3.85.76 \(\int \frac {e^{-10-2 x} (9216-4608 x+(4608+6912 x-4608 x^2+e^{5+x} (576 x-288 x^2)+e^{5+x} (192-96 x) \log (2-x)) \log (x)+(e^{5+x} (96 x+576 x^2-288 x^3)+e^{5+x} (192+96 x-96 x^2) \log (2-x)) \log ^2(x)+(e^{10+2 x} (-12 x^2+9 x^3)+2 e^{10+2 x} x \log (2-x)+e^{10+2 x} (2-x) \log ^2(2-x)) \log ^3(x))}{(-2 x^2+x^3) \log ^3(x)} \, dx\)

Optimal. Leaf size=30 \[ \frac {\left (\log (2-x)+3 \left (x+\frac {16 e^{-5-x}}{\log (x)}\right )\right )^2}{x} \]

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Rubi [F]  time = 14.58, 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^{-10-2 x} \left (9216-4608 x+\left (4608+6912 x-4608 x^2+e^{5+x} \left (576 x-288 x^2\right )+e^{5+x} (192-96 x) \log (2-x)\right ) \log (x)+\left (e^{5+x} \left (96 x+576 x^2-288 x^3\right )+e^{5+x} \left (192+96 x-96 x^2\right ) \log (2-x)\right ) \log ^2(x)+\left (e^{10+2 x} \left (-12 x^2+9 x^3\right )+2 e^{10+2 x} x \log (2-x)+e^{10+2 x} (2-x) \log ^2(2-x)\right ) \log ^3(x)\right )}{\left (-2 x^2+x^3\right ) \log ^3(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(-10 - 2*x)*(9216 - 4608*x + (4608 + 6912*x - 4608*x^2 + E^(5 + x)*(576*x - 288*x^2) + E^(5 + x)*(192 -
96*x)*Log[2 - x])*Log[x] + (E^(5 + x)*(96*x + 576*x^2 - 288*x^3) + E^(5 + x)*(192 + 96*x - 96*x^2)*Log[2 - x]
)*Log[x]^2 + (E^(10 + 2*x)*(-12*x^2 + 9*x^3) + 2*E^(10 + 2*x)*x*Log[2 - x] + E^(10 + 2*x)*(2 - x)*Log[2 - x]^2
)*Log[x]^3))/((-2*x^2 + x^3)*Log[x]^3),x]

[Out]

