3.75.3 \(\int \frac {-15-x-16 x^2-60 x^3+12 x^4-128 x^5+64 x^7-256 x^8+(15+10 x+3 x^2+240 x^3+100 x^4+24 x^5+48 x^8) \log (x)+(-5-80 x^3) \log ^2(x)}{9 x^2+6 x^3+x^4+72 x^5+48 x^6+8 x^7+144 x^8+96 x^9+16 x^{10}+(-6 x^2-2 x^3-48 x^5-16 x^6-96 x^8-32 x^9) \log (x)+(x^2+8 x^5+16 x^8) \log ^2(x)} \, dx\)

Optimal. Leaf size=28 \[ \frac {-4+3 x+\frac {5 \log (x)}{x+4 x^4}}{-3-x+\log (x)} \]

________________________________________________________________________________________

Rubi [F]  time = 4.51, 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 {-15-x-16 x^2-60 x^3+12 x^4-128 x^5+64 x^7-256 x^8+\left (15+10 x+3 x^2+240 x^3+100 x^4+24 x^5+48 x^8\right ) \log (x)+\left (-5-80 x^3\right ) \log ^2(x)}{9 x^2+6 x^3+x^4+72 x^5+48 x^6+8 x^7+144 x^8+96 x^9+16 x^{10}+\left (-6 x^2-2 x^3-48 x^5-16 x^6-96 x^8-32 x^9\right ) \log (x)+\left (x^2+8 x^5+16 x^8\right ) \log ^2(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-15 - x - 16*x^2 - 60*x^3 + 12*x^4 - 128*x^5 + 64*x^7 - 256*x^8 + (15 + 10*x + 3*x^2 + 240*x^3 + 100*x^4
+ 24*x^5 + 48*x^8)*Log[x] + (-5 - 80*x^3)*Log[x]^2)/(9*x^2 + 6*x^3 + x^4 + 72*x^5 + 48*x^6 + 8*x^7 + 144*x^8 +
96*x^9 + 16*x^10 + (-6*x^2 - 2*x^3 - 48*x^5 - 16*x^6 - 96*x^8 - 32*x^9)*Log[x] + (x^2 + 8*x^5 + 16*x^8)*Log[x
]^2),x]

[Out]

