3.85.38 \(\int \frac {e^{-2 x \log (\frac {x}{3+x})+x^2 \log (-3+x) \log (\frac {x}{3+x})} (-9+18 x-5 x^2+(18 x+x^3+x^4) \log (\frac {x}{3+x})+\log (-3+x) (-9 x^2+3 x^3+(-18 x^2+2 x^4) \log (\frac {x}{3+x})))}{-9+x^2} \, dx\)

Optimal. Leaf size=20 \[ x \left (\frac {x}{3+x}\right )^{x (-2+x \log (-3+x))} \]

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Rubi [F]  time = 23.29, 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 {\exp \left (-2 x \log \left (\frac {x}{3+x}\right )+x^2 \log (-3+x) \log \left (\frac {x}{3+x}\right )\right ) \left (-9+18 x-5 x^2+\left (18 x+x^3+x^4\right ) \log \left (\frac {x}{3+x}\right )+\log (-3+x) \left (-9 x^2+3 x^3+\left (-18 x^2+2 x^4\right ) \log \left (\frac {x}{3+x}\right )\right )\right )}{-9+x^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(-2*x*Log[x/(3 + x)] + x^2*Log[-3 + x]*Log[x/(3 + x)])*(-9 + 18*x - 5*x^2 + (18*x + x^3 + x^4)*Log[x/(3
+ x)] + Log[-3 + x]*(-9*x^2 + 3*x^3 + (-18*x^2 + 2*x^4)*Log[x/(3 + x)])))/(-9 + x^2),x]

[Out]