9*x + 6*Log[2 - x] + Log[2 - x]^2/2 + ((2 - x)*Log[2 - x]^2)/(2*x) + (2304*E^(-10 - 2*x))/(x*Log[x]^2) - 288*D
efer[Int][E^(-5 - x)/(x*Log[x]^2), x] - 96*Defer[Int][(E^(-5 - x)*Log[2 - x])/(x^2*Log[x]^2), x] - 288*Defer[I
nt][E^(-5 - x)/Log[x], x] + 48*Defer[Int][E^(-5 - x)/((-2 + x)*Log[x]), x] - 48*Defer[Int][E^(-5 - x)/(x*Log[x
]), x] - 96*Defer[Int][(E^(-5 - x)*Log[2 - x])/(x^2*Log[x]), x] - 96*Defer[Int][(E^(-5 - x)*Log[2 - x])/(x*Log
[x]), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{-10-2 x} \left (9216-4608 x+\left (4608+6912 x-4608 x^2+e^{5+x} \left (576 x-288 x^2\right )+e^{5+x} (192-96 x) \log (2-x)\right ) \log (x)+\left (e^{5+x} \left (96 x+576 x^2-288 x^3\right )+e^{5+x} \left (192+96 x-96 x^2\right ) \log (2-x)\right ) \log ^2(x)+\left (e^{10+2 x} \left (-12 x^2+9 x^3\right )+2 e^{10+2 x} x \log (2-x)+e^{10+2 x} (2-x) \log ^2(2-x)\right ) \log ^3(x)\right )}{(-2+x) x^2 \log ^3(x)} \, dx\\ &=\int \left (\frac {-12 x^2+9 x^3+2 x \log (2-x)+2 \log ^2(2-x)-x \log ^2(2-x)}{(-2+x) x^2}-\frac {2304 e^{-10-2 x} (2+\log (x)+2 x \log (x))}{x^2 \log ^3(x)}-\frac {96 e^{-5-x} \left (-6 x+3 x^2-2 \log (2-x)+x \log (2-x)-x \log (x)-6 x^2 \log (x)+3 x^3 \log (x)-2 \log (2-x) \log (x)-x \log (2-x) \log (x)+x^2 \log (2-x) \log (x)\right )}{(-2+x) x^2 \log ^2(x)}\right ) \, dx\\ &=-\left (96 \int \frac {e^{-5-x} \left (-6 x+3 x^2-2 \log (2-x)+x \log (2-x)-x \log (x)-6 x^2 \log (x)+3 x^3 \log (x)-2 \log (2-x) \log (x)-x \log (2-x) \log (x)+x^2 \log (2-x) \log (x)\right )}{(-2+x) x^2 \log ^2(x)} \, dx\right )-2304 \int \frac {e^{-10-2 x} (2+\log (x)+2 x \log (x))}{x^2 \log ^3(x)} \, dx+\int \frac {-12 x^2+9 x^3+2 x \log (2-x)+2 \log ^2(2-x)-x \log ^2(2-x)}{(-2+x) x^2} \, dx\\ &=\frac {2304 e^{-10-2 x}}{x \log ^2(x)}-96 \int \frac {e^{-5-x} \left (-((-2+x) \log (2-x) (1+(1+x) \log (x)))-x \left (3 (-2+x)+\left (-1-6 x+3 x^2\right ) \log (x)\right )\right )}{(2-x) x^2 \log ^2(x)} \, dx+\int \left (\frac {3 (-4+3 x)}{-2+x}+\frac {2 \log (2-x)}{(-2+x) x}-\frac {\log ^2(2-x)}{x^2}\right ) \, dx\\ &=\frac {2304 e^{-10-2 x}}{x \log ^2(x)}+2 \int \frac {\log (2-x)}{(-2+x) x} \, dx+3 \int \frac {-4+3 x}{-2+x} \, dx-96 \int \left (\frac {e^{-5-x} (3 x+\log (2-x))}{x^2 \log ^2(x)}+\frac {e^{-5-x} \left (-x-6 x^2+3 x^3-2 \log (2-x)-x \log (2-x)+x^2 \log (2-x)\right )}{(-2+x) x^2 \log (x)}\right ) \, dx-\int \frac {\log ^2(2-x)}{x^2} \, dx\\ &=\frac {(2-x) \log ^2(2-x)}{2 x}+\frac {2304 e^{-10-2 x}}{x \log ^2(x)}+2 \operatorname {Subst}\left (\int \frac {\log (x)}{(2-x) x} \, dx,x,2-x\right )+3 \int \left (3+\frac {2}{-2+x}\right ) \, dx-96 \int \frac {e^{-5-x} (3 x+\log (2-x))}{x^2 \log ^2(x)} \, dx-96 \int \frac {e^{-5-x} \left (-x-6 x^2+3 x^3-2 \log (2-x)-x \log (2-x)+x^2 \log (2-x)\right )}{(-2+x) x^2 \log (x)} \, dx+\int \frac {\log (2-x)}{x} \, dx\\ &=9 x+6 \log (2-x)+\frac {(2-x) \log ^2(2-x)}{2 x}+\frac {2304 e^{-10-2 x}}{x \log ^2(x)}+\log (2) \log (x)-96 \int \left (\frac {3 e^{-5-x}}{x \log ^2(x)}+\frac {e^{-5-x} \log (2-x)}{x^2 \log ^2(x)}\right ) \, dx-96 \int \left (\frac {e^{-5-x} \left (x+6 x^2-3 x^3+2 \log (2-x)+x \log (2-x)-x^2 \log (2-x)\right )}{2 x^2 \log (x)}+\frac {e^{-5-x} \left (x+6 x^2-3 x^3+2 \log (2-x)+x \log (2-x)-x^2 \log (2-x)\right )}{4 x \log (x)}+\frac {e^{-5-x} \left (-x-6 x^2+3 x^3-2 \log (2-x)-x \log (2-x)+x^2 \log (2-x)\right )}{4 (-2+x) \log (x)}\right ) \, dx+\int \frac {\log \left (1-\frac {x}{2}\right )}{x} \, dx+\operatorname {Subst}\left (\int \frac {\log (x)}{2-x} \, dx,x,2-x\right )+\operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,2-x\right )\\ &=9 x+6 \log (2-x)+\frac {1}{2} \log ^2(2-x)+\frac {(2-x) \log ^2(2-x)}{2 x}+\frac {2304 e^{-10-2 x}}{x \log ^2(x)}-\text {Li}_2\left (\frac {x}{2}\right )-24 \int \frac {e^{-5-x} \left (x+6 x^2-3 x^3+2 \log (2-x)+x \log (2-x)-x^2 \log (2-x)\right )}{x \log (x)} \, dx-24 \int \frac {e^{-5-x} \left (-x-6 x^2+3 x^3-2 \log (2-x)-x \log (2-x)+x^2 \log (2-x)\right )}{(-2+x) \log (x)} \, dx-48 \int \frac {e^{-5-x} \left (x+6 x^2-3 x^3+2 \log (2-x)+x \log (2-x)-x^2 \log (2-x)\right )}{x^2 \log (x)} \, dx-96 \int \frac {e^{-5-x} \log (2-x)}{x^2 \log ^2(x)} \, dx-288 \int \frac {e^{-5-x}}{x \log ^2(x)} \, dx+\operatorname {Subst}\left (\int \frac {\log \left (\frac {x}{2}\right )}{2-x} \, dx,x,2-x\right )\\ &=9 x+6 \log (2-x)+\frac {1}{2} \log ^2(2-x)+\frac {(2-x) \log ^2(2-x)}{2 x}+\frac {2304 e^{-10-2 x}}{x \log ^2(x)}-24 \int \left (-\frac {e^{-5-x} x}{(-2+x) \log (x)}-\frac {6 e^{-5-x} x^2}{(-2+x) \log (x)}+\frac {3 e^{-5-x} x^3}{(-2+x) \log (x)}-\frac {2 e^{-5-x} \log (2-x)}{(-2+x) \log (x)}-\frac {e^{-5-x} x \log (2-x)}{(-2+x) \log (x)}+\frac {e^{-5-x} x^2 \log (2-x)}{(-2+x) \log (x)}\right ) \, dx-24 \int \frac {e^{-5-x} \left (x+6 x^2-3 x^3+\left (2+x-x^2\right ) \log (2-x)\right )}{x \log (x)} \, dx-48 \int \frac {e^{-5-x} \left (x+6 x^2-3 x^3+\left (2+x-x^2\right ) \log (2-x)\right )}{x^2 \log (x)} \, dx-96 \int \frac {e^{-5-x} \log (2-x)}{x^2 \log ^2(x)} \, dx-288 \int \frac {e^{-5-x}}{x \log ^2(x)} \, dx\\ &=9 x+6 \log (2-x)+\frac {1}{2} \log ^2(2-x)+\frac {(2-x) \log ^2(2-x)}{2 x}+\frac {2304 e^{-10-2 x}}{x \log ^2(x)}-24 \int \left (\frac {e^{-5-x}}{\log (x)}+\frac {6 e^{-5-x} x}{\log (x)}-\frac {3 e^{-5-x} x^2}{\log (x)}+\frac {e^{-5-x} \log (2-x)}{\log (x)}+\frac {2 e^{-5-x} \log (2-x)}{x \log (x)}-\frac {e^{-5-x} x \log (2-x)}{\log (x)}\right ) \, dx+24 \int \frac {e^{-5-x} x}{(-2+x) \log (x)} \, dx+24 \int \frac {e^{-5-x} x \log (2-x)}{(-2+x) \log (x)} \, dx-24 \int \frac {e^{-5-x} x^2 \log (2-x)}{(-2+x) \log (x)} \, dx-48 \int \left (\frac {6 e^{-5-x}}{\log (x)}+\frac {e^{-5-x}}{x \log (x)}-\frac {3 e^{-5-x} x}{\log (x)}-\frac {e^{-5-x} \log (2-x)}{\log (x)}+\frac {2 e^{-5-x} \log (2-x)}{x^2 \log (x)}+\frac {e^{-5-x} \log (2-x)}{x \log (x)}\right ) \, dx+48 \int \frac {e^{-5-x} \log (2-x)}{(-2+x) \log (x)} \, dx-72 \int \frac {e^{-5-x} x^3}{(-2+x) \log (x)} \, dx-96 \int \frac {e^{-5-x} \log (2-x)}{x^2 \log ^2(x)} \, dx+144 \int \frac {e^{-5-x} x^2}{(-2+x) \log (x)} \, dx-288 \int \frac {e^{-5-x}}{x \log ^2(x)} \, dx\\ &=9 x+6 \log (2-x)+\frac {1}{2} \log ^2(2-x)+\frac {(2-x) \log ^2(2-x)}{2 x}+\frac {2304 e^{-10-2 x}}{x \log ^2(x)}+24 \int \left (\frac {e^{-5-x}}{\log (x)}+\frac {2 e^{-5-x}}{(-2+x) \log (x)}\right ) \, dx+24 \int \left (\frac {e^{-5-x} \log (2-x)}{\log (x)}+\frac {2 e^{-5-x} \log (2-x)}{(-2+x) \log (x)}\right ) \, dx-24 \int \left (\frac {2 e^{-5-x} \log (2-x)}{\log (x)}+\frac {4 e^{-5-x} \log (2-x)}{(-2+x) \log (x)}+\frac {e^{-5-x} x \log (2-x)}{\log (x)}\right ) \, dx-24 \int \frac {e^{-5-x}}{\log (x)} \, dx-24 \int \frac {e^{-5-x} \log (2-x)}{\log (x)} \, dx+24 \int \frac {e^{-5-x} x \log (2-x)}{\log (x)} \, dx-48 \int \frac {e^{-5-x}}{x \log (x)} \, dx+48 \int \frac {e^{-5-x} \log (2-x)}{\log (x)} \, dx+48 \int \frac {e^{-5-x} \log (2-x)}{(-2+x) \log (x)} \, dx-2 \left (48 \int \frac {e^{-5-x} \log (2-x)}{x \log (x)} \, dx\right )-72 \int \left (\frac {4 e^{-5-x}}{\log (x)}+\frac {8 e^{-5-x}}{(-2+x) \log (x)}+\frac {2 e^{-5-x} x}{\log (x)}+\frac {e^{-5-x} x^2}{\log (x)}\right ) \, dx+72 \int \frac {e^{-5-x} x^2}{\log (x)} \, dx-96 \int \frac {e^{-5-x} \log (2-x)}{x^2 \log ^2(x)} \, dx-96 \int \frac {e^{-5-x} \log (2-x)}{x^2 \log (x)} \, dx+144 \int \left (\frac {2 e^{-5-x}}{\log (x)}+\frac {4 e^{-5-x}}{(-2+x) \log (x)}+\frac {e^{-5-x} x}{\log (x)}\right ) \, dx-288 \int \frac {e^{-5-x}}{x \log ^2(x)} \, dx-288 \int \frac {e^{-5-x}}{\log (x)} \, dx\\ &=9 x+6 \log (2-x)+\frac {1}{2} \log ^2(2-x)+\frac {(2-x) \log ^2(2-x)}{2 x}+\frac {2304 e^{-10-2 x}}{x \log ^2(x)}+48 \int \frac {e^{-5-x}}{(-2+x) \log (x)} \, dx-48 \int \frac {e^{-5-x}}{x \log (x)} \, dx+2 \left (48 \int \frac {e^{-5-x} \log (2-x)}{(-2+x) \log (x)} \, dx\right )-2 \left (48 \int \frac {e^{-5-x} \log (2-x)}{x \log (x)} \, dx\right )-96 \int \frac {e^{-5-x} \log (2-x)}{x^2 \log ^2(x)} \, dx-96 \int \frac {e^{-5-x} \log (2-x)}{(-2+x) \log (x)} \, dx-96 \int \frac {e^{-5-x} \log (2-x)}{x^2 \log (x)} \, dx-288 \int \frac {e^{-5-x}}{x \log ^2(x)} \, dx-288 \int \frac {e^{-5-x}}{\log (x)} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [C]  time = 0.31, size = 116, normalized size = 3.87 \begin {gather*} 9 x+6 \log (2-x)-\log (2) \log (2-x)+\frac {\log ^2(2-x)}{x}+\frac {2304 e^{-2 (5+x)}}{x \log ^2(x)}+\frac {288 e^{-5-x}}{\log (x)}+\frac {96 e^{-5-x} \log (2-x)}{x \log (x)}-\log (2) \log (x)+\log (2-x) \log (x)+\text {Li}_2\left (1-\frac {x}{2}\right )+\text {Li}_2\left (\frac {x}{2}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(-10 - 2*x)*(9216 - 4608*x + (4608 + 6912*x - 4608*x^2 + E^(5 + x)*(576*x - 288*x^2) + E^(5 + x)*
(192 - 96*x)*Log[2 - x])*Log[x] + (E^(5 + x)*(96*x + 576*x^2 - 288*x^3) + E^(5 + x)*(192 + 96*x - 96*x^2)*Log[
2 - x])*Log[x]^2 + (E^(10 + 2*x)*(-12*x^2 + 9*x^3) + 2*E^(10 + 2*x)*x*Log[2 - x] + E^(10 + 2*x)*(2 - x)*Log[2
- x]^2)*Log[x]^3))/((-2*x^2 + x^3)*Log[x]^3),x]

