3.40.27 \(\int \frac {10 x+2 x^2+\frac {e^{-2 x} (1+2 x)}{x}+(-26+\frac {e^{-2 x}}{x}-10 x-x^2) \log (-26+\frac {e^{-2 x}}{x}-10 x-x^2)}{(-26+\frac {e^{-2 x}}{x}-10 x-x^2) \log ^2(-26+\frac {e^{-2 x}}{x}-10 x-x^2)} \, dx\)

Optimal. Leaf size=23 \[ \frac {x}{\log \left (-1+\frac {e^{-2 x}}{x}-(5+x)^2\right )} \]

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Rubi [F]  time = 6.54, 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 {10 x+2 x^2+\frac {e^{-2 x} (1+2 x)}{x}+\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right ) \log \left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )}{\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(10*x + 2*x^2 + (1 + 2*x)/(E^(2*x)*x) + (-26 + 1/(E^(2*x)*x) - 10*x - x^2)*Log[-26 + 1/(E^(2*x)*x) - 10*x
- x^2])/((-26 + 1/(E^(2*x)*x) - 10*x - x^2)*Log[-26 + 1/(E^(2*x)*x) - 10*x - x^2]^2),x]

[Out]

-2*Defer[Int][Log[-26 + 1/(E^(2*x)*x) - 10*x - x^2]^(-2), x] + (52*I)*Defer[Int][1/(((-10 + 2*I) - 2*x)*Log[-2
6 + 1/(E^(2*x)*x) - 10*x - x^2]^2), x] + (10 + 50*I)*Defer[Int][1/(((10 - 2*I) + 2*x)*Log[-26 + 1/(E^(2*x)*x)
- 10*x - x^2]^2), x] + (10 + 2*I)*Defer[Int][1/(((10 + 2*I) + 2*x)*Log[-26 + 1/(E^(2*x)*x) - 10*x - x^2]^2), x
] + (52*I)*Defer[Int][1/(((-10 + 2*I) - 2*x)*(-1 + 26*E^(2*x)*x + 10*E^(2*x)*x^2 + E^(2*x)*x^3)*Log[-26 + 1/(E
^(2*x)*x) - 10*x - x^2]^2), x] + (10 + 50*I)*Defer[Int][1/(((10 - 2*I) + 2*x)*(-1 + 26*E^(2*x)*x + 10*E^(2*x)*
x^2 + E^(2*x)*x^3)*Log[-26 + 1/(E^(2*x)*x) - 10*x - x^2]^2), x] + (10 + 2*I)*Defer[Int][1/(((10 + 2*I) + 2*x)*
(-1 + 26*E^(2*x)*x + 10*E^(2*x)*x^2 + E^(2*x)*x^3)*Log[-26 + 1/(E^(2*x)*x) - 10*x - x^2]^2), x] - 3*Defer[Int]
[1/((-1 + E^(2*x)*x*(26 + 10*x + x^2))*Log[-26 + 1/(E^(2*x)*x) - 10*x - x^2]^2), x] - 2*Defer[Int][x/((-1 + E^
(2*x)*x*(26 + 10*x + x^2))*Log[-26 + 1/(E^(2*x)*x) - 10*x - x^2]^2), x] + Defer[Int][Log[-26 + 1/(E^(2*x)*x) -
10*x - x^2]^(-1), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {26+72 x+23 x^2+2 x^3}{\left (26+10 x+x^2\right ) \left (-1+26 e^{2 x} x+10 e^{2 x} x^2+e^{2 x} x^3\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )}+\frac {-10 x-2 x^2+26 \log \left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )+10 x \log \left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )+x^2 \log \left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )}{\left (26+10 x+x^2\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )}\right ) \, dx\\ &=-\int \frac {26+72 x+23 x^2+2 x^3}{\left (26+10 x+x^2\right ) \left (-1+26 e^{2 x} x+10 e^{2 x} x^2+e^{2 x} x^3\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx+\int \frac {-10 x-2 x^2+26 \log \left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )+10 x \log \left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )+x^2 \log \left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )}{\left (26+10 x+x^2\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx\\ &=-\int \left (\frac {3}{\left (-1+26 e^{2 x} x+10 e^{2 x} x^2+e^{2 x} x^3\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )}+\frac {2 x}{\left (-1+26 e^{2 x} x+10 e^{2 x} x^2+e^{2 x} x^3\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )}-\frac {2 (26+5 x)}{\left (26+10 x+x^2\right ) \left (-1+26 e^{2 x} x+10 e^{2 x} x^2+e^{2 x} x^3\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )}\right ) \, dx+\int \frac {-\frac {2 x (5+x)}{26+10 x+x^2}+\log \left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )}{\log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx\\ &=-\left (2 \int \frac {x}{\left (-1+26 e^{2 x} x+10 e^{2 x} x^2+e^{2 x} x^3\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx\right )+2 \int \frac {26+5 x}{\left (26+10 x+x^2\right ) \left (-1+26 e^{2 x} x+10 e^{2 x} x^2+e^{2 x} x^3\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx-3 \int \frac {1}{\left (-1+26 e^{2 x} x+10 e^{2 x} x^2+e^{2 x} x^3\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx+\int \left (-\frac {2 x (5+x)}{\left (26+10 x+x^2\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )}+\frac {1}{\log \left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )}\right ) \, dx\\ &=-\left (2 \int \frac {x (5+x)}{\left (26+10 x+x^2\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx\right )+2 \int \frac {-26-5 x}{\left (26+10 x+x^2\right ) \left (1-e^{2 x} x \left (26+10 x+x^2\right )\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx-2 \int \frac {x}{\left (-1+e^{2 x} x \left (26+10 x+x^2\right )\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx-3 \int \frac {1}{\left (-1+e^{2 x} x \left (26+10 x+x^2\right )\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx+\int \frac {1}{\log \left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx\\ &=-\left (2 \int \left (\frac {1}{\log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )}+\frac {-26-5 x}{\left (26+10 x+x^2\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )}\right ) \, dx\right )+2 \int \left (\frac {26}{\left (26+10 x+x^2\right ) \left (-1+26 e^{2 x} x+10 e^{2 x} x^2+e^{2 x} x^3\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )}+\frac {5 x}{\left (26+10 x+x^2\right ) \left (-1+26 e^{2 x} x+10 e^{2 x} x^2+e^{2 x} x^3\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )}\right ) \, dx-2 \int \frac {x}{\left (-1+e^{2 x} x \left (26+10 x+x^2\right )\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx-3 \int \frac {1}{\left (-1+e^{2 x} x \left (26+10 x+x^2\right )\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx+\int \frac {1}{\log \left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx\\ &=-\left (2 \int \frac {1}{\log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx\right )-2 \int \frac {-26-5 x}{\left (26+10 x+x^2\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx-2 \int \frac {x}{\left (-1+e^{2 x} x \left (26+10 x+x^2\right )\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx-3 \int \frac {1}{\left (-1+e^{2 x} x \left (26+10 x+x^2\right )\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx+10 \int \frac {x}{\left (26+10 x+x^2\right ) \left (-1+26 e^{2 x} x+10 e^{2 x} x^2+e^{2 x} x^3\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx+52 \int \frac {1}{\left (26+10 x+x^2\right ) \left (-1+26 e^{2 x} x+10 e^{2 x} x^2+e^{2 x} x^3\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx+\int \frac {1}{\log \left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx\\ &=-\left (2 \int \left (-\frac {26}{\left (26+10 x+x^2\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )}-\frac {5 x}{\left (26+10 x+x^2\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )}\right ) \, dx\right )-2 \int \frac {1}{\log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx-2 \int \frac {x}{\left (-1+e^{2 x} x \left (26+10 x+x^2\right )\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx-3 \int \frac {1}{\left (-1+e^{2 x} x \left (26+10 x+x^2\right )\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx+10 \int \left (\frac {1+5 i}{((10-2 i)+2 x) \left (-1+26 e^{2 x} x+10 e^{2 x} x^2+e^{2 x} x^3\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )}+\frac {1-5 i}{((10+2 i)+2 x) \left (-1+26 e^{2 x} x+10 e^{2 x} x^2+e^{2 x} x^3\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )}\right ) \, dx+52 \int \left (\frac {i}{((-10+2 i)-2 x) \left (-1+26 e^{2 x} x+10 e^{2 x} x^2+e^{2 x} x^3\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )}+\frac {i}{((10+2 i)+2 x) \left (-1+26 e^{2 x} x+10 e^{2 x} x^2+e^{2 x} x^3\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )}\right ) \, dx+\int \frac {1}{\log \left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx\\ &=52 i \int \frac {1}{((-10+2 i)-2 x) \left (-1+26 e^{2 x} x+10 e^{2 x} x^2+e^{2 x} x^3\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx+52 i \int \frac {1}{((10+2 i)+2 x) \left (-1+26 e^{2 x} x+10 e^{2 x} x^2+e^{2 x} x^3\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx-2 \int \frac {1}{\log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx-2 \int \frac {x}{\left (-1+e^{2 x} x \left (26+10 x+x^2\right )\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx-3 \int \frac {1}{\left (-1+e^{2 x} x \left (26+10 x+x^2\right )\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx+10 \int \frac {x}{\left (26+10 x+x^2\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx+(10-50 i) \int \frac {1}{((10+2 i)+2 x) \left (-1+26 e^{2 x} x+10 e^{2 x} x^2+e^{2 x} x^3\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx+(10+50 i) \int \frac {1}{((10-2 i)+2 x) \left (-1+26 e^{2 x} x+10 e^{2 x} x^2+e^{2 x} x^3\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx+52 \int \frac {1}{\left (26+10 x+x^2\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx+\int \frac {1}{\log \left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx\\ &=52 i \int \frac {1}{((-10+2 i)-2 x) \left (-1+26 e^{2 x} x+10 e^{2 x} x^2+e^{2 x} x^3\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx+52 i \int \frac {1}{((10+2 i)+2 x) \left (-1+26 e^{2 x} x+10 e^{2 x} x^2+e^{2 x} x^3\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx-2 \int \frac {1}{\log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx-2 \int \frac {x}{\left (-1+e^{2 x} x \left (26+10 x+x^2\right )\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx-3 \int \frac {1}{\left (-1+e^{2 x} x \left (26+10 x+x^2\right )\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx+10 \int \left (\frac {1+5 i}{((10-2 i)+2 x) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )}+\frac {1-5 i}{((10+2 i)+2 x) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )}\right ) \, dx+(10-50 i) \int \frac {1}{((10+2 i)+2 x) \left (-1+26 e^{2 x} x+10 e^{2 x} x^2+e^{2 x} x^3\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx+(10+50 i) \int \frac {1}{((10-2 i)+2 x) \left (-1+26 e^{2 x} x+10 e^{2 x} x^2+e^{2 x} x^3\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx+52 \int \left (\frac {i}{((-10+2 i)-2 x) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )}+\frac {i}{((10+2 i)+2 x) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )}\right ) \, dx+\int \frac {1}{\log \left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx\\ &=52 i \int \frac {1}{((-10+2 i)-2 x) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx+52 i \int \frac {1}{((10+2 i)+2 x) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx+52 i \int \frac {1}{((-10+2 i)-2 x) \left (-1+26 e^{2 x} x+10 e^{2 x} x^2+e^{2 x} x^3\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx+52 i \int \frac {1}{((10+2 i)+2 x) \left (-1+26 e^{2 x} x+10 e^{2 x} x^2+e^{2 x} x^3\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx-2 \int \frac {1}{\log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx-2 \int \frac {x}{\left (-1+e^{2 x} x \left (26+10 x+x^2\right )\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx-3 \int \frac {1}{\left (-1+e^{2 x} x \left (26+10 x+x^2\right )\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx+(10-50 i) \int \frac {1}{((10+2 i)+2 x) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx+(10-50 i) \int \frac {1}{((10+2 i)+2 x) \left (-1+26 e^{2 x} x+10 e^{2 x} x^2+e^{2 x} x^3\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx+(10+50 i) \int \frac {1}{((10-2 i)+2 x) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx+(10+50 i) \int \frac {1}{((10-2 i)+2 x) \left (-1+26 e^{2 x} x+10 e^{2 x} x^2+e^{2 x} x^3\right ) \log ^2\left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx+\int \frac {1}{\log \left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.08, size = 24, normalized size = 1.04 \begin {gather*} \frac {x}{\log \left (-26+\frac {e^{-2 x}}{x}-10 x-x^2\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(10*x + 2*x^2 + (1 + 2*x)/(E^(2*x)*x) + (-26 + 1/(E^(2*x)*x) - 10*x - x^2)*Log[-26 + 1/(E^(2*x)*x) -
10*x - x^2])/((-26 + 1/(E^(2*x)*x) - 10*x - x^2)*Log[-26 + 1/(E^(2*x)*x) - 10*x - x^2]^2),x]

