3.39.89 \(\int \frac {(-225+x)^{-\frac {e^4}{-e^{2/x}+e^{5+x}}} (e^{4+\frac {2}{x}} x^2-e^{9+x} x^2+(e^{4+\frac {2}{x}} (-450+2 x)+e^{9+x} (-225 x^2+x^3)) \log (-225+x))}{e^{5+\frac {2}{x}+x} (450 x^2-2 x^3)+e^{4/x} (-225 x^2+x^3)+e^{10+2 x} (-225 x^2+x^3)} \, dx\)

Optimal. Leaf size=25 \[ (-225+x)^{\frac {e^4}{e^{2/x}-e^{5+x}}} \]

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Rubi [F]  time = 8.68, 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 {(-225+x)^{-\frac {e^4}{-e^{2/x}+e^{5+x}}} \left (e^{4+\frac {2}{x}} x^2-e^{9+x} x^2+\left (e^{4+\frac {2}{x}} (-450+2 x)+e^{9+x} \left (-225 x^2+x^3\right )\right ) \log (-225+x)\right )}{e^{5+\frac {2}{x}+x} \left (450 x^2-2 x^3\right )+e^{4/x} \left (-225 x^2+x^3\right )+e^{10+2 x} \left (-225 x^2+x^3\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(4 + 2/x)*x^2 - E^(9 + x)*x^2 + (E^(4 + 2/x)*(-450 + 2*x) + E^(9 + x)*(-225*x^2 + x^3))*Log[-225 + x])/
((-225 + x)^(E^4/(-E^(2/x) + E^(5 + x)))*(E^(5 + 2/x + x)*(450*x^2 - 2*x^3) + E^(4/x)*(-225*x^2 + x^3) + E^(10
+ 2*x)*(-225*x^2 + x^3))),x]

[Out]

