3.52.9 \(\int \frac {-512-448 x-226 x^2-56 x^3-8 x^4+e^x (160-218 x-202 x^2-142 x^3-40 x^4-8 x^5+(-32-14 x-4 x^2) \log (2))+e^{2 x} (90 x+30 x^2+20 x^3+(-18 x-6 x^2-4 x^3) \log (2))+(160+294 x+246 x^2+84 x^3+16 x^4+(-32-14 x-4 x^2) \log (2)+e^x (20 x-10 x^2+20 x^3+(-4 x+2 x^2-4 x^3) \log (2))) \log (x)+(-70 x-40 x^2+(14 x+8 x^2) \log (2)) \log ^2(x)}{e^{3 x} x+3 e^{2 x} x \log (x)+3 e^x x \log ^2(x)+x \log ^3(x)} \, dx\)

Optimal. Leaf size=30 \[ \left (-5+\log (2)-\frac {x-x^2-(4+x)^2}{e^x+\log (x)}\right )^2 \]

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Rubi [F]  time = 6.25, 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 {-512-448 x-226 x^2-56 x^3-8 x^4+e^x \left (160-218 x-202 x^2-142 x^3-40 x^4-8 x^5+\left (-32-14 x-4 x^2\right ) \log (2)\right )+e^{2 x} \left (90 x+30 x^2+20 x^3+\left (-18 x-6 x^2-4 x^3\right ) \log (2)\right )+\left (160+294 x+246 x^2+84 x^3+16 x^4+\left (-32-14 x-4 x^2\right ) \log (2)+e^x \left (20 x-10 x^2+20 x^3+\left (-4 x+2 x^2-4 x^3\right ) \log (2)\right )\right ) \log (x)+\left (-70 x-40 x^2+\left (14 x+8 x^2\right ) \log (2)\right ) \log ^2(x)}{e^{3 x} x+3 e^{2 x} x \log (x)+3 e^x x \log ^2(x)+x \log ^3(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-512 - 448*x - 226*x^2 - 56*x^3 - 8*x^4 + E^x*(160 - 218*x - 202*x^2 - 142*x^3 - 40*x^4 - 8*x^5 + (-32 -
14*x - 4*x^2)*Log[2]) + E^(2*x)*(90*x + 30*x^2 + 20*x^3 + (-18*x - 6*x^2 - 4*x^3)*Log[2]) + (160 + 294*x + 246
*x^2 + 84*x^3 + 16*x^4 + (-32 - 14*x - 4*x^2)*Log[2] + E^x*(20*x - 10*x^2 + 20*x^3 + (-4*x + 2*x^2 - 4*x^3)*Lo
g[2]))*Log[x] + (-70*x - 40*x^2 + (14*x + 8*x^2)*Log[2])*Log[x]^2)/(E^(3*x)*x + 3*E^(2*x)*x*Log[x] + 3*E^x*x*L
og[x]^2 + x*Log[x]^3),x]

[Out]