[Out]

x/Log[-26 + 1/(E^(2*x)*x) - 10*x - x^2]

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fricas [A]  time = 0.48, size = 28, normalized size = 1.22 \begin {gather*} \frac {x}{\log \left (-x^{2} - 10 \, x + e^{\left (-2 \, x + \log \left (\frac {e^{\left (-1\right )}}{x}\right ) + 1\right )} - 26\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((exp(log(1/x/exp(1))+1-2*x)-x^2-10*x-26)*log(exp(log(1/x/exp(1))+1-2*x)-x^2-10*x-26)+(2*x+1)*exp(lo
g(1/x/exp(1))+1-2*x)+2*x^2+10*x)/(exp(log(1/x/exp(1))+1-2*x)-x^2-10*x-26)/log(exp(log(1/x/exp(1))+1-2*x)-x^2-1
0*x-26)^2,x, algorithm="fricas")

[Out]

x/log(-x^2 - 10*x + e^(-2*x + log(e^(-1)/x) + 1) - 26)

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giac [A]  time = 0.74, size = 28, normalized size = 1.22 \begin {gather*} \frac {x}{\log \left (-x^{3} - 10 \, x^{2} - 26 \, x + e^{\left (-2 \, x\right )}\right ) - \log \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((exp(log(1/x/exp(1))+1-2*x)-x^2-10*x-26)*log(exp(log(1/x/exp(1))+1-2*x)-x^2-10*x-26)+(2*x+1)*exp(lo
g(1/x/exp(1))+1-2*x)+2*x^2+10*x)/(exp(log(1/x/exp(1))+1-2*x)-x^2-10*x-26)/log(exp(log(1/x/exp(1))+1-2*x)-x^2-1
0*x-26)^2,x, algorithm="giac")

[Out]

x/(log(-x^3 - 10*x^2 - 26*x + e^(-2*x)) - log(x))

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maple [F]  time = 0.07, size = 0, normalized size = 0.00 \[\int \frac {\left ({\mathrm e}^{\ln \left (\frac {{\mathrm e}^{-1}}{x}\right )-2 x +1}-x^{2}-10 x -26\right ) \ln \left ({\mathrm e}^{\ln \left (\frac {{\mathrm e}^{-1}}{x}\right )-2 x +1}-x^{2}-10 x -26\right )+\left (2 x +1\right ) {\mathrm e}^{\ln \left (\frac {{\mathrm e}^{-1}}{x}\right )-2 x +1}+2 x^{2}+10 x}{\left ({\mathrm e}^{\ln \left (\frac {{\mathrm e}^{-1}}{x}\right )-2 x +1}-x^{2}-10 x -26\right ) \ln \left ({\mathrm e}^{\ln \left (\frac {{\mathrm e}^{-1}}{x}\right )-2 x +1}-x^{2}-10 x -26\right )^{2}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((exp(ln(1/x/exp(1))+1-2*x)-x^2-10*x-26)*ln(exp(ln(1/x/exp(1))+1-2*x)-x^2-10*x-26)+(2*x+1)*exp(ln(1/x/exp(
1))+1-2*x)+2*x^2+10*x)/(exp(ln(1/x/exp(1))+1-2*x)-x^2-10*x-26)/ln(exp(ln(1/x/exp(1))+1-2*x)-x^2-10*x-26)^2,x)