5/(x*(1 + 4*x^3)) - 7*Defer[Int][(3 + x - Log[x])^(-2), x] - 15*Defer[Int][1/(x^2*(3 + x - Log[x])^2), x] + 14
*Defer[Int][1/(x*(3 + x - Log[x])^2), x] + 3*Defer[Int][x/(3 + x - Log[x])^2, x] - (5*Defer[Int][1/((-1 - (-2)
^(2/3)*x)*(3 + x - Log[x])^2), x])/3 + 10*(-2)^(1/3)*Defer[Int][1/((1 + (-2)^(2/3)*x)*(3 + x - Log[x])^2), x]
- (5*Defer[Int][1/((-1 - 2^(2/3)*x)*(3 + x - Log[x])^2), x])/3 - 10*2^(1/3)*Defer[Int][1/((1 + 2^(2/3)*x)*(3 +
x - Log[x])^2), x] - (10*2^(2/3)*Defer[Int][1/((1 + 2^(2/3)*x)*(3 + x - Log[x])^2), x])/3 - (10*2^(2/3)*Defer
[Int][1/((-(-1)^(1/3) + 2^(2/3)*x)*(3 + x - Log[x])^2), x])/3 - (10*2^(2/3)*Defer[Int][1/(((-1)^(2/3) + 2^(2/3
)*x)*(3 + x - Log[x])^2), x])/3 - 10*(-1)^(2/3)*2^(1/3)*Defer[Int][1/((1 - (-1)^(1/3)*2^(2/3)*x)*(3 + x - Log[
x])^2), x] - (5*Defer[Int][1/((-1 + (-1)^(1/3)*2^(2/3)*x)*(3 + x - Log[x])^2), x])/3 - 3*Defer[Int][(3 + x - L
og[x])^(-1), x] + 15*Defer[Int][1/(x^2*(3 + x - Log[x])), x] - 10*(-2)^(1/3)*Defer[Int][1/((1 + (-2)^(2/3)*x)*
(3 + x - Log[x])), x] + 10*2^(1/3)*Defer[Int][1/((1 + 2^(2/3)*x)*(3 + x - Log[x])), x] + 10*(-1)^(2/3)*2^(1/3)
*Defer[Int][1/((1 - (-1)^(1/3)*2^(2/3)*x)*(3 + x - Log[x])), x] + 180*Defer[Int][x/((1 + 4*x^3)^2*(3 + x - Log
[x])), x] + 60*Defer[Int][x^2/((1 + 4*x^3)^2*(3 + x - Log[x])), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-15-x-16 x^2-60 x^3+12 x^4-128 x^5+64 x^7-256 x^8+\left (15+10 x+3 x^2+240 x^3+100 x^4+24 x^5+48 x^8\right ) \log (x)-\left (5+80 x^3\right ) \log ^2(x)}{x^2 \left (1+4 x^3\right )^2 (3+x-\log (x))^2} \, dx\\ &=\int \left (-\frac {5 \left (1+16 x^3\right )}{x^2 \left (1+4 x^3\right )^2}+\frac {-15+14 x-2 x^2+3 x^3+16 x^4-28 x^5+12 x^6}{x^2 \left (1+4 x^3\right ) (3+x-\log (x))^2}-\frac {3 \left (-5+x^2-80 x^3-20 x^4+8 x^5+16 x^8\right )}{x^2 \left (1+4 x^3\right )^2 (3+x-\log (x))}\right ) \, dx\\ &=-\left (3 \int \frac {-5+x^2-80 x^3-20 x^4+8 x^5+16 x^8}{x^2 \left (1+4 x^3\right )^2 (3+x-\log (x))} \, dx\right )-5 \int \frac {1+16 x^3}{x^2 \left (1+4 x^3\right )^2} \, dx+\int \frac {-15+14 x-2 x^2+3 x^3+16 x^4-28 x^5+12 x^6}{x^2 \left (1+4 x^3\right ) (3+x-\log (x))^2} \, dx\\ &=\frac {5}{x \left (1+4 x^3\right )}-3 \int \left (\frac {1}{3+x-\log (x)}-\frac {5}{x^2 (3+x-\log (x))}-\frac {20 x (3+x)}{\left (1+4 x^3\right )^2 (3+x-\log (x))}+\frac {20 x}{\left (1+4 x^3\right ) (3+x-\log (x))}\right ) \, dx+\int \left (-\frac {7}{(3+x-\log (x))^2}-\frac {15}{x^2 (3+x-\log (x))^2}+\frac {14}{x (3+x-\log (x))^2}+\frac {3 x}{(3+x-\log (x))^2}-\frac {5 \left (-1-12 x+8 x^2\right )}{\left (1+4 x^3\right ) (3+x-\log (x))^2}\right ) \, dx\\ &=\frac {5}{x \left (1+4 x^3\right )}+3 \int \frac {x}{(3+x-\log (x))^2} \, dx-3 \int \frac {1}{3+x-\log (x)} \, dx-5 \int \frac {-1-12 x+8 x^2}{\left (1+4 x^3\right ) (3+x-\log (x))^2} \, dx-7 \int \frac {1}{(3+x-\log (x))^2} \, dx+14 \int \frac {1}{x (3+x-\log (x))^2} \, dx-15 \int \frac {1}{x^2 (3+x-\log (x))^2} \, dx+15 \int \frac {1}{x^2 (3+x-\log (x))} \, dx+60 \int \frac {x (3+x)}{\left (1+4 x^3\right )^2 (3+x-\log (x))} \, dx-60 \int \frac {x}{\left (1+4 x^3\right ) (3+x-\log (x))} \, dx\\ &=\frac {5}{x \left (1+4 x^3\right )}+3 \int \frac {x}{(3+x-\log (x))^2} \, dx-3 \int \frac {1}{3+x-\log (x)} \, dx-5 \int \left (-\frac {1}{\left (1+4 x^3\right ) (3+x-\log (x))^2}-\frac {12 x}{\left (1+4 x^3\right ) (3+x-\log (x))^2}+\frac {8 x^2}{\left (1+4 x^3\right ) (3+x-\log (x))^2}\right ) \, dx-7 \int \frac {1}{(3+x-\log (x))^2} \, dx+14 \int \frac {1}{x (3+x-\log (x))^2} \, dx-15 \int \frac {1}{x^2 (3+x-\log (x))^2} \, dx+15 \int \frac {1}{x^2 (3+x-\log (x))} \, dx-60 \int \left (\frac {\sqrt [3]{-1}}{3\ 2^{2/3} \left (1+(-2)^{2/3} x\right ) (3+x-\log (x))}-\frac {1}{3\ 2^{2/3} \left (1+2^{2/3} x\right ) (3+x-\log (x))}-\frac {\left (-\frac {1}{2}\right )^{2/3}}{3 \left (1-\sqrt [3]{-1} 2^{2/3} x\right ) (3+x-\log (x))}\right ) \, dx+60 \int \left (\frac {3 x}{\left (1+4 x^3\right )^2 (3+x-\log (x))}+\frac {x^2}{\left (1+4 x^3\right )^2 (3+x-\log (x))}\right ) \, dx\\ &=\frac {5}{x \left (1+4 x^3\right )}+3 \int \frac {x}{(3+x-\log (x))^2} \, dx-3 \int \frac {1}{3+x-\log (x)} \, dx+5 \int \frac {1}{\left (1+4 x^3\right ) (3+x-\log (x))^2} \, dx-7 \int \frac {1}{(3+x-\log (x))^2} \, dx+14 \int \frac {1}{x (3+x-\log (x))^2} \, dx-15 \int \frac {1}{x^2 (3+x-\log (x))^2} \, dx+15 \int \frac {1}{x^2 (3+x-\log (x))} \, dx-40 \int \frac {x^2}{\left (1+4 x^3\right ) (3+x-\log (x))^2} \, dx+60 \int \frac {x}{\left (1+4 x^3\right ) (3+x-\log (x))^2} \, dx+60 \int \frac {x^2}{\left (1+4 x^3\right )^2 (3+x-\log (x))} \, dx+180 \int \frac {x}{\left (1+4 x^3\right )^2 (3+x-\log (x))} \, dx-\left (10 \sqrt [3]{-2}\right ) \int \frac {1}{\left (1+(-2)^{2/3} x\right ) (3+x-\log (x))} \, dx+\left (10 \sqrt [3]{2}\right ) \int \frac {1}{\left (1+2^{2/3} x\right ) (3+x-\log (x))} \, dx+\left (10 (-1)^{2/3} \sqrt [3]{2}\right ) \int \frac {1}{\left (1-\sqrt [3]{-1} 2^{2/3} x\right ) (3+x-\log (x))} \, dx\\ &=\frac {5}{x \left (1+4 x^3\right )}+3 \int \frac {x}{(3+x-\log (x))^2} \, dx-3 \int \frac {1}{3+x-\log (x)} \, dx+5 \int \left (-\frac {1}{3 \left (-1-(-2)^{2/3} x\right ) (3+x-\log (x))^2}-\frac {1}{3 \left (-1-2^{2/3} x\right ) (3+x-\log (x))^2}-\frac {1}{3 \left (-1+\sqrt [3]{-1} 2^{2/3} x\right ) (3+x-\log (x))^2}\right ) \, dx-7 \int \frac {1}{(3+x-\log (x))^2} \, dx+14 \int \frac {1}{x (3+x-\log (x))^2} \, dx-15 \int \frac {1}{x^2 (3+x-\log (x))^2} \, dx+15 \int \frac {1}{x^2 (3+x-\log (x))} \, dx-40 \int \left (\frac {1}{6 \sqrt [3]{2} \left (1+2^{2/3} x\right ) (3+x-\log (x))^2}+\frac {1}{6 \sqrt [3]{2} \left (-\sqrt [3]{-1}+2^{2/3} x\right ) (3+x-\log (x))^2}+\frac {1}{6 \sqrt [3]{2} \left ((-1)^{2/3}+2^{2/3} x\right ) (3+x-\log (x))^2}\right ) \, dx+60 \int \left (\frac {\sqrt [3]{-1}}{3\ 2^{2/3} \left (1+(-2)^{2/3} x\right ) (3+x-\log (x))^2}-\frac {1}{3\ 2^{2/3} \left (1+2^{2/3} x\right ) (3+x-\log (x))^2}-\frac {\left (-\frac {1}{2}\right )^{2/3}}{3 \left (1-\sqrt [3]{-1} 2^{2/3} x\right ) (3+x-\log (x))^2}\right ) \, dx+60 \int \frac {x^2}{\left (1+4 x^3\right )^2 (3+x-\log (x))} \, dx+180 \int \frac {x}{\left (1+4 x^3\right )^2 (3+x-\log (x))} \, dx-\left (10 \sqrt [3]{-2}\right ) \int \frac {1}{\left (1+(-2)^{2/3} x\right ) (3+x-\log (x))} \, dx+\left (10 \sqrt [3]{2}\right ) \int \frac {1}{\left (1+2^{2/3} x\right ) (3+x-\log (x))} \, dx+\left (10 (-1)^{2/3} \sqrt [3]{2}\right ) \int \frac {1}{\left (1-\sqrt [3]{-1} 2^{2/3} x\right ) (3+x-\log (x))} \, dx\\ &=\frac {5}{x \left (1+4 x^3\right )}-\frac {5}{3} \int \frac {1}{\left (-1-(-2)^{2/3} x\right ) (3+x-\log (x))^2} \, dx-\frac {5}{3} \int \frac {1}{\left (-1-2^{2/3} x\right ) (3+x-\log (x))^2} \, dx-\frac {5}{3} \int \frac {1}{\left (-1+\sqrt [3]{-1} 2^{2/3} x\right ) (3+x-\log (x))^2} \, dx+3 \int \frac {x}{(3+x-\log (x))^2} \, dx-3 \int \frac {1}{3+x-\log (x)} \, dx-7 \int \frac {1}{(3+x-\log (x))^2} \, dx+14 \int \frac {1}{x (3+x-\log (x))^2} \, dx-15 \int \frac {1}{x^2 (3+x-\log (x))^2} \, dx+15 \int \frac {1}{x^2 (3+x-\log (x))} \, dx+60 \int \frac {x^2}{\left (1+4 x^3\right )^2 (3+x-\log (x))} \, dx+180 \int \frac {x}{\left (1+4 x^3\right )^2 (3+x-\log (x))} \, dx+\left (10 \sqrt [3]{-2}\right ) \int \frac {1}{\left (1+(-2)^{2/3} x\right ) (3+x-\log (x))^2} \, dx-\left (10 \sqrt [3]{-2}\right ) \int \frac {1}{\left (1+(-2)^{2/3} x\right ) (3+x-\log (x))} \, dx-\left (10 \sqrt [3]{2}\right ) \int \frac {1}{\left (1+2^{2/3} x\right ) (3+x-\log (x))^2} \, dx+\left (10 \sqrt [3]{2}\right ) \int \frac {1}{\left (1+2^{2/3} x\right ) (3+x-\log (x))} \, dx-\left (10 (-1)^{2/3} \sqrt [3]{2}\right ) \int \frac {1}{\left (1-\sqrt [3]{-1} 2^{2/3} x\right ) (3+x-\log (x))^2} \, dx+\left (10 (-1)^{2/3} \sqrt [3]{2}\right ) \int \frac {1}{\left (1-\sqrt [3]{-1} 2^{2/3} x\right ) (3+x-\log (x))} \, dx-\frac {1}{3} \left (10\ 2^{2/3}\right ) \int \frac {1}{\left (1+2^{2/3} x\right ) (3+x-\log (x))^2} \, dx-\frac {1}{3} \left (10\ 2^{2/3}\right ) \int \frac {1}{\left (-\sqrt [3]{-1}+2^{2/3} x\right ) (3+x-\log (x))^2} \, dx-\frac {1}{3} \left (10\ 2^{2/3}\right ) \int \frac {1}{\left ((-1)^{2/3}+2^{2/3} x\right ) (3+x-\log (x))^2} \, dx\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.07, size = 45, normalized size = 1.61 \begin {gather*} -\frac {x \left (-4+3 x-16 x^3+12 x^4\right )+5 \log (x)}{x \left (1+4 x^3\right ) (3+x-\log (x))} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-15 - x - 16*x^2 - 60*x^3 + 12*x^4 - 128*x^5 + 64*x^7 - 256*x^8 + (15 + 10*x + 3*x^2 + 240*x^3 + 10
0*x^4 + 24*x^5 + 48*x^8)*Log[x] + (-5 - 80*x^3)*Log[x]^2)/(9*x^2 + 6*x^3 + x^4 + 72*x^5 + 48*x^6 + 8*x^7 + 144
*x^8 + 96*x^9 + 16*x^10 + (-6*x^2 - 2*x^3 - 48*x^5 - 16*x^6 - 96*x^8 - 32*x^9)*Log[x] + (x^2 + 8*x^5 + 16*x^8)
*Log[x]^2),x]

