^{25}\right ) \int \frac {-3+x^2}{x^2 \log (x) \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )} \, dx\\ &=2 \int \frac {2 \left (-3+x^2\right )+\left (3+x^2\right ) \log (x) \log \left (e^{-18 e^{2 x}} \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )^2\right )}{x^2 \log (x)} \, dx-72 \int \frac {e^{25+2 x} x}{e^{25}+e^{9 e^{2 x}} \log (x)} \, dx+216 \int \frac {e^{25+2 x}}{e^{25} x+e^{9 e^{2 x}} x \log (x)} \, dx-\left (4 e^{25}\right ) \int \left (\frac {1}{\log (x) \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )}-\frac {3}{x^2 \log (x) \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )}\right ) \, dx\\ &=2 \int \left (\frac {2 \left (-3+x^2\right )}{x^2 \log (x)}+\frac {\left (3+x^2\right ) \log \left (e^{-18 e^{2 x}} \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )^2\right )}{x^2}\right ) \, dx-72 \int \frac {e^{25+2 x} x}{e^{25}+e^{9 e^{2 x}} \log (x)} \, dx+216 \int \frac {e^{25+2 x}}{e^{25} x+e^{9 e^{2 x}} x \log (x)} \, dx-\left (4 e^{25}\right ) \int \frac {1}{\log (x) \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )} \, dx+\left (12 e^{25}\right ) \int \frac {1}{x^2 \log (x) \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )} \, dx\\ &=2 \int \frac {\left (3+x^2\right ) \log \left (e^{-18 e^{2 x}} \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )^2\right )}{x^2} \, dx+4 \int \frac {-3+x^2}{x^2 \log (x)} \, dx-72 \int \frac {e^{25+2 x} x}{e^{25}+e^{9 e^{2 x}} \log (x)} \, dx+216 \int \frac {e^{25+2 x}}{e^{25} x+e^{9 e^{2 x}} x \log (x)} \, dx-\left (4 e^{25}\right ) \int \frac {1}{\log (x) \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )} \, dx+\left (12 e^{25}\right ) \int \frac {1}{x^2 \log (x) \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )} \, dx\\ &=-\frac {6 \log \left (e^{-18 e^{2 x}} \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )^2\right )}{x}+2 x \log \left (e^{-18 e^{2 x}} \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )^2\right )-2 \int \frac {2 \left (e^{9 e^{2 x}}-18 e^{25+2 x} x\right ) \left (-3+x^2\right )}{x^2 \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )} \, dx+4 \int \left (\frac {1}{\log (x)}-\frac {3}{x^2 \log (x)}\right ) \, dx-72 \int \frac {e^{25+2 x} x}{e^{25}+e^{9 e^{2 x}} \log (x)} \, dx+216 \int \frac {e^{25+2 x}}{e^{25} x+e^{9 e^{2 x}} x \log (x)} \, dx-\left (4 e^{25}\right ) \int \frac {1}{\log (x) \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )} \, dx+\left (12 e^{25}\right ) \int \frac {1}{x^2 \log (x) \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )} \, dx\\ &=-\frac {6 \log \left (e^{-18 e^{2 x}} \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )^2\right )}{x}+2 x \log \left (e^{-18 e^{2 x}} \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )^2\right )+4 \int \frac {1}{\log (x)} \, dx-4 \int \frac {\left (e^{9 e^{2 x}}-18 e^{25+2 x} x\right ) \left (-3+x^2\right )}{x^2 \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )} \, dx-12 \int \frac {1}{x^2 \log (x)} \, dx-72 \int \frac {e^{25+2 x} x}{e^{25}+e^{9 e^{2 x}} \log (x)} \, dx+216 \int \frac {e^{25+2 x}}{e^{25} x+e^{9 e^{2 x}} x \log (x)} \, dx-\left (4 e^{25}\right ) \int \frac {1}{\log (x) \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )} \, dx+\left (12 e^{25}\right ) \int \frac {1}{x^2 \log (x) \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )} \, dx\\ &=-\frac {6 \log \left (e^{-18 e^{2 x}} \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )^2\right )}{x}+2 x \log \left (e^{-18 e^{2 x}} \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )^2\right )+4 \text {li}(x)-4 \int \left (\frac {e^{9 e^{2 x}} \left (-3+x^2\right )}{x^2 \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )}-\frac {18 e^{25+2 x} \left (-3+x^2\right )}{x \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )}\right ) \, dx-12 \operatorname {Subst}\left (\int \frac {e^{-x}}{x} \, dx,x,\log (x)\right )-72 \int \frac {e^{25+2 x} x}{e^{25}+e^{9 e^{2 x}} \log (x)} \, dx+216 \int \frac {e^{25+2 x}}{e^{25} x+e^{9 e^{2 x}} x \log (x)} \, dx-\left (4 e^{25}\right ) \int \frac {1}{\log (x) \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )} \, dx+\left (12 e^{25}\right ) \int \frac {1}{x^2 \log (x) \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )} \, dx\\ &=-12 \text {Ei}(-\log (x))-\frac {6 \log \left (e^{-18 e^{2 x}} \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )^2\right )}{x}+2 x \log \left (e^{-18 e^{2 x}} \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )^2\right )+4 \text {li}(x)-4 \int \frac {e^{9 e^{2 x}} \left (-3+x^2\right )}{x^2 \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )} \, dx-72 \int \frac {e^{25+2 x} x}{e^{25}+e^{9 e^{2 x}} \log (x)} \, dx+72 \int \frac {e^{25+2 x} \left (-3+x^2\right )}{x \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )} \, dx+216 \int \frac {e^{25+2 x}}{e^{25} x+e^{9 e^{2 x}} x \log (x)} \, dx-\left (4 e^{25}\right ) \int \frac {1}{\log (x) \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )} \, dx+\left (12 e^{25}\right ) \int \frac {1}{x^2 \log (x) \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )} \, dx\\ &=-12 \text {Ei}(-\log (x))-\frac {6 \log \left (e^{-18 e^{2 x}} \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )^2\right )}{x}+2 x \log \left (e^{-18 e^{2 x}} \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )^2\right )+4 \text {li}(x)-4 \int \left (\frac {e^{9 e^{2 x}}}{e^{25}+e^{9 e^{2 x}} \log (x)}-\frac {3 e^{9 e^{2 x}}}{x^2 \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )}\right ) \, dx-72 \int \frac {e^{25+2 x} x}{e^{25}+e^{9 e^{2 x}} \log (x)} \, dx+72 \int \left (\frac {e^{25+2 x} x}{e^{25}+e^{9 e^{2 x}} \log (x)}-\frac {3 e^{25+2 x}}{e^{25} x+e^{9 e^{2 x}} x \log (x)}\right ) \, dx+216 \int \frac {e^{25+2 x}}{e^{25} x+e^{9 e^{2 x}} x \log (x)} \, dx-\left (4 e^{25}\right ) \int \frac {1}{\log (x) \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )} \, dx+\left (12 e^{25}\right ) \int \frac {1}{x^2 \log (x) \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )} \, dx\\ &=-12 \text {Ei}(-\log (x))-\frac {6 \log \left (e^{-18 e^{2 x}} \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )^2\right )}{x}+2 x \log \left (e^{-18 e^{2 x}} \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )^2\right )+4 \text {li}(x)-4 \int \frac {e^{9 e^{2 x}}}{e^{25}+e^{9 e^{2 x}} \log (x)} \, dx+12 \int \frac {e^{9 e^{2 x}}}{x^2 \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )} \, dx-\left (4 e^{25}\right ) \int \frac {1}{\log (x) \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )} \, dx+\left (12 e^{25}\right ) \int \frac {1}{x^2 \log (x) \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.16, size = 39, normalized size = 1.50 \begin {gather*} \frac {2 \left (-3+x^2\right ) \log \left (e^{-18 e^{2 x}} \left (e^{25}+e^{9 e^{2 x}} \log (x)\right )^2\right )}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-12 + 4*x^2 + E^(25 - 9*E^(2*x) + 2*x)*(216*x - 72*x^3) + (E^(25 - 9*E^(2*x))*(6 + 2*x^2) + (6 + 2*
x^2)*Log[x])*Log[E^(50 - 18*E^(2*x)) + 2*E^(25 - 9*E^(2*x))*Log[x] + Log[x]^2])/(E^(25 - 9*E^(2*x))*x^2 + x^2*
Log[x]),x]

