3.87.81 \(\int \frac {e^{-1-e^{25}} (e^{4 x} (-10-3 x+x^2)+e^{2 x} (25+50 x+10 x^2)+(-2 e^{4 x}+e^{2 x} (5+10 x)) \log (x))}{25+e^{2 x} (-20+10 x)+e^{4 x} (4-4 x+x^2)} \, dx\)

Optimal. Leaf size=28 \[ \frac {e^{-1-e^{25}} x (4+x+\log (x))}{-2+5 e^{-2 x}+x} \]

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Rubi [F]  time = 7.74, 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 {e^{-1-e^{25}} \left (e^{4 x} \left (-10-3 x+x^2\right )+e^{2 x} \left (25+50 x+10 x^2\right )+\left (-2 e^{4 x}+e^{2 x} (5+10 x)\right ) \log (x)\right )}{25+e^{2 x} (-20+10 x)+e^{4 x} \left (4-4 x+x^2\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(-1 - E^25)*(E^(4*x)*(-10 - 3*x + x^2) + E^(2*x)*(25 + 50*x + 10*x^2) + (-2*E^(4*x) + E^(2*x)*(5 + 10*x
))*Log[x]))/(25 + E^(2*x)*(-20 + 10*x) + E^(4*x)*(4 - 4*x + x^2)),x]

[Out]