[Out]

-((x*(-4 + 3*x - 16*x^3 + 12*x^4) + 5*Log[x])/(x*(1 + 4*x^3)*(3 + x - Log[x])))

________________________________________________________________________________________

fricas [A]  time = 0.96, size = 55, normalized size = 1.96 \begin {gather*} -\frac {12 \, x^{5} - 16 \, x^{4} + 3 \, x^{2} - 4 \, x + 5 \, \log \relax (x)}{4 \, x^{5} + 12 \, x^{4} + x^{2} - {\left (4 \, x^{4} + x\right )} \log \relax (x) + 3 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-80*x^3-5)*log(x)^2+(48*x^8+24*x^5+100*x^4+240*x^3+3*x^2+10*x+15)*log(x)-256*x^8+64*x^7-128*x^5+12
*x^4-60*x^3-16*x^2-x-15)/((16*x^8+8*x^5+x^2)*log(x)^2+(-32*x^9-96*x^8-16*x^6-48*x^5-2*x^3-6*x^2)*log(x)+16*x^1
0+96*x^9+144*x^8+8*x^7+48*x^6+72*x^5+x^4+6*x^3+9*x^2),x, algorithm="fricas")

[Out]

-(12*x^5 - 16*x^4 + 3*x^2 - 4*x + 5*log(x))/(4*x^5 + 12*x^4 + x^2 - (4*x^4 + x)*log(x) + 3*x)

________________________________________________________________________________________

giac [B]  time = 0.23, size = 71, normalized size = 2.54 \begin {gather*} -\frac {20 \, x^{2}}{4 \, x^{3} + 1} - \frac {12 \, x^{5} - 16 \, x^{4} + 3 \, x^{2} + x + 15}{4 \, x^{5} - 4 \, x^{4} \log \relax (x) + 12 \, x^{4} + x^{2} - x \log \relax (x) + 3 \, x} + \frac {5}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-80*x^3-5)*log(x)^2+(48*x^8+24*x^5+100*x^4+240*x^3+3*x^2+10*x+15)*log(x)-256*x^8+64*x^7-128*x^5+12
*x^4-60*x^3-16*x^2-x-15)/((16*x^8+8*x^5+x^2)*log(x)^2+(-32*x^9-96*x^8-16*x^6-48*x^5-2*x^3-6*x^2)*log(x)+16*x^1
0+96*x^9+144*x^8+8*x^7+48*x^6+72*x^5+x^4+6*x^3+9*x^2),x, algorithm="giac")

[Out]

-20*x^2/(4*x^3 + 1) - (12*x^5 - 16*x^4 + 3*x^2 + x + 15)/(4*x^5 - 4*x^4*log(x) + 12*x^4 + x^2 - x*log(x) + 3*x
) + 5/x

________________________________________________________________________________________

maple [A]  time = 0.03, size = 57, normalized size = 2.04

method	result	size
risch	\(\frac {5}{\left (4 x^{3}+1\right ) x}-\frac {12 x^{5}-16 x^{4}+3 x^{2}+x +15}{\left (4 x^{3}+1\right ) x \left (-\ln \relax (x )+3+x \right )}\)	\(57\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-80*x^3-5)*ln(x)^2+(48*x^8+24*x^5+100*x^4+240*x^3+3*x^2+10*x+15)*ln(x)-256*x^8+64*x^7-128*x^5+12*x^4-60*
x^3-16*x^2-x-15)/((16*x^8+8*x^5+x^2)*ln(x)^2+(-32*x^9-96*x^8-16*x^6-48*x^5-2*x^3-6*x^2)*ln(x)+16*x^10+96*x^9+1
44*x^8+8*x^7+48*x^6+72*x^5+x^4+6*x^3+9*x^2),x,method=_RETURNVERBOSE)