-448*Defer[Int][(E^x + Log[x])^(-3), x] - 512*Defer[Int][1/(x*(E^x + Log[x])^3), x] - 226*Defer[Int][x/(E^x +
Log[x])^3, x] - 56*Defer[Int][x^2/(E^x + Log[x])^3, x] - 8*Defer[Int][x^3/(E^x + Log[x])^3, x] + 512*Defer[Int
][Log[x]/(E^x + Log[x])^3, x] + 448*Defer[Int][(x*Log[x])/(E^x + Log[x])^3, x] + 226*Defer[Int][(x^2*Log[x])/(
E^x + Log[x])^3, x] + 56*Defer[Int][(x^3*Log[x])/(E^x + Log[x])^3, x] + 8*Defer[Int][(x^4*Log[x])/(E^x + Log[x
])^3, x] - 288*Defer[Int][(E^x + Log[x])^(-2), x] + 14*(5 - Log[2])*Defer[Int][(E^x + Log[x])^(-2), x] + 32*(5
- Log[2])*Defer[Int][1/(x*(E^x + Log[x])^2), x] - 222*Defer[Int][x/(E^x + Log[x])^2, x] + 4*(5 - Log[2])*Defe
r[Int][x/(E^x + Log[x])^2, x] - 142*Defer[Int][x^2/(E^x + Log[x])^2, x] - 40*Defer[Int][x^3/(E^x + Log[x])^2,
x] - 8*Defer[Int][x^4/(E^x + Log[x])^2, x] - 32*(5 - Log[2])*Defer[Int][Log[x]/(E^x + Log[x])^2, x] - 14*(5 -
Log[2])*Defer[Int][(x*Log[x])/(E^x + Log[x])^2, x] - 4*(5 - Log[2])*Defer[Int][(x^2*Log[x])/(E^x + Log[x])^2,
x] + 18*(5 - Log[2])*Defer[Int][(E^x + Log[x])^(-1), x] + 6*(5 - Log[2])*Defer[Int][x/(E^x + Log[x]), x] + 4*(
5 - Log[2])*Defer[Int][x^2/(E^x + Log[x]), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 \left (16+\left (7+9 e^x\right ) x+\left (2+3 e^x\right ) x^2+2 e^x x^3-x (7+4 x) \log (x)\right ) \left (-16-7 x-2 x^2-e^x (-5+\log (2))-(-5+\log (2)) \log (x)\right )}{x \left (e^x+\log (x)\right )^3} \, dx\\ &=2 \int \frac {\left (16+\left (7+9 e^x\right ) x+\left (2+3 e^x\right ) x^2+2 e^x x^3-x (7+4 x) \log (x)\right ) \left (-16-7 x-2 x^2-e^x (-5+\log (2))-(-5+\log (2)) \log (x)\right )}{x \left (e^x+\log (x)\right )^3} \, dx\\ &=2 \int \left (-\frac {\left (9+3 x+2 x^2\right ) (-5+\log (2))}{e^x+\log (x)}+\frac {\left (16+7 x+2 x^2\right )^2 (-1+x \log (x))}{x \left (e^x+\log (x)\right )^3}+\frac {\left (16+7 x+2 x^2\right ) \left (-9 x-3 x^2-2 x^3+5 \left (1-\frac {\log (2)}{5}\right )-5 x \left (1-\frac {\log (2)}{5}\right ) \log (x)\right )}{x \left (e^x+\log (x)\right )^2}\right ) \, dx\\ &=2 \int \frac {\left (16+7 x+2 x^2\right )^2 (-1+x \log (x))}{x \left (e^x+\log (x)\right )^3} \, dx+2 \int \frac {\left (16+7 x+2 x^2\right ) \left (-9 x-3 x^2-2 x^3+5 \left (1-\frac {\log (2)}{5}\right )-5 x \left (1-\frac {\log (2)}{5}\right ) \log (x)\right )}{x \left (e^x+\log (x)\right )^2} \, dx+(2 (5-\log (2))) \int \frac {9+3 x+2 x^2}{e^x+\log (x)} \, dx\\ &=2 \int \left (\frac {224 (-1+x \log (x))}{\left (e^x+\log (x)\right )^3}+\frac {256 (-1+x \log (x))}{x \left (e^x+\log (x)\right )^3}+\frac {113 x (-1+x \log (x))}{\left (e^x+\log (x)\right )^3}+\frac {28 x^2 (-1+x \log (x))}{\left (e^x+\log (x)\right )^3}+\frac {4 x^3 (-1+x \log (x))}{\left (e^x+\log (x)\right )^3}\right ) \, dx+2 \int \left (\frac {7 \left (-9 x-3 x^2-2 x^3+5 \left (1-\frac {\log (2)}{5}\right )-5 x \left (1-\frac {\log (2)}{5}\right ) \log (x)\right )}{\left (e^x+\log (x)\right )^2}+\frac {16 \left (-9 x-3 x^2-2 x^3+5 \left (1-\frac {\log (2)}{5}\right )-5 x \left (1-\frac {\log (2)}{5}\right ) \log (x)\right )}{x \left (e^x+\log (x)\right )^2}+\frac {2 x \left (-9 x-3 x^2-2 x^3+5 \left (1-\frac {\log (2)}{5}\right )-5 x \left (1-\frac {\log (2)}{5}\right ) \log (x)\right )}{\left (e^x+\log (x)\right )^2}\right ) \, dx+(2 (5-\log (2))) \int \left (\frac {9}{e^x+\log (x)}+\frac {3 x}{e^x+\log (x)}+\frac {2 x^2}{e^x+\log (x)}\right ) \, dx\\ &=4 \int \frac {x \left (-9 x-3 x^2-2 x^3+5 \left (1-\frac {\log (2)}{5}\right )-5 x \left (1-\frac {\log (2)}{5}\right ) \log (x)\right )}{\left (e^x+\log (x)\right )^2} \, dx+8 \int \frac {x^3 (-1+x \log (x))}{\left (e^x+\log (x)\right )^3} \, dx+14 \int \frac {-9 x-3 x^2-2 x^3+5 \left (1-\frac {\log (2)}{5}\right )-5 x \left (1-\frac {\log (2)}{5}\right ) \log (x)}{\left (e^x+\log (x)\right )^2} \, dx+32 \int \frac {-9 x-3 x^2-2 x^3+5 \left (1-\frac {\log (2)}{5}\right )-5 x \left (1-\frac {\log (2)}{5}\right ) \log (x)}{x \left (e^x+\log (x)\right )^2} \, dx+56 \int \frac {x^2 (-1+x \log (x))}{\left (e^x+\log (x)\right )^3} \, dx+226 \int \frac {x (-1+x \log (x))}{\left (e^x+\log (x)\right )^3} \, dx+448 \int \frac {-1+x \log (x)}{\left (e^x+\log (x)\right )^3} \, dx+512 \int \frac {-1+x \log (x)}{x \left (e^x+\log (x)\right )^3} \, dx+(4 (5-\log (2))) \int \frac {x^2}{e^x+\log (x)} \, dx+(6 (5-\log (2))) \int \frac {x}{e^x+\log (x)} \, dx+(18 (5-\log (2))) \int \frac {1}{e^x+\log (x)} \, dx\\ &=4 \int \left (-\frac {9 x^2}{\left (e^x+\log (x)\right )^2}-\frac {3 x^3}{\left (e^x+\log (x)\right )^2}-\frac {2 x^4}{\left (e^x+\log (x)\right )^2}-\frac {x (-5+\log (2))}{\left (e^x+\log (x)\right )^2}+\frac {x^2 (-5+\log (2)) \log (x)}{\left (e^x+\log (x)\right )^2}\right ) \, dx+8 \int \left (-\frac {x^3}{\left (e^x+\log (x)\right )^3}+\frac {x^4 \log (x)}{\left (e^x+\log (x)\right )^3}\right ) \, dx+14 \int \left (-\frac {9 x}{\left (e^x+\log (x)\right )^2}-\frac {3 x^2}{\left (e^x+\log (x)\right )^2}-\frac {2 x^3}{\left (e^x+\log (x)\right )^2}-\frac {-5+\log (2)}{\left (e^x+\log (x)\right )^2}+\frac {x (-5+\log (2)) \log (x)}{\left (e^x+\log (x)\right )^2}\right ) \, dx+32 \int \left (-\frac {9}{\left (e^x+\log (x)\right )^2}-\frac {3 x}{\left (e^x+\log (x)\right )^2}-\frac {2 x^2}{\left (e^x+\log (x)\right )^2}-\frac {-5+\log (2)}{x \left (e^x+\log (x)\right )^2}+\frac {(-5+\log (2)) \log (x)}{\left (e^x+\log (x)\right )^2}\right ) \, dx+56 \int \left (-\frac {x^2}{\left (e^x+\log (x)\right )^3}+\frac {x^3 \log (x)}{\left (e^x+\log (x)\right )^3}\right ) \, dx+226 \int \left (-\frac {x}{\left (e^x+\log (x)\right )^3}+\frac {x^2 \log (x)}{\left (e^x+\log (x)\right )^3}\right ) \, dx+448 \int \left (-\frac {1}{\left (e^x+\log (x)\right )^3}+\frac {x \log (x)}{\left (e^x+\log (x)\right )^3}\right ) \, dx+512 \int \left (-\frac {1}{x \left (e^x+\log (x)\right )^3}+\frac {\log (x)}{\left (e^x+\log (x)\right )^3}\right ) \, dx+(4 (5-\log (2))) \int \frac {x^2}{e^x+\log (x)} \, dx+(6 (5-\log (2))) \int \frac {x}{e^x+\log (x)} \, dx+(18 (5-\log (2))) \int \frac {1}{e^x+\log (x)} \, dx\\ &=-\left (8 \int \frac {x^3}{\left (e^x+\log (x)\right )^3} \, dx\right )+8 \int \frac {x^4 \log (x)}{\left (e^x+\log (x)\right )^3} \, dx-8 \int \frac {x^4}{\left (e^x+\log (x)\right )^2} \, dx-12 \int \frac {x^3}{\left (e^x+\log (x)\right )^2} \, dx-28 \int \frac {x^3}{\left (e^x+\log (x)\right )^2} \, dx-36 \int \frac {x^2}{\left (e^x+\log (x)\right )^2} \, dx-42 \int \frac {x^2}{\left (e^x+\log (x)\right )^2} \, dx-56 \int \frac {x^2}{\left (e^x+\log (x)\right )^3} \, dx+56 \int \frac {x^3 \log (x)}{\left (e^x+\log (x)\right )^3} \, dx-64 \int \frac {x^2}{\left (e^x+\log (x)\right )^2} \, dx-96 \int \frac {x}{\left (e^x+\log (x)\right )^2} \, dx-126 \int \frac {x}{\left (e^x+\log (x)\right )^2} \, dx-226 \int \frac {x}{\left (e^x+\log (x)\right )^3} \, dx+226 \int \frac {x^2 \log (x)}{\left (e^x+\log (x)\right )^3} \, dx-288 \int \frac {1}{\left (e^x+\log (x)\right )^2} \, dx-448 \int \frac {1}{\left (e^x+\log (x)\right )^3} \, dx+448 \int \frac {x \log (x)}{\left (e^x+\log (x)\right )^3} \, dx-512 \int \frac {1}{x \left (e^x+\log (x)\right )^3} \, dx+512 \int \frac {\log (x)}{\left (e^x+\log (x)\right )^3} \, dx+(4 (5-\log (2))) \int \frac {x}{\left (e^x+\log (x)\right )^2} \, dx+(4 (5-\log (2))) \int \frac {x^2}{e^x+\log (x)} \, dx+(6 (5-\log (2))) \int \frac {x}{e^x+\log (x)} \, dx+(14 (5-\log (2))) \int \frac {1}{\left (e^x+\log (x)\right )^2} \, dx-(14 (5-\log (2))) \int \frac {x \log (x)}{\left (e^x+\log (x)\right )^2} \, dx+(18 (5-\log (2))) \int \frac {1}{e^x+\log (x)} \, dx+(32 (5-\log (2))) \int \frac {1}{x \left (e^x+\log (x)\right )^2} \, dx-(32 (5-\log (2))) \int \frac {\log (x)}{\left (e^x+\log (x)\right )^2} \, dx+(4 (-5+\log (2))) \int \frac {x^2 \log (x)}{\left (e^x+\log (x)\right )^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 1.13, size = 44, normalized size = 1.47 \begin {gather*} \frac {\left (16+7 x+2 x^2\right ) \left (16+7 x+2 x^2+e^x (-10+\log (4))+(-10+\log (4)) \log (x)\right )}{\left (e^x+\log (x)\right )^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-512 - 448*x - 226*x^2 - 56*x^3 - 8*x^4 + E^x*(160 - 218*x - 202*x^2 - 142*x^3 - 40*x^4 - 8*x^5 + (
-32 - 14*x - 4*x^2)*Log[2]) + E^(2*x)*(90*x + 30*x^2 + 20*x^3 + (-18*x - 6*x^2 - 4*x^3)*Log[2]) + (160 + 294*x
+ 246*x^2 + 84*x^3 + 16*x^4 + (-32 - 14*x - 4*x^2)*Log[2] + E^x*(20*x - 10*x^2 + 20*x^3 + (-4*x + 2*x^2 - 4*x
^3)*Log[2]))*Log[x] + (-70*x - 40*x^2 + (14*x + 8*x^2)*Log[2])*Log[x]^2)/(E^(3*x)*x + 3*E^(2*x)*x*Log[x] + 3*E
^x*x*Log[x]^2 + x*Log[x]^3),x]