[Out]

(2*(-3 + x^2)*Log[(E^25 + E^(9*E^(2*x))*Log[x])^2/E^(18*E^(2*x))])/x

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fricas [B]  time = 1.21, size = 54, normalized size = 2.08 \begin {gather*} \frac {2 \, {\left (x^{2} - 3\right )} \log \left ({\left (e^{\left (4 \, x\right )} \log \relax (x)^{2} + 2 \, e^{\left (4 \, x - 9 \, e^{\left (2 \, x\right )} + 25\right )} \log \relax (x) + e^{\left (4 \, x - 18 \, e^{\left (2 \, x\right )} + 50\right )}\right )} e^{\left (-4 \, x\right )}\right )}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x^2+6)*exp(-9*exp(x)^2+25)+(2*x^2+6)*log(x))*log(exp(-9*exp(x)^2+25)^2+2*log(x)*exp(-9*exp(x)^2
+25)+log(x)^2)+(-72*x^3+216*x)*exp(x)^2*exp(-9*exp(x)^2+25)+4*x^2-12)/(x^2*exp(-9*exp(x)^2+25)+x^2*log(x)),x,
algorithm="fricas")

[Out]

2*(x^2 - 3)*log((e^(4*x)*log(x)^2 + 2*e^(4*x - 9*e^(2*x) + 25)*log(x) + e^(4*x - 18*e^(2*x) + 50))*e^(-4*x))/x

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giac [B]  time = 0.51, size = 86, normalized size = 3.31 \begin {gather*} -\frac {2 \, {\left (18 \, x^{2} e^{\left (2 \, x\right )} - x^{2} \log \left (e^{\left (18 \, e^{\left (2 \, x\right )}\right )} \log \relax (x)^{2} + 2 \, e^{\left (9 \, e^{\left (2 \, x\right )} + 25\right )} \log \relax (x) + e^{50}\right ) - 54 \, e^{\left (2 \, x\right )} + 3 \, \log \left (e^{\left (18 \, e^{\left (2 \, x\right )}\right )} \log \relax (x)^{2} + 2 \, e^{\left (9 \, e^{\left (2 \, x\right )} + 25\right )} \log \relax (x) + e^{50}\right )\right )}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x^2+6)*exp(-9*exp(x)^2+25)+(2*x^2+6)*log(x))*log(exp(-9*exp(x)^2+25)^2+2*log(x)*exp(-9*exp(x)^2
+25)+log(x)^2)+(-72*x^3+216*x)*exp(x)^2*exp(-9*exp(x)^2+25)+4*x^2-12)/(x^2*exp(-9*exp(x)^2+25)+x^2*log(x)),x,
algorithm="giac")

[Out]

-2*(18*x^2*e^(2*x) - x^2*log(e^(18*e^(2*x))*log(x)^2 + 2*e^(9*e^(2*x) + 25)*log(x) + e^50) - 54*e^(2*x) + 3*lo
g(e^(18*e^(2*x))*log(x)^2 + 2*e^(9*e^(2*x) + 25)*log(x) + e^50))/x

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maple [C]  time = 0.14, size = 214, normalized size = 8.23

method	result	size
risch	\(\frac {4 \left (x^{2}-3\right ) \ln \left (\ln \relax (x )+{\mathrm e}^{-9 \,{\mathrm e}^{2 x}+25}\right )}{x}-\frac {i \pi \,\mathrm {csgn}\left (i \left (\ln \relax (x )+{\mathrm e}^{-9 \,{\mathrm e}^{2 x}+25}\right )^{2}\right ) \left (x^{2} \mathrm {csgn}\left (i \left (\ln \relax (x )+{\mathrm e}^{-9 \,{\mathrm e}^{2 x}+25}\right )\right )^{2}-2 x^{2} \mathrm {csgn}\left (i \left (\ln \relax (x )+{\mathrm e}^{-9 \,{\mathrm e}^{2 x}+25}\right )\right ) \mathrm {csgn}\left (i \left (\ln \relax (x )+{\mathrm e}^{-9 \,{\mathrm e}^{2 x}+25}\right )^{2}\right )+x^{2} \mathrm {csgn}\left (i \left (\ln \relax (x )+{\mathrm e}^{-9 \,{\mathrm e}^{2 x}+25}\right )^{2}\right )^{2}-3 \mathrm {csgn}\left (i \left (\ln \relax (x )+{\mathrm e}^{-9 \,{\mathrm e}^{2 x}+25}\right )\right )^{2}+6 \,\mathrm {csgn}\left (i \left (\ln \relax (x )+{\mathrm e}^{-9 \,{\mathrm e}^{2 x}+25}\right )^{2}\right ) \mathrm {csgn}\left (i \left (\ln \relax (x )+{\mathrm e}^{-9 \,{\mathrm e}^{2 x}+25}\right )\right )-3 \mathrm {csgn}\left (i \left (\ln \relax (x )+{\mathrm e}^{-9 \,{\mathrm e}^{2 x}+25}\right )^{2}\right )^{2}\right )}{x}\)	\(214\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((2*x^2+6)*exp(-9*exp(x)^2+25)+(2*x^2+6)*ln(x))*ln(exp(-9*exp(x)^2+25)^2+2*ln(x)*exp(-9*exp(x)^2+25)+ln(x
)^2)+(-72*x^3+216*x)*exp(x)^2*exp(-9*exp(x)^2+25)+4*x^2-12)/(x^2*exp(-9*exp(x)^2+25)+x^2*ln(x)),x,method=_RETU
RNVERBOSE)