-225*E^4*Log[-225 + x]*Defer[Int][(E^(2/x)*(-225 + x)^(-1 + E^4/(E^(2/x) - E^(5 + x))))/(E^(2/x) - E^(5 + x))^
2, x] + E^4*Defer[Int][(-225 + x)^(-1 + E^4/(E^(2/x) - E^(5 + x)))/(E^(2/x) - E^(5 + x)), x] + 225*E^4*Log[-22
5 + x]*Defer[Int][(-225 + x)^(-1 + E^4/(E^(2/x) - E^(5 + x)))/(E^(2/x) - E^(5 + x)), x] - 450*E^4*Log[-225 + x
]*Defer[Int][(E^(2/x)*(-225 + x)^(-1 + E^4/(E^(2/x) - E^(5 + x))))/((E^(2/x) - E^(5 + x))^2*x^2), x] + 2*E^4*L
og[-225 + x]*Defer[Int][(E^(2/x)*(-225 + x)^(-1 + E^4/(E^(2/x) - E^(5 + x))))/((E^(2/x) - E^(5 + x))^2*x), x]
+ E^4*Log[-225 + x]*Defer[Int][(E^(2/x)*(-225 + x)^(-1 + E^4/(E^(2/x) - E^(5 + x)))*x)/(E^(2/x) - E^(5 + x))^2
, x] - E^4*Log[-225 + x]*Defer[Int][((-225 + x)^(-1 + E^4/(E^(2/x) - E^(5 + x)))*x)/(E^(2/x) - E^(5 + x)), x]
+ 225*E^4*Defer[Int][Defer[Int][(E^(2/x)*(-225 + x)^(-1 + E^4/(E^(2/x) - E^(5 + x))))/(E^(2/x) - E^(5 + x))^2,
x]/(-225 + x), x] - 225*E^4*Defer[Int][Defer[Int][(-225 + x)^(-1 + E^4/(E^(2/x) - E^(5 + x)))/(E^(2/x) - E^(5
+ x)), x]/(-225 + x), x] + 450*E^4*Defer[Int][Defer[Int][(E^(2/x)*(-225 + x)^(-1 + E^4/(E^(2/x) - E^(5 + x)))
)/((E^(2/x) - E^(5 + x))^2*x^2), x]/(-225 + x), x] - 2*E^4*Defer[Int][Defer[Int][(E^(2/x)*(-225 + x)^(-1 + E^4
/(E^(2/x) - E^(5 + x))))/((E^(2/x) - E^(5 + x))^2*x), x]/(-225 + x), x] - E^4*Defer[Int][Defer[Int][(E^(2/x)*(
-225 + x)^(-1 + E^4/(E^(2/x) - E^(5 + x)))*x)/(E^(2/x) - E^(5 + x))^2, x]/(-225 + x), x] + E^4*Defer[Int][Defe
r[Int][((-225 + x)^(-1 + E^4/(E^(2/x) - E^(5 + x)))*x)/(E^(2/x) - E^(5 + x)), x]/(-225 + x), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^4 (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} \left (\left (e^{2/x}-e^{5+x}\right ) x^2+(-225+x) \left (2 e^{2/x}+e^{5+x} x^2\right ) \log (-225+x)\right )}{\left (e^{2/x}-e^{5+x}\right )^2 x^2} \, dx\\ &=e^4 \int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} \left (\left (e^{2/x}-e^{5+x}\right ) x^2+(-225+x) \left (2 e^{2/x}+e^{5+x} x^2\right ) \log (-225+x)\right )}{\left (e^{2/x}-e^{5+x}\right )^2 x^2} \, dx\\ &=e^4 \int \left (\frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} \left (-450+2 x-225 x^2+x^3\right ) \log (-225+x)}{\left (e^{2/x}-e^{5+x}\right )^2 x^2}-\frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} (-1-225 \log (-225+x)+x \log (-225+x))}{e^{2/x}-e^{5+x}}\right ) \, dx\\ &=e^4 \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} \left (-450+2 x-225 x^2+x^3\right ) \log (-225+x)}{\left (e^{2/x}-e^{5+x}\right )^2 x^2} \, dx-e^4 \int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} (-1-225 \log (-225+x)+x \log (-225+x))}{e^{2/x}-e^{5+x}} \, dx\\ &=-\left (e^4 \int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} (-1+(-225+x) \log (-225+x))}{e^{2/x}-e^{5+x}} \, dx\right )-e^4 \int \frac {-225 \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx-450 \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x^2} \, dx+2 \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x} \, dx+\int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx}{-225+x} \, dx+\left (e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx+\left (2 e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x} \, dx-\left (225 e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx-\left (450 e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x^2} \, dx\\ &=-\left (e^4 \int \left (-\frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{e^{2/x}-e^{5+x}}-\frac {225 (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} \log (-225+x)}{e^{2/x}-e^{5+x}}+\frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x \log (-225+x)}{e^{2/x}-e^{5+x}}\right ) \, dx\right )-e^4 \int \left (\frac {-225 \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx-450 \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x^2} \, dx+2 \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x} \, dx}{-225+x}+\frac {\int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx}{-225+x}\right ) \, dx+\left (e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx+\left (2 e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x} \, dx-\left (225 e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx-\left (450 e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x^2} \, dx\\ &=e^4 \int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{e^{2/x}-e^{5+x}} \, dx-e^4 \int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x \log (-225+x)}{e^{2/x}-e^{5+x}} \, dx-e^4 \int \frac {-225 \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx-450 \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x^2} \, dx+2 \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x} \, dx}{-225+x} \, dx-e^4 \int \frac {\int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx}{-225+x} \, dx+\left (225 e^4\right ) \int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} \log (-225+x)}{e^{2/x}-e^{5+x}} \, dx+\left (e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx+\left (2 e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x} \, dx-\left (225 e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx-\left (450 e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x^2} \, dx\\ &=e^4 \int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{e^{2/x}-e^{5+x}} \, dx-e^4 \int \left (-\frac {225 \left (\int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx+2 \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x^2} \, dx\right )}{-225+x}+\frac {2 \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x} \, dx}{-225+x}\right ) \, dx-e^4 \int \frac {\int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx}{-225+x} \, dx+e^4 \int \frac {\int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{e^{2/x}-e^{5+x}} \, dx}{-225+x} \, dx-\left (225 e^4\right ) \int \frac {\int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{e^{2/x}-e^{5+x}} \, dx}{-225+x} \, dx+\left (e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx-\left (e^4 \log (-225+x)\right ) \int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{e^{2/x}-e^{5+x}} \, dx+\left (2 e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x} \, dx-\left (225 e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx+\left (225 e^4 \log (-225+x)\right ) \int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{e^{2/x}-e^{5+x}} \, dx-\left (450 e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x^2} \, dx\\ &=e^4 \int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{e^{2/x}-e^{5+x}} \, dx-e^4 \int \frac {\int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx}{-225+x} \, dx+e^4 \int \frac {\int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{e^{2/x}-e^{5+x}} \, dx}{-225+x} \, dx-\left (2 e^4\right ) \int \frac {\int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x} \, dx}{-225+x} \, dx-\left (225 e^4\right ) \int \frac {\int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{e^{2/x}-e^{5+x}} \, dx}{-225+x} \, dx+\left (225 e^4\right ) \int \frac {\int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx+2 \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x^2} \, dx}{-225+x} \, dx+\left (e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx-\left (e^4 \log (-225+x)\right ) \int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{e^{2/x}-e^{5+x}} \, dx+\left (2 e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x} \, dx-\left (225 e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx+\left (225 e^4 \log (-225+x)\right ) \int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{e^{2/x}-e^{5+x}} \, dx-\left (450 e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x^2} \, dx\\ &=e^4 \int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{e^{2/x}-e^{5+x}} \, dx-e^4 \int \frac {\int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx}{-225+x} \, dx+e^4 \int \frac {\int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{e^{2/x}-e^{5+x}} \, dx}{-225+x} \, dx-\left (2 e^4\right ) \int \frac {\int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x} \, dx}{-225+x} \, dx-\left (225 e^4\right ) \int \frac {\int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{e^{2/x}-e^{5+x}} \, dx}{-225+x} \, dx+\left (225 e^4\right ) \int \left (\frac {\int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx}{-225+x}+\frac {2 \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x^2} \, dx}{-225+x}\right ) \, dx+\left (e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx-\left (e^4 \log (-225+x)\right ) \int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{e^{2/x}-e^{5+x}} \, dx+\left (2 e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x} \, dx-\left (225 e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx+\left (225 e^4 \log (-225+x)\right ) \int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{e^{2/x}-e^{5+x}} \, dx-\left (450 e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x^2} \, dx\\ &=e^4 \int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{e^{2/x}-e^{5+x}} \, dx-e^4 \int \frac {\int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx}{-225+x} \, dx+e^4 \int \frac {\int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{e^{2/x}-e^{5+x}} \, dx}{-225+x} \, dx-\left (2 e^4\right ) \int \frac {\int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x} \, dx}{-225+x} \, dx+\left (225 e^4\right ) \int \frac {\int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx}{-225+x} \, dx-\left (225 e^4\right ) \int \frac {\int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{e^{2/x}-e^{5+x}} \, dx}{-225+x} \, dx+\left (450 e^4\right ) \int \frac {\int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x^2} \, dx}{-225+x} \, dx+\left (e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx-\left (e^4 \log (-225+x)\right ) \int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{e^{2/x}-e^{5+x}} \, dx+\left (2 e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x} \, dx-\left (225 e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx+\left (225 e^4 \log (-225+x)\right ) \int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{e^{2/x}-e^{5+x}} \, dx-\left (450 e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.24, size = 26, normalized size = 1.04 \begin {gather*} (-225+x)^{-\frac {e^4}{-e^{2/x}+e^{5+x}}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(4 + 2/x)*x^2 - E^(9 + x)*x^2 + (E^(4 + 2/x)*(-450 + 2*x) + E^(9 + x)*(-225*x^2 + x^3))*Log[-225
+ x])/((-225 + x)^(E^4/(-E^(2/x) + E^(5 + x)))*(E^(5 + 2/x + x)*(450*x^2 - 2*x^3) + E^(4/x)*(-225*x^2 + x^3) +
E^(10 + 2*x)*(-225*x^2 + x^3))),x]