[Out]

((16 + 7*x + 2*x^2)*(16 + 7*x + 2*x^2 + E^x*(-10 + Log[4]) + (-10 + Log[4])*Log[x]))/(E^x + Log[x])^2

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fricas [B]  time = 0.79, size = 94, normalized size = 3.13 \begin {gather*} \frac {4 \, x^{4} + 28 \, x^{3} + 113 \, x^{2} - 2 \, {\left (10 \, x^{2} - {\left (2 \, x^{2} + 7 \, x + 16\right )} \log \relax (2) + 35 \, x + 80\right )} e^{x} - 2 \, {\left (10 \, x^{2} - {\left (2 \, x^{2} + 7 \, x + 16\right )} \log \relax (2) + 35 \, x + 80\right )} \log \relax (x) + 224 \, x + 256}{2 \, e^{x} \log \relax (x) + \log \relax (x)^{2} + e^{\left (2 \, x\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((8*x^2+14*x)*log(2)-40*x^2-70*x)*log(x)^2+(((-4*x^3+2*x^2-4*x)*log(2)+20*x^3-10*x^2+20*x)*exp(x)+(
-4*x^2-14*x-32)*log(2)+16*x^4+84*x^3+246*x^2+294*x+160)*log(x)+((-4*x^3-6*x^2-18*x)*log(2)+20*x^3+30*x^2+90*x)
*exp(x)^2+((-4*x^2-14*x-32)*log(2)-8*x^5-40*x^4-142*x^3-202*x^2-218*x+160)*exp(x)-8*x^4-56*x^3-226*x^2-448*x-5
12)/(x*log(x)^3+3*x*exp(x)*log(x)^2+3*x*exp(x)^2*log(x)+x*exp(x)^3),x, algorithm="fricas")

[Out]

(4*x^4 + 28*x^3 + 113*x^2 - 2*(10*x^2 - (2*x^2 + 7*x + 16)*log(2) + 35*x + 80)*e^x - 2*(10*x^2 - (2*x^2 + 7*x
+ 16)*log(2) + 35*x + 80)*log(x) + 224*x + 256)/(2*e^x*log(x) + log(x)^2 + e^(2*x))