[Out]

9*x + 6*Log[2 - x] - Log[2]*Log[2 - x] + Log[2 - x]^2/x + 2304/(E^(2*(5 + x))*x*Log[x]^2) + (288*E^(-5 - x))/L
og[x] + (96*E^(-5 - x)*Log[2 - x])/(x*Log[x]) - Log[2]*Log[x] + Log[2 - x]*Log[x] + PolyLog[2, 1 - x/2] + Poly
Log[2, x/2]

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fricas [B]  time = 0.64, size = 86, normalized size = 2.87 \begin {gather*} \frac {{\left ({\left (9 \, x^{2} e^{\left (2 \, x + 10\right )} + 6 \, x e^{\left (2 \, x + 10\right )} \log \left (-x + 2\right ) + e^{\left (2 \, x + 10\right )} \log \left (-x + 2\right )^{2}\right )} \log \relax (x)^{2} + 96 \, {\left (3 \, x e^{\left (x + 5\right )} + e^{\left (x + 5\right )} \log \left (-x + 2\right )\right )} \log \relax (x) + 2304\right )} e^{\left (-2 \, x - 10\right )}}{x \log \relax (x)^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2-x)*exp(5+x)^2*log(2-x)^2+2*x*exp(5+x)^2*log(2-x)+(9*x^3-12*x^2)*exp(5+x)^2)*log(x)^3+((-96*x^2+
96*x+192)*exp(5+x)*log(2-x)+(-288*x^3+576*x^2+96*x)*exp(5+x))*log(x)^2+((-96*x+192)*exp(5+x)*log(2-x)+(-288*x^
2+576*x)*exp(5+x)-4608*x^2+6912*x+4608)*log(x)-4608*x+9216)/(x^3-2*x^2)/exp(5+x)^2/log(x)^3,x, algorithm="fric
as")

[Out]

((9*x^2*e^(2*x + 10) + 6*x*e^(2*x + 10)*log(-x + 2) + e^(2*x + 10)*log(-x + 2)^2)*log(x)^2 + 96*(3*x*e^(x + 5)
+ e^(x + 5)*log(-x + 2))*log(x) + 2304)*e^(-2*x - 10)/(x*log(x)^2)

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giac [B]  time = 0.17, size = 85, normalized size = 2.83 \begin {gather*} \frac {{\left (9 \, x^{2} e^{15} \log \relax (x)^{2} + 6 \, x e^{15} \log \left (x - 2\right ) \log \relax (x)^{2} + e^{15} \log \relax (x)^{2} \log \left (-x + 2\right )^{2} + 288 \, x e^{\left (-x + 10\right )} \log \relax (x) + 96 \, e^{\left (-x + 10\right )} \log \relax (x) \log \left (-x + 2\right ) + 2304 \, e^{\left (-2 \, x + 5\right )}\right )} e^{\left (-15\right )}}{x \log \relax (x)^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2-x)*exp(5+x)^2*log(2-x)^2+2*x*exp(5+x)^2*log(2-x)+(9*x^3-12*x^2)*exp(5+x)^2)*log(x)^3+((-96*x^2+
96*x+192)*exp(5+x)*log(2-x)+(-288*x^3+576*x^2+96*x)*exp(5+x))*log(x)^2+((-96*x+192)*exp(5+x)*log(2-x)+(-288*x^
2+576*x)*exp(5+x)-4608*x^2+6912*x+4608)*log(x)-4608*x+9216)/(x^3-2*x^2)/exp(5+x)^2/log(x)^3,x, algorithm="giac
")