[Out]

4*(x^2-3)/x*ln(ln(x)+exp(-9*exp(2*x)+25))-I*Pi*csgn(I*(ln(x)+exp(-9*exp(2*x)+25))^2)*(x^2*csgn(I*(ln(x)+exp(-9
*exp(2*x)+25)))^2-2*x^2*csgn(I*(ln(x)+exp(-9*exp(2*x)+25)))*csgn(I*(ln(x)+exp(-9*exp(2*x)+25))^2)+x^2*csgn(I*(
ln(x)+exp(-9*exp(2*x)+25))^2)^2-3*csgn(I*(ln(x)+exp(-9*exp(2*x)+25)))^2+6*csgn(I*(ln(x)+exp(-9*exp(2*x)+25))^2
)*csgn(I*(ln(x)+exp(-9*exp(2*x)+25)))-3*csgn(I*(ln(x)+exp(-9*exp(2*x)+25))^2)^2)/x

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maxima [A]  time = 0.50, size = 38, normalized size = 1.46 \begin {gather*} -\frac {4 \, {\left (9 \, {\left (x^{2} - 3\right )} e^{\left (2 \, x\right )} - {\left (x^{2} - 3\right )} \log \left (e^{\left (9 \, e^{\left (2 \, x\right )}\right )} \log \relax (x) + e^{25}\right )\right )}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x^2+6)*exp(-9*exp(x)^2+25)+(2*x^2+6)*log(x))*log(exp(-9*exp(x)^2+25)^2+2*log(x)*exp(-9*exp(x)^2
+25)+log(x)^2)+(-72*x^3+216*x)*exp(x)^2*exp(-9*exp(x)^2+25)+4*x^2-12)/(x^2*exp(-9*exp(x)^2+25)+x^2*log(x)),x,
algorithm="maxima")

[Out]

-4*(9*(x^2 - 3)*e^(2*x) - (x^2 - 3)*log(e^(9*e^(2*x))*log(x) + e^25))/x

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mupad [B]  time = 1.26, size = 48, normalized size = 1.85 \begin {gather*} \ln \left ({\ln \relax (x)}^2+2\,{\mathrm {e}}^{-9\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^{25}\,\ln \relax (x)+{\mathrm {e}}^{-18\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^{50}\right )\,\left (4\,x-\frac {2\,x^3+6\,x}{x^2}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(exp(50 - 18*exp(2*x)) + log(x)^2 + 2*exp(25 - 9*exp(2*x))*log(x))*(exp(25 - 9*exp(2*x))*(2*x^2 + 6) +
log(x)*(2*x^2 + 6)) + 4*x^2 + exp(2*x)*exp(25 - 9*exp(2*x))*(216*x - 72*x^3) - 12)/(x^2*log(x) + x^2*exp(25 -
9*exp(2*x))),x)

[Out]

log(log(x)^2 + exp(-18*exp(2*x))*exp(50) + 2*exp(-9*exp(2*x))*exp(25)*log(x))*(4*x - (6*x + 2*x^3)/x^2)

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sympy [A]  time = 2.11, size = 39, normalized size = 1.50 \begin {gather*} \frac {\left (2 x^{2} - 6\right ) \log {\left (2 e^{25 - 9 e^{2 x}} \log {\relax (x )} + e^{50 - 18 e^{2 x}} + \log {\relax (x )}^{2} \right )}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x**2+6)*exp(-9*exp(x)**2+25)+(2*x**2+6)*ln(x))*ln(exp(-9*exp(x)**2+25)**2+2*ln(x)*exp(-9*exp(x)
**2+25)+ln(x)**2)+(-72*x**3+216*x)*exp(x)**2*exp(-9*exp(x)**2+25)+4*x**2-12)/(x**2*exp(-9*exp(x)**2+25)+x**2*l
n(x)),x)

[Out]

(2*x**2 - 6)*log(2*exp(25 - 9*exp(2*x))*log(x) + exp(50 - 18*exp(2*x)) + log(x)**2)/x

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