[Out]

5/(4*x^3+1)/x-(12*x^5-16*x^4+3*x^2+x+15)/(4*x^3+1)/x/(-ln(x)+3+x)

________________________________________________________________________________________

maxima [A]  time = 0.41, size = 55, normalized size = 1.96 \begin {gather*} -\frac {12 \, x^{5} - 16 \, x^{4} + 3 \, x^{2} - 4 \, x + 5 \, \log \relax (x)}{4 \, x^{5} + 12 \, x^{4} + x^{2} - {\left (4 \, x^{4} + x\right )} \log \relax (x) + 3 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-80*x^3-5)*log(x)^2+(48*x^8+24*x^5+100*x^4+240*x^3+3*x^2+10*x+15)*log(x)-256*x^8+64*x^7-128*x^5+12
*x^4-60*x^3-16*x^2-x-15)/((16*x^8+8*x^5+x^2)*log(x)^2+(-32*x^9-96*x^8-16*x^6-48*x^5-2*x^3-6*x^2)*log(x)+16*x^1
0+96*x^9+144*x^8+8*x^7+48*x^6+72*x^5+x^4+6*x^3+9*x^2),x, algorithm="maxima")

[Out]

-(12*x^5 - 16*x^4 + 3*x^2 - 4*x + 5*log(x))/(4*x^5 + 12*x^4 + x^2 - (4*x^4 + x)*log(x) + 3*x)

________________________________________________________________________________________

mupad [B]  time = 4.65, size = 46, normalized size = 1.64 \begin {gather*} -\frac {5\,\ln \relax (x)+x\,\left (3\,\ln \relax (x)-13\right )+x^4\,\left (12\,\ln \relax (x)-52\right )}{x\,\left (4\,x^3+1\right )\,\left (x-\ln \relax (x)+3\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(x + log(x)^2*(80*x^3 + 5) - log(x)*(10*x + 3*x^2 + 240*x^3 + 100*x^4 + 24*x^5 + 48*x^8 + 15) + 16*x^2 +
60*x^3 - 12*x^4 + 128*x^5 - 64*x^7 + 256*x^8 + 15)/(log(x)^2*(x^2 + 8*x^5 + 16*x^8) + 9*x^2 + 6*x^3 + x^4 + 72
*x^5 + 48*x^6 + 8*x^7 + 144*x^8 + 96*x^9 + 16*x^10 - log(x)*(6*x^2 + 2*x^3 + 48*x^5 + 16*x^6 + 96*x^8 + 32*x^9
)),x)

[Out]

-(5*log(x) + x*(3*log(x) - 13) + x^4*(12*log(x) - 52))/(x*(4*x^3 + 1)*(x - log(x) + 3))

________________________________________________________________________________________

sympy [B]  time = 0.31, size = 53, normalized size = 1.89 \begin {gather*} \frac {12 x^{5} - 16 x^{4} + 3 x^{2} + x + 15}{- 4 x^{5} - 12 x^{4} - x^{2} - 3 x + \left (4 x^{4} + x\right ) \log {\relax (x )}} + \frac {5}{4 x^{4} + x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-80*x**3-5)*ln(x)**2+(48*x**8+24*x**5+100*x**4+240*x**3+3*x**2+10*x+15)*ln(x)-256*x**8+64*x**7-128
*x**5+12*x**4-60*x**3-16*x**2-x-15)/((16*x**8+8*x**5+x**2)*ln(x)**2+(-32*x**9-96*x**8-16*x**6-48*x**5-2*x**3-6
*x**2)*ln(x)+16*x**10+96*x**9+144*x**8+8*x**7+48*x**6+72*x**5+x**4+6*x**3+9*x**2),x)

[Out]

(12*x**5 - 16*x**4 + 3*x**2 + x + 15)/(-4*x**5 - 12*x**4 - x**2 - 3*x + (4*x**4 + x)*log(x)) + 5/(4*x**4 + x)

________________________________________________________________________________________