-5*Defer[Int][(x/(3 + x))^(-2*x + x^2*Log[-3 + x]), x] + 9*Defer[Int][(x/(3 + x))^(-2*x + x^2*Log[-3 + x])/(3
- x), x] + 9*Defer[Int][(x/(3 + x))^(-2*x + x^2*Log[-3 + x])/(-3 + x), x] + 18*Defer[Int][(x/(3 + x))^(-2*x +
x^2*Log[-3 + x])/(3 + x), x] - 9*Defer[Int][(x/(3 + x))^(-2*x + x^2*Log[-3 + x])*Log[-3 + x], x] + 3*Defer[Int
][x*(x/(3 + x))^(-2*x + x^2*Log[-3 + x])*Log[-3 + x], x] + 27*Defer[Int][((x/(3 + x))^(-2*x + x^2*Log[-3 + x])
*Log[-3 + x])/(3 + x), x] + 9*Defer[Int][(x/(3 + x))^(-2*x + x^2*Log[-3 + x])*Log[x/(3 + x)], x] + 27*Defer[In
t][((x/(3 + x))^(-2*x + x^2*Log[-3 + x])*Log[x/(3 + x)])/(-3 + x), x] + Defer[Int][x*(x/(3 + x))^(-2*x + x^2*L
og[-3 + x])*Log[x/(3 + x)], x] + Defer[Int][x^2*(x/(3 + x))^(-2*x + x^2*Log[-3 + x])*Log[x/(3 + x)], x] + 2*De
fer[Int][x^2*(x/(3 + x))^(-2*x + x^2*Log[-3 + x])*Log[-3 + x]*Log[x/(3 + x)], x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {9 \left (\frac {x}{3+x}\right )^{x (-2+x \log (-3+x))}}{-9+x^2}+\frac {18 x \left (\frac {x}{3+x}\right )^{x (-2+x \log (-3+x))}}{-9+x^2}-\frac {5 x^2 \left (\frac {x}{3+x}\right )^{x (-2+x \log (-3+x))}}{-9+x^2}-\frac {9 x^2 \left (\frac {x}{3+x}\right )^{x (-2+x \log (-3+x))} \log (-3+x)}{-9+x^2}+\frac {3 x^3 \left (\frac {x}{3+x}\right )^{x (-2+x \log (-3+x))} \log (-3+x)}{-9+x^2}+\frac {x \left (\frac {x}{3+x}\right )^{x (-2+x \log (-3+x))} \left (6-2 x+x^2-6 x \log (-3+x)+2 x^2 \log (-3+x)\right ) \log \left (\frac {x}{3+x}\right )}{-3+x}\right ) \, dx\\ &=3 \int \frac {x^3 \left (\frac {x}{3+x}\right )^{x (-2+x \log (-3+x))} \log (-3+x)}{-9+x^2} \, dx-5 \int \frac {x^2 \left (\frac {x}{3+x}\right )^{x (-2+x \log (-3+x))}}{-9+x^2} \, dx-9 \int \frac {\left (\frac {x}{3+x}\right )^{x (-2+x \log (-3+x))}}{-9+x^2} \, dx-9 \int \frac {x^2 \left (\frac {x}{3+x}\right )^{x (-2+x \log (-3+x))} \log (-3+x)}{-9+x^2} \, dx+18 \int \frac {x \left (\frac {x}{3+x}\right )^{x (-2+x \log (-3+x))}}{-9+x^2} \, dx+\int \frac {x \left (\frac {x}{3+x}\right )^{x (-2+x \log (-3+x))} \left (6-2 x+x^2-6 x \log (-3+x)+2 x^2 \log (-3+x)\right ) \log \left (\frac {x}{3+x}\right )}{-3+x} \, dx\\ &=3 \int \left (\frac {9 \left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \log (-3+x)}{2 (-3+x)}+x \left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \log (-3+x)+\frac {9 \left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \log (-3+x)}{2 (3+x)}\right ) \, dx-5 \int \left (\left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)}+\frac {9 \left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)}}{-9+x^2}\right ) \, dx-9 \int \left (-\frac {\left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)}}{6 (3-x)}-\frac {\left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)}}{6 (3+x)}\right ) \, dx-9 \int \left (\left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \log (-3+x)+\frac {9 \left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \log (-3+x)}{-9+x^2}\right ) \, dx+18 \int \left (\frac {\left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)}}{2 (-3+x)}+\frac {\left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)}}{2 (3+x)}\right ) \, dx+\int \frac {x \left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \left (-6+2 x-x^2+6 x \log (-3+x)-2 x^2 \log (-3+x)\right ) \log \left (\frac {x}{3+x}\right )}{3-x} \, dx\\ &=\frac {3}{2} \int \frac {\left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)}}{3-x} \, dx+\frac {3}{2} \int \frac {\left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)}}{3+x} \, dx+3 \int x \left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \log (-3+x) \, dx-5 \int \left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \, dx+9 \int \frac {\left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)}}{-3+x} \, dx+9 \int \frac {\left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)}}{3+x} \, dx-9 \int \left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \log (-3+x) \, dx+\frac {27}{2} \int \frac {\left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \log (-3+x)}{-3+x} \, dx+\frac {27}{2} \int \frac {\left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \log (-3+x)}{3+x} \, dx-45 \int \frac {\left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)}}{-9+x^2} \, dx-81 \int \frac {\left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \log (-3+x)}{-9+x^2} \, dx+\int \left (\left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \left (6-2 x+x^2-6 x \log (-3+x)+2 x^2 \log (-3+x)\right ) \log \left (\frac {x}{3+x}\right )+\frac {3 \left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \left (6-2 x+x^2-6 x \log (-3+x)+2 x^2 \log (-3+x)\right ) \log \left (\frac {x}{3+x}\right )}{-3+x}\right ) \, dx\\ &=\frac {3}{2} \int \frac {\left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)}}{3-x} \, dx+\frac {3}{2} \int \frac {\left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)}}{3+x} \, dx+3 \int x \left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \log (-3+x) \, dx+3 \int \frac {\left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \left (6-2 x+x^2-6 x \log (-3+x)+2 x^2 \log (-3+x)\right ) \log \left (\frac {x}{3+x}\right )}{-3+x} \, dx-5 \int \left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \, dx+9 \int \frac {\left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)}}{-3+x} \, dx+9 \int \frac {\left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)}}{3+x} \, dx-9 \int \left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \log (-3+x) \, dx+\frac {27}{2} \int \frac {\left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \log (-3+x)}{-3+x} \, dx+\frac {27}{2} \int \frac {\left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \log (-3+x)}{3+x} \, dx-45 \int \left (-\frac {\left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)}}{6 (3-x)}-\frac {\left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)}}{6 (3+x)}\right ) \, dx-81 \int \left (\frac {\left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \log (-3+x)}{6 (-3+x)}-\frac {\left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \log (-3+x)}{6 (3+x)}\right ) \, dx+\int \left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \left (6-2 x+x^2-6 x \log (-3+x)+2 x^2 \log (-3+x)\right ) \log \left (\frac {x}{3+x}\right ) \, dx\\ &=\frac {3}{2} \int \frac {\left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)}}{3-x} \, dx+\frac {3}{2} \int \frac {\left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)}}{3+x} \, dx+3 \int x \left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \log (-3+x) \, dx+3 \int \left (\frac {6 \left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \log \left (\frac {x}{3+x}\right )}{-3+x}-\frac {2 x \left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \log \left (\frac {x}{3+x}\right )}{-3+x}+\frac {x^2 \left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \log \left (\frac {x}{3+x}\right )}{-3+x}-\frac {6 x \left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \log (-3+x) \log \left (\frac {x}{3+x}\right )}{-3+x}+\frac {2 x^2 \left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \log (-3+x) \log \left (\frac {x}{3+x}\right )}{-3+x}\right ) \, dx-5 \int \left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \, dx+\frac {15}{2} \int \frac {\left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)}}{3-x} \, dx+\frac {15}{2} \int \frac {\left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)}}{3+x} \, dx+9 \int \frac {\left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)}}{-3+x} \, dx+9 \int \frac {\left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)}}{3+x} \, dx-9 \int \left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \log (-3+x) \, dx+2 \left (\frac {27}{2} \int \frac {\left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \log (-3+x)}{3+x} \, dx\right )+\int \left (6 \left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \log \left (\frac {x}{3+x}\right )-2 x \left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \log \left (\frac {x}{3+x}\right )+x^2 \left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \log \left (\frac {x}{3+x}\right )-6 x \left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \log (-3+x) \log \left (\frac {x}{3+x}\right )+2 x^2 \left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \log (-3+x) \log \left (\frac {x}{3+x}\right )\right ) \, dx\\ &=\frac {3}{2} \int \frac {\left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)}}{3-x} \, dx+\frac {3}{2} \int \frac {\left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)}}{3+x} \, dx-2 \int x \left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \log \left (\frac {x}{3+x}\right ) \, dx+2 \int x^2 \left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \log (-3+x) \log \left (\frac {x}{3+x}\right ) \, dx+3 \int x \left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \log (-3+x) \, dx+3 \int \frac {x^2 \left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \log \left (\frac {x}{3+x}\right )}{-3+x} \, dx-5 \int \left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \, dx+6 \int \left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \log \left (\frac {x}{3+x}\right ) \, dx-6 \int \frac {x \left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \log \left (\frac {x}{3+x}\right )}{-3+x} \, dx-6 \int x \left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \log (-3+x) \log \left (\frac {x}{3+x}\right ) \, dx+6 \int \frac {x^2 \left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \log (-3+x) \log \left (\frac {x}{3+x}\right )}{-3+x} \, dx+\frac {15}{2} \int \frac {\left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)}}{3-x} \, dx+\frac {15}{2} \int \frac {\left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)}}{3+x} \, dx+9 \int \frac {\left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)}}{-3+x} \, dx+9 \int \frac {\left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)}}{3+x} \, dx-9 \int \left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \log (-3+x) \, dx+2 \left (\frac {27}{2} \int \frac {\left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \log (-3+x)}{3+x} \, dx\right )+18 \int \frac {\left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \log \left (\frac {x}{3+x}\right )}{-3+x} \, dx-18 \int \frac {x \left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \log (-3+x) \log \left (\frac {x}{3+x}\right )}{-3+x} \, dx+\int x^2 \left (\frac {x}{3+x}\right )^{-2 x+x^2 \log (-3+x)} \log \left (\frac {x}{3+x}\right ) \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.11, size = 29, normalized size = 1.45 \begin {gather*} (-3+x)^{x^2 \log \left (\frac {x}{3+x}\right )} x \left (\frac {x}{3+x}\right )^{-2 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(-2*x*Log[x/(3 + x)] + x^2*Log[-3 + x]*Log[x/(3 + x)])*(-9 + 18*x - 5*x^2 + (18*x + x^3 + x^4)*Lo
g[x/(3 + x)] + Log[-3 + x]*(-9*x^2 + 3*x^3 + (-18*x^2 + 2*x^4)*Log[x/(3 + x)])))/(-9 + x^2),x]