[Out]

(9*x^2*e^15*log(x)^2 + 6*x*e^15*log(x - 2)*log(x)^2 + e^15*log(x)^2*log(-x + 2)^2 + 288*x*e^(-x + 10)*log(x) +
96*e^(-x + 10)*log(x)*log(-x + 2) + 2304*e^(-2*x + 5))*e^(-15)/(x*log(x)^2)

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maple [B]  time = 0.38, size = 93, normalized size = 3.10

method	result	size
risch	\(\frac {\ln \left (2-x \right )^{2}}{x}+\frac {96 \,{\mathrm e}^{-x -5} \ln \left (2-x \right )}{x \ln \relax (x )}+\frac {3 \left (2 \ln \left (x -2\right ) x \,{\mathrm e}^{2 x +10} \ln \relax (x )^{2}+3 \ln \relax (x )^{2} x^{2} {\mathrm e}^{2 x +10}+96 \ln \relax (x ) {\mathrm e}^{5+x} x +768\right ) {\mathrm e}^{-2 x -10}}{x \ln \relax (x )^{2}}\)	\(93\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((2-x)*exp(5+x)^2*ln(2-x)^2+2*x*exp(5+x)^2*ln(2-x)+(9*x^3-12*x^2)*exp(5+x)^2)*ln(x)^3+((-96*x^2+96*x+192)
*exp(5+x)*ln(2-x)+(-288*x^3+576*x^2+96*x)*exp(5+x))*ln(x)^2+((-96*x+192)*exp(5+x)*ln(2-x)+(-288*x^2+576*x)*exp
(5+x)-4608*x^2+6912*x+4608)*ln(x)-4608*x+9216)/(x^3-2*x^2)/exp(5+x)^2/ln(x)^3,x,method=_RETURNVERBOSE)

[Out]

1/x*ln(2-x)^2+96/x*exp(-x-5)/ln(x)*ln(2-x)+3*(2*ln(x-2)*x*exp(2*x+10)*ln(x)^2+3*ln(x)^2*x^2*exp(2*x+10)+96*ln(
x)*exp(5+x)*x+768)/x*exp(-2*x-10)/ln(x)^2

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maxima [B]  time = 0.43, size = 81, normalized size = 2.70 \begin {gather*} \frac {{\left (9 \, x^{2} e^{10} \log \relax (x)^{2} + e^{10} \log \relax (x)^{2} \log \left (-x + 2\right )^{2} + 288 \, x e^{\left (-x + 5\right )} \log \relax (x) + 6 \, {\left (x e^{10} \log \relax (x)^{2} + 16 \, e^{\left (-x + 5\right )} \log \relax (x)\right )} \log \left (-x + 2\right ) + 2304 \, e^{\left (-2 \, x\right )}\right )} e^{\left (-10\right )}}{x \log \relax (x)^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2-x)*exp(5+x)^2*log(2-x)^2+2*x*exp(5+x)^2*log(2-x)+(9*x^3-12*x^2)*exp(5+x)^2)*log(x)^3+((-96*x^2+
96*x+192)*exp(5+x)*log(2-x)+(-288*x^3+576*x^2+96*x)*exp(5+x))*log(x)^2+((-96*x+192)*exp(5+x)*log(2-x)+(-288*x^
2+576*x)*exp(5+x)-4608*x^2+6912*x+4608)*log(x)-4608*x+9216)/(x^3-2*x^2)/exp(5+x)^2/log(x)^3,x, algorithm="maxi
ma")

[Out]