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giac [B]  time = 0.32, size = 114, normalized size = 3.80 \begin {gather*} \frac {4 \, x^{4} + 4 \, x^{2} e^{x} \log \relax (2) + 4 \, x^{2} \log \relax (2) \log \relax (x) + 28 \, x^{3} - 20 \, x^{2} e^{x} + 14 \, x e^{x} \log \relax (2) - 20 \, x^{2} \log \relax (x) + 14 \, x \log \relax (2) \log \relax (x) + 113 \, x^{2} - 70 \, x e^{x} + 32 \, e^{x} \log \relax (2) - 70 \, x \log \relax (x) + 32 \, \log \relax (2) \log \relax (x) + 224 \, x - 160 \, e^{x} - 160 \, \log \relax (x) + 256}{2 \, e^{x} \log \relax (x) + \log \relax (x)^{2} + e^{\left (2 \, x\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((8*x^2+14*x)*log(2)-40*x^2-70*x)*log(x)^2+(((-4*x^3+2*x^2-4*x)*log(2)+20*x^3-10*x^2+20*x)*exp(x)+(
-4*x^2-14*x-32)*log(2)+16*x^4+84*x^3+246*x^2+294*x+160)*log(x)+((-4*x^3-6*x^2-18*x)*log(2)+20*x^3+30*x^2+90*x)
*exp(x)^2+((-4*x^2-14*x-32)*log(2)-8*x^5-40*x^4-142*x^3-202*x^2-218*x+160)*exp(x)-8*x^4-56*x^3-226*x^2-448*x-5
12)/(x*log(x)^3+3*x*exp(x)*log(x)^2+3*x*exp(x)^2*log(x)+x*exp(x)^3),x, algorithm="giac")

[Out]

(4*x^4 + 4*x^2*e^x*log(2) + 4*x^2*log(2)*log(x) + 28*x^3 - 20*x^2*e^x + 14*x*e^x*log(2) - 20*x^2*log(x) + 14*x
*log(2)*log(x) + 113*x^2 - 70*x*e^x + 32*e^x*log(2) - 70*x*log(x) + 32*log(2)*log(x) + 224*x - 160*e^x - 160*l
og(x) + 256)/(2*e^x*log(x) + log(x)^2 + e^(2*x))

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maple [B]  time = 0.07, size = 105, normalized size = 3.50

method	result	size
risch	\(\frac {4 x^{2} \ln \relax (2) {\mathrm e}^{x}+4 x^{2} \ln \relax (2) \ln \relax (x )+4 x^{4}+14 x \ln \relax (2) {\mathrm e}^{x}+14 x \ln \relax (2) \ln \relax (x )+28 x^{3}-20 \,{\mathrm e}^{x} x^{2}-20 x^{2} \ln \relax (x )+32 \,{\mathrm e}^{x} \ln \relax (2)+32 \ln \relax (2) \ln \relax (x )+113 x^{2}-70 \,{\mathrm e}^{x} x -70 x \ln \relax (x )+224 x -160 \,{\mathrm e}^{x}-160 \ln \relax (x )+256}{\left (\ln \relax (x )+{\mathrm e}^{x}\right )^{2}}\)	\(105\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((8*x^2+14*x)*ln(2)-40*x^2-70*x)*ln(x)^2+(((-4*x^3+2*x^2-4*x)*ln(2)+20*x^3-10*x^2+20*x)*exp(x)+(-4*x^2-14
*x-32)*ln(2)+16*x^4+84*x^3+246*x^2+294*x+160)*ln(x)+((-4*x^3-6*x^2-18*x)*ln(2)+20*x^3+30*x^2+90*x)*exp(x)^2+((
-4*x^2-14*x-32)*ln(2)-8*x^5-40*x^4-142*x^3-202*x^2-218*x+160)*exp(x)-8*x^4-56*x^3-226*x^2-448*x-512)/(x*ln(x)^
3+3*x*exp(x)*ln(x)^2+3*x*exp(x)^2*ln(x)+x*exp(x)^3),x,method=_RETURNVERBOSE)

[Out]