[Out]

int(((exp(ln(1/x/exp(1))+1-2*x)-x^2-10*x-26)*ln(exp(ln(1/x/exp(1))+1-2*x)-x^2-10*x-26)+(2*x+1)*exp(ln(1/x/exp(
1))+1-2*x)+2*x^2+10*x)/(exp(ln(1/x/exp(1))+1-2*x)-x^2-10*x-26)/ln(exp(ln(1/x/exp(1))+1-2*x)-x^2-10*x-26)^2,x)

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maxima [A]  time = 0.41, size = 34, normalized size = 1.48 \begin {gather*} -\frac {x}{2 \, x - \log \left (-{\left (x^{3} + 10 \, x^{2} + 26 \, x\right )} e^{\left (2 \, x\right )} + 1\right ) + \log \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((exp(log(1/x/exp(1))+1-2*x)-x^2-10*x-26)*log(exp(log(1/x/exp(1))+1-2*x)-x^2-10*x-26)+(2*x+1)*exp(lo
g(1/x/exp(1))+1-2*x)+2*x^2+10*x)/(exp(log(1/x/exp(1))+1-2*x)-x^2-10*x-26)/log(exp(log(1/x/exp(1))+1-2*x)-x^2-1
0*x-26)^2,x, algorithm="maxima")

[Out]

-x/(2*x - log(-(x^3 + 10*x^2 + 26*x)*e^(2*x) + 1) + log(x))

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int -\frac {10\,x+{\mathrm {e}}^{\ln \left (\frac {{\mathrm {e}}^{-1}}{x}\right )-2\,x+1}\,\left (2\,x+1\right )+2\,x^2-\ln \left ({\mathrm {e}}^{\ln \left (\frac {{\mathrm {e}}^{-1}}{x}\right )-2\,x+1}-10\,x-x^2-26\right )\,\left (10\,x-{\mathrm {e}}^{\ln \left (\frac {{\mathrm {e}}^{-1}}{x}\right )-2\,x+1}+x^2+26\right )}{{\ln \left ({\mathrm {e}}^{\ln \left (\frac {{\mathrm {e}}^{-1}}{x}\right )-2\,x+1}-10\,x-x^2-26\right )}^2\,\left (10\,x-{\mathrm {e}}^{\ln \left (\frac {{\mathrm {e}}^{-1}}{x}\right )-2\,x+1}+x^2+26\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(10*x + exp(log(exp(-1)/x) - 2*x + 1)*(2*x + 1) + 2*x^2 - log(exp(log(exp(-1)/x) - 2*x + 1) - 10*x - x^2
- 26)*(10*x - exp(log(exp(-1)/x) - 2*x + 1) + x^2 + 26))/(log(exp(log(exp(-1)/x) - 2*x + 1) - 10*x - x^2 - 26)
^2*(10*x - exp(log(exp(-1)/x) - 2*x + 1) + x^2 + 26)),x)

[Out]

int(-(10*x + exp(log(exp(-1)/x) - 2*x + 1)*(2*x + 1) + 2*x^2 - log(exp(log(exp(-1)/x) - 2*x + 1) - 10*x - x^2
- 26)*(10*x - exp(log(exp(-1)/x) - 2*x + 1) + x^2 + 26))/(log(exp(log(exp(-1)/x) - 2*x + 1) - 10*x - x^2 - 26)
^2*(10*x - exp(log(exp(-1)/x) - 2*x + 1) + x^2 + 26)), x)

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sympy [A]  time = 0.41, size = 22, normalized size = 0.96 \begin {gather*} \frac {x}{\log {\left (- x^{2} - 10 x - 26 + \frac {e^{1 - 2 x}}{e x} \right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((exp(ln(1/x/exp(1))+1-2*x)-x**2-10*x-26)*ln(exp(ln(1/x/exp(1))+1-2*x)-x**2-10*x-26)+(2*x+1)*exp(ln(
1/x/exp(1))+1-2*x)+2*x**2+10*x)/(exp(ln(1/x/exp(1))+1-2*x)-x**2-10*x-26)/ln(exp(ln(1/x/exp(1))+1-2*x)-x**2-10*
x-26)**2,x)

[Out]

x/log(-x**2 - 10*x - 26 + exp(-1)*exp(1 - 2*x)/x)

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