[Out]

((-3 + x)^(x^2*Log[x/(3 + x)])*x)/(x/(3 + x))^(2*x)

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fricas [A]  time = 1.55, size = 31, normalized size = 1.55 \begin {gather*} x e^{\left (x^{2} \log \left (x - 3\right ) \log \left (\frac {x}{x + 3}\right ) - 2 \, x \log \left (\frac {x}{x + 3}\right )\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x^4-18*x^2)*log(x/(3+x))+3*x^3-9*x^2)*log(x-3)+(x^4+x^3+18*x)*log(x/(3+x))-5*x^2+18*x-9)*exp(x^
2*log(x/(3+x))*log(x-3)-2*x*log(x/(3+x)))/(x^2-9),x, algorithm="fricas")

[Out]

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

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -\frac {{\left (5 \, x^{2} - {\left (3 \, x^{3} - 9 \, x^{2} + 2 \, {\left (x^{4} - 9 \, x^{2}\right )} \log \left (\frac {x}{x + 3}\right )\right )} \log \left (x - 3\right ) - {\left (x^{4} + x^{3} + 18 \, x\right )} \log \left (\frac {x}{x + 3}\right ) - 18 \, x + 9\right )} e^{\left (x^{2} \log \left (x - 3\right ) \log \left (\frac {x}{x + 3}\right ) - 2 \, x \log \left (\frac {x}{x + 3}\right )\right )}}{x^{2} - 9}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x^4-18*x^2)*log(x/(3+x))+3*x^3-9*x^2)*log(x-3)+(x^4+x^3+18*x)*log(x/(3+x))-5*x^2+18*x-9)*exp(x^
2*log(x/(3+x))*log(x-3)-2*x*log(x/(3+x)))/(x^2-9),x, algorithm="giac")

[Out]

integrate(-(5*x^2 - (3*x^3 - 9*x^2 + 2*(x^4 - 9*x^2)*log(x/(x + 3)))*log(x - 3) - (x^4 + x^3 + 18*x)*log(x/(x
+ 3)) - 18*x + 9)*e^(x^2*log(x - 3)*log(x/(x + 3)) - 2*x*log(x/(x + 3)))/(x^2 - 9), x)

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maple [C]  time = 0.53, size = 191, normalized size = 9.55