(4*x^2*ln(2)*exp(x)+4*x^2*ln(2)*ln(x)+4*x^4+14*x*ln(2)*exp(x)+14*x*ln(2)*ln(x)+28*x^3-20*exp(x)*x^2-20*x^2*ln(
x)+32*exp(x)*ln(2)+32*ln(2)*ln(x)+113*x^2-70*exp(x)*x-70*x*ln(x)+224*x-160*exp(x)-160*ln(x)+256)/(ln(x)+exp(x)
)^2

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maxima [B]  time = 0.50, size = 90, normalized size = 3.00 \begin {gather*} \frac {4 \, x^{4} + 28 \, x^{3} + 113 \, x^{2} + 2 \, {\left (2 \, x^{2} {\left (\log \relax (2) - 5\right )} + 7 \, x {\left (\log \relax (2) - 5\right )} + 16 \, \log \relax (2) - 80\right )} e^{x} + 2 \, {\left (2 \, x^{2} {\left (\log \relax (2) - 5\right )} + 7 \, x {\left (\log \relax (2) - 5\right )} + 16 \, \log \relax (2) - 80\right )} \log \relax (x) + 224 \, x + 256}{2 \, e^{x} \log \relax (x) + \log \relax (x)^{2} + e^{\left (2 \, x\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((8*x^2+14*x)*log(2)-40*x^2-70*x)*log(x)^2+(((-4*x^3+2*x^2-4*x)*log(2)+20*x^3-10*x^2+20*x)*exp(x)+(
-4*x^2-14*x-32)*log(2)+16*x^4+84*x^3+246*x^2+294*x+160)*log(x)+((-4*x^3-6*x^2-18*x)*log(2)+20*x^3+30*x^2+90*x)
*exp(x)^2+((-4*x^2-14*x-32)*log(2)-8*x^5-40*x^4-142*x^3-202*x^2-218*x+160)*exp(x)-8*x^4-56*x^3-226*x^2-448*x-5
12)/(x*log(x)^3+3*x*exp(x)*log(x)^2+3*x*exp(x)^2*log(x)+x*exp(x)^3),x, algorithm="maxima")

[Out]

(4*x^4 + 28*x^3 + 113*x^2 + 2*(2*x^2*(log(2) - 5) + 7*x*(log(2) - 5) + 16*log(2) - 80)*e^x + 2*(2*x^2*(log(2)
- 5) + 7*x*(log(2) - 5) + 16*log(2) - 80)*log(x) + 224*x + 256)/(2*e^x*log(x) + log(x)^2 + e^(2*x))

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {448\,x+{\ln \relax (x)}^2\,\left (70\,x-\ln \relax (2)\,\left (8\,x^2+14\,x\right )+40\,x^2\right )+{\mathrm {e}}^x\,\left (218\,x+\ln \relax (2)\,\left (4\,x^2+14\,x+32\right )+202\,x^2+142\,x^3+40\,x^4+8\,x^5-160\right )-\ln \relax (x)\,\left (294\,x-\ln \relax (2)\,\left (4\,x^2+14\,x+32\right )+{\mathrm {e}}^x\,\left (20\,x-\ln \relax (2)\,\left (4\,x^3-2\,x^2+4\,x\right )-10\,x^2+20\,x^3\right )+246\,x^2+84\,x^3+16\,x^4+160\right )-{\mathrm {e}}^{2\,x}\,\left (90\,x-\ln \relax (2)\,\left (4\,x^3+6\,x^2+18\,x\right )+30\,x^2+20\,x^3\right )+226\,x^2+56\,x^3+8\,x^4+512}{x\,{\ln \relax (x)}^3+3\,x\,{\mathrm {e}}^x\,{\ln \relax (x)}^2+3\,x\,{\mathrm {e}}^{2\,x}\,\ln \relax (x)+x\,{\mathrm {e}}^{3\,x}} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(448*x + log(x)^2*(70*x - log(2)*(14*x + 8*x^2) + 40*x^2) + exp(x)*(218*x + log(2)*(14*x + 4*x^2 + 32) +
202*x^2 + 142*x^3 + 40*x^4 + 8*x^5 - 160) - log(x)*(294*x - log(2)*(14*x + 4*x^2 + 32) + exp(x)*(20*x - log(2)
*(4*x - 2*x^2 + 4*x^3) - 10*x^2 + 20*x^3) + 246*x^2 + 84*x^3 + 16*x^4 + 160) - exp(2*x)*(90*x - log(2)*(18*x +
6*x^2 + 4*x^3) + 30*x^2 + 20*x^3) + 226*x^2 + 56*x^3 + 8*x^4 + 512)/(x*exp(3*x) + x*log(x)^3 + 3*x*exp(2*x)*l
og(x) + 3*x*exp(x)*log(x)^2),x)