30*E^(-1 - E^25)*Defer[Int][E^(2*x)/(5 + E^(2*x)*(-2 + x))^2, x] + 5*E^(-1 - E^25)*Log[x]*Defer[Int][E^(2*x)/(
5 + E^(2*x)*(-2 + x))^2, x] - E^(-1 - E^25)*Defer[Int][E^(2*x)/(5 + E^(2*x)*(-2 + x)), x] + 60*E^(-1 - E^25)*D
efer[Int][E^(2*x)/((5 + E^(2*x)*(-2 + x))^2*(-2 + x)), x] + 10*E^(-1 - E^25)*Log[x]*Defer[Int][E^(2*x)/((5 + E
^(2*x)*(-2 + x))^2*(-2 + x)), x] + 45*E^(-1 - E^25)*Defer[Int][(E^(2*x)*x)/(5 + E^(2*x)*(-2 + x))^2, x] + 10*E
^(-1 - E^25)*Log[x]*Defer[Int][(E^(2*x)*x)/(5 + E^(2*x)*(-2 + x))^2, x] + E^(-1 - E^25)*Defer[Int][(E^(2*x)*x)
/(5 + E^(2*x)*(-2 + x)), x] + 10*E^(-1 - E^25)*Defer[Int][(E^(2*x)*x^2)/(5 + E^(2*x)*(-2 + x))^2, x] - 12*E^(-
1 - E^25)*Defer[Int][E^(2*x)/((-2 + x)*(5 - 2*E^(2*x) + E^(2*x)*x)), x] - 2*E^(-1 - E^25)*Log[x]*Defer[Int][E^
(2*x)/((-2 + x)*(5 - 2*E^(2*x) + E^(2*x)*x)), x] - 5*E^(-1 - E^25)*Defer[Int][Defer[Int][E^(2*x)/(5 + E^(2*x)*
(-2 + x))^2, x]/x, x] - 10*E^(-1 - E^25)*Defer[Int][Defer[Int][E^(2*x)/((5 + E^(2*x)*(-2 + x))^2*(-2 + x)), x]
/x, x] + 2*E^(-1 - E^25)*Defer[Int][Defer[Int][E^(2*x)/((5 + E^(2*x)*(-2 + x))*(-2 + x)), x]/x, x] - 10*E^(-1
- E^25)*Defer[Int][Defer[Int][(E^(2*x)*x)/(5 + E^(2*x)*(-2 + x))^2, x]/x, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=e^{-1-e^{25}} \int \frac {e^{4 x} \left (-10-3 x+x^2\right )+e^{2 x} \left (25+50 x+10 x^2\right )+\left (-2 e^{4 x}+e^{2 x} (5+10 x)\right ) \log (x)}{25+e^{2 x} (-20+10 x)+e^{4 x} \left (4-4 x+x^2\right )} \, dx\\ &=e^{-1-e^{25}} \int \frac {e^{2 x} \left (e^{2 x} \left (-10-3 x+x^2\right )+5 \left (5+10 x+2 x^2\right )+\left (5-2 e^{2 x}+10 x\right ) \log (x)\right )}{\left (5+e^{2 x} (-2+x)\right )^2} \, dx\\ &=e^{-1-e^{25}} \int \left (\frac {e^{2 x} \left (-10-3 x+x^2-2 \log (x)\right )}{(-2+x) \left (5-2 e^{2 x}+e^{2 x} x\right )}+\frac {5 e^{2 x} x (-3+2 x) (4+x+\log (x))}{(-2+x) \left (5-2 e^{2 x}+e^{2 x} x\right )^2}\right ) \, dx\\ &=e^{-1-e^{25}} \int \frac {e^{2 x} \left (-10-3 x+x^2-2 \log (x)\right )}{(-2+x) \left (5-2 e^{2 x}+e^{2 x} x\right )} \, dx+\left (5 e^{-1-e^{25}}\right ) \int \frac {e^{2 x} x (-3+2 x) (4+x+\log (x))}{(-2+x) \left (5-2 e^{2 x}+e^{2 x} x\right )^2} \, dx\\ &=e^{-1-e^{25}} \int \left (-\frac {10 e^{2 x}}{(-2+x) \left (5-2 e^{2 x}+e^{2 x} x\right )}-\frac {3 e^{2 x} x}{(-2+x) \left (5-2 e^{2 x}+e^{2 x} x\right )}+\frac {e^{2 x} x^2}{(-2+x) \left (5-2 e^{2 x}+e^{2 x} x\right )}-\frac {2 e^{2 x} \log (x)}{(-2+x) \left (5-2 e^{2 x}+e^{2 x} x\right )}\right ) \, dx+\left (5 e^{-1-e^{25}}\right ) \int \left (\frac {e^{2 x} (4+x+\log (x))}{\left (5-2 e^{2 x}+e^{2 x} x\right )^2}+\frac {2 e^{2 x} (4+x+\log (x))}{(-2+x) \left (5-2 e^{2 x}+e^{2 x} x\right )^2}+\frac {2 e^{2 x} x (4+x+\log (x))}{\left (5-2 e^{2 x}+e^{2 x} x\right )^2}\right ) \, dx\\ &=e^{-1-e^{25}} \int \frac {e^{2 x} x^2}{(-2+x) \left (5-2 e^{2 x}+e^{2 x} x\right )} \, dx-\left (2 e^{-1-e^{25}}\right ) \int \frac {e^{2 x} \log (x)}{(-2+x) \left (5-2 e^{2 x}+e^{2 x} x\right )} \, dx-\left (3 e^{-1-e^{25}}\right ) \int \frac {e^{2 x} x}{(-2+x) \left (5-2 e^{2 x}+e^{2 x} x\right )} \, dx+\left (5 e^{-1-e^{25}}\right ) \int \frac {e^{2 x} (4+x+\log (x))}{\left (5-2 e^{2 x}+e^{2 x} x\right )^2} \, dx-\left (10 e^{-1-e^{25}}\right ) \int \frac {e^{2 x}}{(-2+x) \left (5-2 e^{2 x}+e^{2 x} x\right )} \, dx+\left (10 e^{-1-e^{25}}\right ) \int \frac {e^{2 x} (4+x+\log (x))}{(-2+x) \left (5-2 e^{2 x}+e^{2 x} x\right )^2} \, dx+\left (10 e^{-1-e^{25}}\right ) \int \frac {e^{2 x} x (4+x+\log (x))}{\left (5-2 e^{2 x}+e^{2 x} x\right )^2} \, dx\\ &=e^{-1-e^{25}} \int \left (\frac {2 e^{2 x}}{5-2 e^{2 x}+e^{2 x} x}+\frac {4 e^{2 x}}{(-2+x) \left (5-2 e^{2 x}+e^{2 x} x\right )}+\frac {e^{2 x} x}{5-2 e^{2 x}+e^{2 x} x}\right ) \, dx+\left (2 e^{-1-e^{25}}\right ) \int \frac {\int \frac {e^{2 x}}{\left (5+e^{2 x} (-2+x)\right ) (-2+x)} \, dx}{x} \, dx-\left (3 e^{-1-e^{25}}\right ) \int \left (\frac {e^{2 x}}{5-2 e^{2 x}+e^{2 x} x}+\frac {2 e^{2 x}}{(-2+x) \left (5-2 e^{2 x}+e^{2 x} x\right )}\right ) \, dx+\left (5 e^{-1-e^{25}}\right ) \int \frac {e^{2 x} (4+x+\log (x))}{\left (5+e^{2 x} (-2+x)\right )^2} \, dx-\left (10 e^{-1-e^{25}}\right ) \int \frac {e^{2 x}}{(-2+x) \left (5-2 e^{2 x}+e^{2 x} x\right )} \, dx+\left (10 e^{-1-e^{25}}\right ) \int \frac {e^{2 x} x (4+x+\log (x))}{\left (5+e^{2 x} (-2+x)\right )^2} \, dx+\left (10 e^{-1-e^{25}}\right ) \int \left (\frac {4 e^{2 x}}{(-2+x) \left (5-2 e^{2 x}+e^{2 x} x\right )^2}+\frac {e^{2 x} x}{(-2+x) \left (5-2 e^{2 x}+e^{2 x} x\right )^2}+\frac {e^{2 x} \log (x)}{(-2+x) \left (5-2 e^{2 x}+e^{2 x} x\right )^2}\right ) \, dx-\left (2 e^{-1-e^{25}} \log (x)\right ) \int \frac {e^{2 x}}{(-2+x) \left (5-2 e^{2 x}+e^{2 x} x\right )} \, dx\\ &=e^{-1-e^{25}} \int \frac {e^{2 x} x}{5-2 e^{2 x}+e^{2 x} x} \, dx+\left (2 e^{-1-e^{25}}\right ) \int \frac {e^{2 x}}{5-2 e^{2 x}+e^{2 x} x} \, dx+\left (2 e^{-1-e^{25}}\right ) \int \frac {\int \frac {e^{2 x}}{\left (5+e^{2 x} (-2+x)\right ) (-2+x)} \, dx}{x} \, dx-\left (3 e^{-1-e^{25}}\right ) \int \frac {e^{2 x}}{5-2 e^{2 x}+e^{2 x} x} \, dx+\left (4 e^{-1-e^{25}}\right ) \int \frac {e^{2 x}}{(-2+x) \left (5-2 e^{2 x}+e^{2 x} x\right )} \, dx+\left (5 e^{-1-e^{25}}\right ) \int \left (\frac {4 e^{2 x}}{\left (5-2 e^{2 x}+e^{2 x} x\right )^2}+\frac {e^{2 x} x}{\left (5-2 e^{2 x}+e^{2 x} x\right )^2}+\frac {e^{2 x} \log (x)}{\left (5-2 e^{2 x}+e^{2 x} x\right )^2}\right ) \, dx-\left (6 e^{-1-e^{25}}\right ) \int \frac {e^{2 x}}{(-2+x) \left (5-2 e^{2 x}+e^{2 x} x\right )} \, dx+\left (10 e^{-1-e^{25}}\right ) \int \frac {e^{2 x} x}{(-2+x) \left (5-2 e^{2 x}+e^{2 x} x\right )^2} \, dx-\left (10 e^{-1-e^{25}}\right ) \int \frac {e^{2 x}}{(-2+x) \left (5-2 e^{2 x}+e^{2 x} x\right )} \, dx+\left (10 e^{-1-e^{25}}\right ) \int \frac {e^{2 x} \log (x)}{(-2+x) \left (5-2 e^{2 x}+e^{2 x} x\right )^2} \, dx+\left (10 e^{-1-e^{25}}\right ) \int \left (\frac {4 e^{2 x} x}{\left (5-2 e^{2 x}+e^{2 x} x\right )^2}+\frac {e^{2 x} x^2}{\left (5-2 e^{2 x}+e^{2 x} x\right )^2}+\frac {e^{2 x} x \log (x)}{\left (5-2 e^{2 x}+e^{2 x} x\right )^2}\right ) \, dx+\left (40 e^{-1-e^{25}}\right ) \int \frac {e^{2 x}}{(-2+x) \left (5-2 e^{2 x}+e^{2 x} x\right )^2} \, dx-\left (2 e^{-1-e^{25}} \log (x)\right ) \int \frac {e^{2 x}}{(-2+x) \left (5-2 e^{2 x}+e^{2 x} x\right )} \, dx\\ &=e^{-1-e^{25}} \int \frac {e^{2 x} x}{5+e^{2 x} (-2+x)} \, dx+\left (2 e^{-1-e^{25}}\right ) \int \frac {e^{2 x}}{5+e^{2 x} (-2+x)} \, dx+\left (2 e^{-1-e^{25}}\right ) \int \frac {\int \frac {e^{2 x}}{\left (5+e^{2 x} (-2+x)\right ) (-2+x)} \, dx}{x} \, dx-\left (3 e^{-1-e^{25}}\right ) \int \frac {e^{2 x}}{5+e^{2 x} (-2+x)} \, dx+\left (4 e^{-1-e^{25}}\right ) \int \frac {e^{2 x}}{(-2+x) \left (5-2 e^{2 x}+e^{2 x} x\right )} \, dx+\left (5 e^{-1-e^{25}}\right ) \int \frac {e^{2 x} x}{\left (5-2 e^{2 x}+e^{2 x} x\right )^2} \, dx+\left (5 e^{-1-e^{25}}\right ) \int \frac {e^{2 x} \log (x)}{\left (5-2 e^{2 x}+e^{2 x} x\right )^2} \, dx-\left (6 e^{-1-e^{25}}\right ) \int \frac {e^{2 x}}{(-2+x) \left (5-2 e^{2 x}+e^{2 x} x\right )} \, dx+\left (10 e^{-1-e^{25}}\right ) \int \frac {e^{2 x} x}{\left (5+e^{2 x} (-2+x)\right )^2 (-2+x)} \, dx+\left (10 e^{-1-e^{25}}\right ) \int \frac {e^{2 x} x^2}{\left (5-2 e^{2 x}+e^{2 x} x\right )^2} \, dx-\left (10 e^{-1-e^{25}}\right ) \int \frac {e^{2 x}}{(-2+x) \left (5-2 e^{2 x}+e^{2 x} x\right )} \, dx+\left (10 e^{-1-e^{25}}\right ) \int \frac {e^{2 x} x \log (x)}{\left (5-2 e^{2 x}+e^{2 x} x\right )^2} \, dx-\left (10 e^{-1-e^{25}}\right ) \int \frac {\int \frac {e^{2 x}}{\left (5+e^{2 x} (-2+x)\right )^2 (-2+x)} \, dx}{x} \, dx+\left (20 e^{-1-e^{25}}\right ) \int \frac {e^{2 x}}{\left (5-2 e^{2 x}+e^{2 x} x\right )^2} \, dx+\left (40 e^{-1-e^{25}}\right ) \int \frac {e^{2 x}}{\left (5+e^{2 x} (-2+x)\right )^2 (-2+x)} \, dx+\left (40 e^{-1-e^{25}}\right ) \int \frac {e^{2 x} x}{\left (5-2 e^{2 x}+e^{2 x} x\right )^2} \, dx-\left (2 e^{-1-e^{25}} \log (x)\right ) \int \frac {e^{2 x}}{(-2+x) \left (5-2 e^{2 x}+e^{2 x} x\right )} \, dx+\left (10 e^{-1-e^{25}} \log (x)\right ) \int \frac {e^{2 x}}{\left (5+e^{2 x} (-2+x)\right )^2 (-2+x)} \, dx\\ &=e^{-1-e^{25}} \int \frac {e^{2 x} x}{5+e^{2 x} (-2+x)} \, dx+\left (2 e^{-1-e^{25}}\right ) \int \frac {e^{2 x}}{5+e^{2 x} (-2+x)} \, dx+\left (2 e^{-1-e^{25}}\right ) \int \frac {\int \frac {e^{2 x}}{\left (5+e^{2 x} (-2+x)\right ) (-2+x)} \, dx}{x} \, dx-\left (3 e^{-1-e^{25}}\right ) \int \frac {e^{2 x}}{5+e^{2 x} (-2+x)} \, dx+\left (4 e^{-1-e^{25}}\right ) \int \frac {e^{2 x}}{(-2+x) \left (5-2 e^{2 x}+e^{2 x} x\right )} \, dx+\left (5 e^{-1-e^{25}}\right ) \int \frac {e^{2 x} x}{\left (5+e^{2 x} (-2+x)\right )^2} \, dx-\left (5 e^{-1-e^{25}}\right ) \int \frac {\int \frac {e^{2 x}}{\left (5+e^{2 x} (-2+x)\right )^2} \, dx}{x} \, dx-\left (6 e^{-1-e^{25}}\right ) \int \frac {e^{2 x}}{(-2+x) \left (5-2 e^{2 x}+e^{2 x} x\right )} \, dx+\left (10 e^{-1-e^{25}}\right ) \int \frac {e^{2 x} x^2}{\left (5+e^{2 x} (-2+x)\right )^2} \, dx-\left (10 e^{-1-e^{25}}\right ) \int \frac {e^{2 x}}{(-2+x) \left (5-2 e^{2 x}+e^{2 x} x\right )} \, dx+\left (10 e^{-1-e^{25}}\right ) \int \left (\frac {e^{2 x}}{\left (5-2 e^{2 x}+e^{2 x} x\right )^2}+\frac {2 e^{2 x}}{(-2+x) \left (5-2 e^{2 x}+e^{2 x} x\right )^2}\right ) \, dx-\left (10 e^{-1-e^{25}}\right ) \int \frac {\int \frac {e^{2 x}}{\left (5+e^{2 x} (-2+x)\right )^2 (-2+x)} \, dx}{x} \, dx-\left (10 e^{-1-e^{25}}\right ) \int \frac {\int \frac {e^{2 x} x}{\left (5+e^{2 x} (-2+x)\right )^2} \, dx}{x} \, dx+\left (20 e^{-1-e^{25}}\right ) \int \frac {e^{2 x}}{\left (5+e^{2 x} (-2+x)\right )^2} \, dx+\left (40 e^{-1-e^{25}}\right ) \int \frac {e^{2 x}}{\left (5+e^{2 x} (-2+x)\right )^2 (-2+x)} \, dx+\left (40 e^{-1-e^{25}}\right ) \int \frac {e^{2 x} x}{\left (5+e^{2 x} (-2+x)\right )^2} \, dx-\left (2 e^{-1-e^{25}} \log (x)\right ) \int \frac {e^{2 x}}{(-2+x) \left (5-2 e^{2 x}+e^{2 x} x\right )} \, dx+\left (5 e^{-1-e^{25}} \log (x)\right ) \int \frac {e^{2 x}}{\left (5+e^{2 x} (-2+x)\right )^2} \, dx+\left (10 e^{-1-e^{25}} \log (x)\right ) \int \frac {e^{2 x}}{\left (5+e^{2 x} (-2+x)\right )^2 (-2+x)} \, dx+\left (10 e^{-1-e^{25}} \log (x)\right ) \int \frac {e^{2 x} x}{\left (5+e^{2 x} (-2+x)\right )^2} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 1.89, size = 48, normalized size = 1.71 \begin {gather*} \frac {e^{-1-e^{25}} \left (-30+e^{2 x} \left (12-2 x+x^2\right )+e^{2 x} x \log (x)\right )}{5+e^{2 x} (-2+x)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(-1 - E^25)*(E^(4*x)*(-10 - 3*x + x^2) + E^(2*x)*(25 + 50*x + 10*x^2) + (-2*E^(4*x) + E^(2*x)*(5
+ 10*x))*Log[x]))/(25 + E^(2*x)*(-20 + 10*x) + E^(4*x)*(4 - 4*x + x^2)),x]