[Out]

(-225 + x)^(-(E^4/(-E^(2/x) + E^(5 + x))))

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fricas [A]  time = 0.53, size = 37, normalized size = 1.48 \begin {gather*} \frac {1}{{\left (x - 225\right )}^{\frac {e^{\left (x + 17\right )}}{e^{\left (2 \, x + 18\right )} - e^{\left (\frac {x^{2} + 5 \, x + 2}{x} + 8\right )}}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x^3-225*x^2)*exp(4)*exp(5+x)+(2*x-450)*exp(4)*exp(2/x))*log(x-225)-x^2*exp(4)*exp(5+x)+x^2*exp(4)
*exp(2/x))*exp(-exp(4)*log(x-225)/(exp(5+x)-exp(2/x)))/((x^3-225*x^2)*exp(5+x)^2+(-2*x^3+450*x^2)*exp(2/x)*exp
(5+x)+(x^3-225*x^2)*exp(2/x)^2),x, algorithm="fricas")

[Out]

1/((x - 225)^(e^(x + 17)/(e^(2*x + 18) - e^((x^2 + 5*x + 2)/x + 8))))

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x^3-225*x^2)*exp(4)*exp(5+x)+(2*x-450)*exp(4)*exp(2/x))*log(x-225)-x^2*exp(4)*exp(5+x)+x^2*exp(4)
*exp(2/x))*exp(-exp(4)*log(x-225)/(exp(5+x)-exp(2/x)))/((x^3-225*x^2)*exp(5+x)^2+(-2*x^3+450*x^2)*exp(2/x)*exp
(5+x)+(x^3-225*x^2)*exp(2/x)^2),x, algorithm="giac")

[Out]

Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,sageVARx):;OUTP
UT:Evaluation time: 1.63Polynomial exponent overflow. Error: Bad Argument Value

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maple [A]  time = 0.05, size = 24, normalized size = 0.96

method	result	size
risch	\(\left (x -225\right )^{-\frac {{\mathrm e}^{4}}{{\mathrm e}^{5+x}-{\mathrm e}^{\frac {2}{x}}}}\)	\(24\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((x^3-225*x^2)*exp(4)*exp(5+x)+(2*x-450)*exp(4)*exp(2/x))*ln(x-225)-x^2*exp(4)*exp(5+x)+x^2*exp(4)*exp(2/
x))*exp(-exp(4)*ln(x-225)/(exp(5+x)-exp(2/x)))/((x^3-225*x^2)*exp(5+x)^2+(-2*x^3+450*x^2)*exp(2/x)*exp(5+x)+(x
^3-225*x^2)*exp(2/x)^2),x,method=_RETURNVERBOSE)

[Out]

(x-225)^(-exp(4)/(exp(5+x)-exp(2/x)))

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maxima [A]  time = 0.87, size = 24, normalized size = 0.96 \begin {gather*} \frac {1}{{\left (x - 225\right )}^{\frac {e^{4}}{e^{\left (x + 5\right )} - e^{\frac {2}{x}}}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x^3-225*x^2)*exp(4)*exp(5+x)+(2*x-450)*exp(4)*exp(2/x))*log(x-225)-x^2*exp(4)*exp(5+x)+x^2*exp(4)
*exp(2/x))*exp(-exp(4)*log(x-225)/(exp(5+x)-exp(2/x)))/((x^3-225*x^2)*exp(5+x)^2+(-2*x^3+450*x^2)*exp(2/x)*exp
(5+x)+(x^3-225*x^2)*exp(2/x)^2),x, algorithm="maxima")

[Out]

1/((x - 225)^(e^4/(e^(x + 5) - e^(2/x))))

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mupad [B]  time = 3.00, size = 24, normalized size = 0.96 \begin {gather*} \frac {1}{{\left (x-225\right )}^{\frac {{\mathrm {e}}^4}{{\mathrm {e}}^{x+5}-{\mathrm {e}}^{2/x}}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(-(log(x - 225)*exp(4))/(exp(x + 5) - exp(2/x)))*(log(x - 225)*(exp(4)*exp(2/x)*(2*x - 450) - exp(x +
5)*exp(4)*(225*x^2 - x^3)) + x^2*exp(4)*exp(2/x) - x^2*exp(x + 5)*exp(4)))/(exp(2*x + 10)*(225*x^2 - x^3) + e
xp(4/x)*(225*x^2 - x^3) - exp(x + 5)*exp(2/x)*(450*x^2 - 2*x^3)),x)

[Out]

1/(x - 225)^(exp(4)/(exp(x + 5) - exp(2/x)))

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sympy [A]  time = 12.64, size = 20, normalized size = 0.80 \begin {gather*} e^{- \frac {e^{4} \log {\left (x - 225 \right )}}{- e^{\frac {2}{x}} + e^{x + 5}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x**3-225*x**2)*exp(4)*exp(5+x)+(2*x-450)*exp(4)*exp(2/x))*ln(x-225)-x**2*exp(4)*exp(5+x)+x**2*exp
(4)*exp(2/x))*exp(-exp(4)*ln(x-225)/(exp(5+x)-exp(2/x)))/((x**3-225*x**2)*exp(5+x)**2+(-2*x**3+450*x**2)*exp(2
/x)*exp(5+x)+(x**3-225*x**2)*exp(2/x)**2),x)

[Out]

exp(-exp(4)*log(x - 225)/(-exp(2/x) + exp(x + 5)))

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