[Out]

int(-(448*x + log(x)^2*(70*x - log(2)*(14*x + 8*x^2) + 40*x^2) + exp(x)*(218*x + log(2)*(14*x + 4*x^2 + 32) +
202*x^2 + 142*x^3 + 40*x^4 + 8*x^5 - 160) - log(x)*(294*x - log(2)*(14*x + 4*x^2 + 32) + exp(x)*(20*x - log(2)
*(4*x - 2*x^2 + 4*x^3) - 10*x^2 + 20*x^3) + 246*x^2 + 84*x^3 + 16*x^4 + 160) - exp(2*x)*(90*x - log(2)*(18*x +
6*x^2 + 4*x^3) + 30*x^2 + 20*x^3) + 226*x^2 + 56*x^3 + 8*x^4 + 512)/(x*exp(3*x) + x*log(x)^3 + 3*x*exp(2*x)*l
og(x) + 3*x*exp(x)*log(x)^2), x)

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sympy [B]  time = 0.43, size = 122, normalized size = 4.07 \begin {gather*} \frac {4 x^{4} + 28 x^{3} - 20 x^{2} \log {\relax (x )} + 4 x^{2} \log {\relax (2 )} \log {\relax (x )} + 113 x^{2} - 70 x \log {\relax (x )} + 14 x \log {\relax (2 )} \log {\relax (x )} + 224 x + \left (- 20 x^{2} + 4 x^{2} \log {\relax (2 )} - 70 x + 14 x \log {\relax (2 )} - 160 + 32 \log {\relax (2 )}\right ) e^{x} - 160 \log {\relax (x )} + 32 \log {\relax (2 )} \log {\relax (x )} + 256}{e^{2 x} + 2 e^{x} \log {\relax (x )} + \log {\relax (x )}^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((8*x**2+14*x)*ln(2)-40*x**2-70*x)*ln(x)**2+(((-4*x**3+2*x**2-4*x)*ln(2)+20*x**3-10*x**2+20*x)*exp(
x)+(-4*x**2-14*x-32)*ln(2)+16*x**4+84*x**3+246*x**2+294*x+160)*ln(x)+((-4*x**3-6*x**2-18*x)*ln(2)+20*x**3+30*x
**2+90*x)*exp(x)**2+((-4*x**2-14*x-32)*ln(2)-8*x**5-40*x**4-142*x**3-202*x**2-218*x+160)*exp(x)-8*x**4-56*x**3
-226*x**2-448*x-512)/(x*ln(x)**3+3*x*exp(x)*ln(x)**2+3*x*exp(x)**2*ln(x)+x*exp(x)**3),x)

[Out]

(4*x**4 + 28*x**3 - 20*x**2*log(x) + 4*x**2*log(2)*log(x) + 113*x**2 - 70*x*log(x) + 14*x*log(2)*log(x) + 224*
x + (-20*x**2 + 4*x**2*log(2) - 70*x + 14*x*log(2) - 160 + 32*log(2))*exp(x) - 160*log(x) + 32*log(2)*log(x) +
256)/(exp(2*x) + 2*exp(x)*log(x) + log(x)**2)

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