[Out]

(E^(-1 - E^25)*(-30 + E^(2*x)*(12 - 2*x + x^2) + E^(2*x)*x*Log[x]))/(5 + E^(2*x)*(-2 + x))

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fricas [A]  time = 1.44, size = 43, normalized size = 1.54 \begin {gather*} \frac {{\left (x e^{\left (2 \, x\right )} \log \relax (x) + {\left (x^{2} - 2 \, x + 12\right )} e^{\left (2 \, x\right )} - 30\right )} e^{\left (-e^{25} - 1\right )}}{{\left (x - 2\right )} e^{\left (2 \, x\right )} + 5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*exp(x)^4+(10*x+5)*exp(x)^2)*log(x)+(x^2-3*x-10)*exp(x)^4+(10*x^2+50*x+25)*exp(x)^2)/((x^2-4*x+4
)*exp(x)^4+(10*x-20)*exp(x)^2+25)/exp(exp(25)+1),x, algorithm="fricas")

[Out]

(x*e^(2*x)*log(x) + (x^2 - 2*x + 12)*e^(2*x) - 30)*e^(-e^25 - 1)/((x - 2)*e^(2*x) + 5)

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giac [B]  time = 0.18, size = 55, normalized size = 1.96 \begin {gather*} \frac {{\left (x^{2} e^{\left (2 \, x\right )} + x e^{\left (2 \, x\right )} \log \relax (x) - 2 \, x e^{\left (2 \, x\right )} + 12 \, e^{\left (2 \, x\right )} - 30\right )} e^{\left (-e^{25} - 1\right )}}{x e^{\left (2 \, x\right )} - 2 \, e^{\left (2 \, x\right )} + 5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*exp(x)^4+(10*x+5)*exp(x)^2)*log(x)+(x^2-3*x-10)*exp(x)^4+(10*x^2+50*x+25)*exp(x)^2)/((x^2-4*x+4
)*exp(x)^4+(10*x-20)*exp(x)^2+25)/exp(exp(25)+1),x, algorithm="giac")

[Out]

(x^2*e^(2*x) + x*e^(2*x)*log(x) - 2*x*e^(2*x) + 12*e^(2*x) - 30)*e^(-e^25 - 1)/(x*e^(2*x) - 2*e^(2*x) + 5)

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maple [B]  time = 0.07, size = 103, normalized size = 3.68

method	result	size
risch	\(\frac {\ln \relax (x ) \left (2 \,{\mathrm e}^{2 x}-5\right ) {\mathrm e}^{-{\mathrm e}^{25}-1}}{x \,{\mathrm e}^{2 x}-2 \,{\mathrm e}^{2 x}+5}+\frac {\left (\ln \relax (x ) {\mathrm e}^{2 x} x +{\mathrm e}^{2 x} x^{2}-2 \ln \relax (x ) {\mathrm e}^{2 x}-2 x \,{\mathrm e}^{2 x}+12 \,{\mathrm e}^{2 x}+5 \ln \relax (x )-30\right ) {\mathrm e}^{-{\mathrm e}^{25}-1}}{x \,{\mathrm e}^{2 x}-2 \,{\mathrm e}^{2 x}+5}\)	\(103\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-2*exp(x)^4+(10*x+5)*exp(x)^2)*ln(x)+(x^2-3*x-10)*exp(x)^4+(10*x^2+50*x+25)*exp(x)^2)/((x^2-4*x+4)*exp(x
)^4+(10*x-20)*exp(x)^2+25)/exp(exp(25)+1),x,method=_RETURNVERBOSE)

[Out]

ln(x)/(x*exp(2*x)-2*exp(2*x)+5)*(2*exp(2*x)-5)*exp(-exp(25)-1)+1/(x*exp(2*x)-2*exp(2*x)+5)*(ln(x)*exp(2*x)*x+e
xp(2*x)*x^2-2*ln(x)*exp(2*x)-2*x*exp(2*x)+12*exp(2*x)+5*ln(x)-30)*exp(-exp(25)-1)