(9*x^2*e^10*log(x)^2 + e^10*log(x)^2*log(-x + 2)^2 + 288*x*e^(-x + 5)*log(x) + 6*(x*e^10*log(x)^2 + 16*e^(-x +
5)*log(x))*log(-x + 2) + 2304*e^(-2*x))*e^(-10)/(x*log(x)^2)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {{\mathrm {e}}^{-2\,x-10}\,\left (\left (-{\mathrm {e}}^{2\,x+10}\,\left (x-2\right )\,{\ln \left (2-x\right )}^2+2\,x\,{\mathrm {e}}^{2\,x+10}\,\ln \left (2-x\right )-{\mathrm {e}}^{2\,x+10}\,\left (12\,x^2-9\,x^3\right )\right )\,{\ln \relax (x)}^3+\left ({\mathrm {e}}^{x+5}\,\left (-288\,x^3+576\,x^2+96\,x\right )+{\mathrm {e}}^{x+5}\,\ln \left (2-x\right )\,\left (-96\,x^2+96\,x+192\right )\right )\,{\ln \relax (x)}^2+\left (6912\,x+{\mathrm {e}}^{x+5}\,\left (576\,x-288\,x^2\right )-4608\,x^2-{\mathrm {e}}^{x+5}\,\ln \left (2-x\right )\,\left (96\,x-192\right )+4608\right )\,\ln \relax (x)-4608\,x+9216\right )}{{\ln \relax (x)}^3\,\left (2\,x^2-x^3\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(- 2*x - 10)*(log(x)*(6912*x + exp(x + 5)*(576*x - 288*x^2) - 4608*x^2 - exp(x + 5)*log(2 - x)*(96*x
- 192) + 4608) - 4608*x - log(x)^3*(exp(2*x + 10)*(12*x^2 - 9*x^3) - 2*x*exp(2*x + 10)*log(2 - x) + exp(2*x +
10)*log(2 - x)^2*(x - 2)) + log(x)^2*(exp(x + 5)*(96*x + 576*x^2 - 288*x^3) + exp(x + 5)*log(2 - x)*(96*x - 96
*x^2 + 192)) + 9216))/(log(x)^3*(2*x^2 - x^3)),x)

[Out]

int(-(exp(- 2*x - 10)*(log(x)*(6912*x + exp(x + 5)*(576*x - 288*x^2) - 4608*x^2 - exp(x + 5)*log(2 - x)*(96*x
- 192) + 4608) - 4608*x - log(x)^3*(exp(2*x + 10)*(12*x^2 - 9*x^3) - 2*x*exp(2*x + 10)*log(2 - x) + exp(2*x +
10)*log(2 - x)^2*(x - 2)) + log(x)^2*(exp(x + 5)*(96*x + 576*x^2 - 288*x^3) + exp(x + 5)*log(2 - x)*(96*x - 96
*x^2 + 192)) + 9216))/(log(x)^3*(2*x^2 - x^3)), x)

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sympy [B]  time = 0.71, size = 71, normalized size = 2.37 \begin {gather*} 9 x + 6 \log {\left (x - 2 \right )} + \frac {\log {\left (2 - x \right )}^{2}}{x} + \frac {2304 x e^{- 2 x - 10} \log {\relax (x )} + \left (288 x^{2} \log {\relax (x )}^{2} + 96 x \log {\relax (x )}^{2} \log {\left (2 - x \right )}\right ) e^{- x - 5}}{x^{2} \log {\relax (x )}^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2-x)*exp(5+x)**2*ln(2-x)**2+2*x*exp(5+x)**2*ln(2-x)+(9*x**3-12*x**2)*exp(5+x)**2)*ln(x)**3+((-96*
x**2+96*x+192)*exp(5+x)*ln(2-x)+(-288*x**3+576*x**2+96*x)*exp(5+x))*ln(x)**2+((-96*x+192)*exp(5+x)*ln(2-x)+(-2
88*x**2+576*x)*exp(5+x)-4608*x**2+6912*x+4608)*ln(x)-4608*x+9216)/(x**3-2*x**2)/exp(5+x)**2/ln(x)**3,x)

[Out]

9*x + 6*log(x - 2) + log(2 - x)**2/x + (2304*x*exp(-2*x - 10)*log(x) + (288*x**2*log(x)**2 + 96*x*log(x)**2*lo
g(2 - x))*exp(-x - 5))/(x**2*log(x)**3)

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