method	result	size
risch	\(x \left (x -3\right )^{-\frac {x^{2} \left (i \pi \,\mathrm {csgn}\left (\frac {i x}{3+x}\right )-i \pi \,\mathrm {csgn}\left (i x \right )-i \pi \,\mathrm {csgn}\left (\frac {i}{3+x}\right )+i \pi \,\mathrm {csgn}\left (\frac {i x}{3+x}\right ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (\frac {i}{3+x}\right )-2 \ln \relax (x )+2 \ln \left (3+x \right )\right )}{2}} {\mathrm e}^{x \left (i \pi \mathrm {csgn}\left (\frac {i x}{3+x}\right )^{3}-i \pi \mathrm {csgn}\left (\frac {i x}{3+x}\right )^{2} \mathrm {csgn}\left (i x \right )-i \pi \mathrm {csgn}\left (\frac {i x}{3+x}\right )^{2} \mathrm {csgn}\left (\frac {i}{3+x}\right )+i \pi \,\mathrm {csgn}\left (\frac {i x}{3+x}\right ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (\frac {i}{3+x}\right )-2 \ln \relax (x )+2 \ln \left (3+x \right )\right )}\)	\(191\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((2*x^4-18*x^2)*ln(x/(3+x))+3*x^3-9*x^2)*ln(x-3)+(x^4+x^3+18*x)*ln(x/(3+x))-5*x^2+18*x-9)*exp(x^2*ln(x/(3
+x))*ln(x-3)-2*x*ln(x/(3+x)))/(x^2-9),x,method=_RETURNVERBOSE)

[Out]

x*(x-3)^(-1/2*x^2*(I*Pi*csgn(I*x/(3+x))-I*Pi*csgn(I*x)-I*Pi*csgn(I/(3+x))+I*Pi*csgn(I*x/(3+x))*csgn(I*x)*csgn(
I/(3+x))-2*ln(x)+2*ln(3+x)))*exp(x*(I*Pi*csgn(I*x/(3+x))^3-I*Pi*csgn(I*x/(3+x))^2*csgn(I*x)-I*Pi*csgn(I*x/(3+x
))^2*csgn(I/(3+x))+I*Pi*csgn(I*x/(3+x))*csgn(I*x)*csgn(I/(3+x))-2*ln(x)+2*ln(3+x)))

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maxima [A]  time = 0.46, size = 39, normalized size = 1.95 \begin {gather*} x e^{\left (-x^{2} \log \left (x + 3\right ) \log \left (x - 3\right ) + x^{2} \log \left (x - 3\right ) \log \relax (x) + 2 \, x \log \left (x + 3\right ) - 2 \, x \log \relax (x)\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x^4-18*x^2)*log(x/(3+x))+3*x^3-9*x^2)*log(x-3)+(x^4+x^3+18*x)*log(x/(3+x))-5*x^2+18*x-9)*exp(x^
2*log(x/(3+x))*log(x-3)-2*x*log(x/(3+x)))/(x^2-9),x, algorithm="maxima")

[Out]

x*e^(-x^2*log(x + 3)*log(x - 3) + x^2*log(x - 3)*log(x) + 2*x*log(x + 3) - 2*x*log(x))

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mupad [B]  time = 5.50, size = 31, normalized size = 1.55 \begin {gather*} \frac {x\,{\left (x-3\right )}^{x^2\,\ln \left (\frac {x}{x+3}\right )}}{{\left (\frac {x}{x+3}\right )}^{2\,x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(x^2*log(x - 3)*log(x/(x + 3)) - 2*x*log(x/(x + 3)))*(log(x - 3)*(log(x/(x + 3))*(18*x^2 - 2*x^4) + 9
*x^2 - 3*x^3) - 18*x - log(x/(x + 3))*(18*x + x^3 + x^4) + 5*x^2 + 9))/(x^2 - 9),x)

[Out]

(x*(x - 3)^(x^2*log(x/(x + 3))))/(x/(x + 3))^(2*x)

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sympy [A]  time = 16.39, size = 27, normalized size = 1.35 \begin {gather*} x e^{x^{2} \log {\left (\frac {x}{x + 3} \right )} \log {\left (x - 3 \right )} - 2 x \log {\left (\frac {x}{x + 3} \right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x**4-18*x**2)*ln(x/(3+x))+3*x**3-9*x**2)*ln(x-3)+(x**4+x**3+18*x)*ln(x/(3+x))-5*x**2+18*x-9)*ex
p(x**2*ln(x/(3+x))*ln(x-3)-2*x*ln(x/(3+x)))/(x**2-9),x)

[Out]

x*exp(x**2*log(x/(x + 3))*log(x - 3) - 2*x*log(x/(x + 3)))

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