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maxima [A]  time = 0.40, size = 39, normalized size = 1.39 \begin {gather*} \frac {{\left ({\left (x^{2} + x \log \relax (x) - 2 \, x + 12\right )} e^{\left (2 \, x\right )} - 30\right )} e^{\left (-e^{25} - 1\right )}}{{\left (x - 2\right )} e^{\left (2 \, x\right )} + 5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*exp(x)^4+(10*x+5)*exp(x)^2)*log(x)+(x^2-3*x-10)*exp(x)^4+(10*x^2+50*x+25)*exp(x)^2)/((x^2-4*x+4
)*exp(x)^4+(10*x-20)*exp(x)^2+25)/exp(exp(25)+1),x, algorithm="maxima")

[Out]

((x^2 + x*log(x) - 2*x + 12)*e^(2*x) - 30)*e^(-e^25 - 1)/((x - 2)*e^(2*x) + 5)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} -\int \frac {{\mathrm {e}}^{-{\mathrm {e}}^{25}-1}\,\left ({\mathrm {e}}^{4\,x}\,\left (-x^2+3\,x+10\right )-{\mathrm {e}}^{2\,x}\,\left (10\,x^2+50\,x+25\right )+\ln \relax (x)\,\left (2\,{\mathrm {e}}^{4\,x}-{\mathrm {e}}^{2\,x}\,\left (10\,x+5\right )\right )\right )}{{\mathrm {e}}^{4\,x}\,\left (x^2-4\,x+4\right )+{\mathrm {e}}^{2\,x}\,\left (10\,x-20\right )+25} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(- exp(25) - 1)*(exp(4*x)*(3*x - x^2 + 10) - exp(2*x)*(50*x + 10*x^2 + 25) + log(x)*(2*exp(4*x) - exp
(2*x)*(10*x + 5))))/(exp(4*x)*(x^2 - 4*x + 4) + exp(2*x)*(10*x - 20) + 25),x)

[Out]

-int((exp(- exp(25) - 1)*(exp(4*x)*(3*x - x^2 + 10) - exp(2*x)*(50*x + 10*x^2 + 25) + log(x)*(2*exp(4*x) - exp
(2*x)*(10*x + 5))))/(exp(4*x)*(x^2 - 4*x + 4) + exp(2*x)*(10*x - 20) + 25), x)

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sympy [B]  time = 0.64, size = 146, normalized size = 5.21 \begin {gather*} \frac {x}{e e^{e^{25}}} + \frac {- 5 x^{2} - 5 x \log {\relax (x )} - 20 x}{5 e x e^{e^{25}} + \left (e x^{2} e^{e^{25}} - 4 e x e^{e^{25}} + 4 e e^{e^{25}}\right ) e^{2 x} - 10 e e^{e^{25}}} + \frac {\log {\relax (x )}}{e e^{e^{25}}} + \frac {2 \log {\relax (x )}}{e x e^{e^{25}} - 2 e e^{e^{25}}} + \frac {12}{e x e^{e^{25}} - 2 e e^{e^{25}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*exp(x)**4+(10*x+5)*exp(x)**2)*ln(x)+(x**2-3*x-10)*exp(x)**4+(10*x**2+50*x+25)*exp(x)**2)/((x**2
-4*x+4)*exp(x)**4+(10*x-20)*exp(x)**2+25)/exp(exp(25)+1),x)

[Out]

x*exp(-1)*exp(-exp(25)) + (-5*x**2 - 5*x*log(x) - 20*x)/(5*E*x*exp(exp(25)) + (E*x**2*exp(exp(25)) - 4*E*x*exp
(exp(25)) + 4*E*exp(exp(25)))*exp(2*x) - 10*E*exp(exp(25))) + exp(-1)*exp(-exp(25))*log(x) + 2*log(x)/(E*x*exp
(exp(25)) - 2*E*exp(exp(25))) + 12/(E*x*exp(exp(25)) - 2*E*exp(exp(25)))

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