\(\int \frac {-15-x-16 x^2-60 x^3+12 x^4-128 x^5+64 x^7-256 x^8+(15+10 x+3 x^2+240 x^3+100 x^4+24 x^5+48 x^8) \log (x)+(-5-80 x^3) \log ^2(x)}{9 x^2+6 x^3+x^4+72 x^5+48 x^6+8 x^7+144 x^8+96 x^9+16 x^{10}+(-6 x^2-2 x^3-48 x^5-16 x^6-96 x^8-32 x^9) \log (x)+(x^2+8 x^5+16 x^8) \log ^2(x)} \, dx\) [7403]

Optimal result

Integrand size = 180, antiderivative size = 28 \[ \int \frac {-15-x-16 x^2-60 x^3+12 x^4-128 x^5+64 x^7-256 x^8+\left (15+10 x+3 x^2+240 x^3+100 x^4+24 x^5+48 x^8\right ) \log (x)+\left (-5-80 x^3\right ) \log ^2(x)}{9 x^2+6 x^3+x^4+72 x^5+48 x^6+8 x^7+144 x^8+96 x^9+16 x^{10}+\left (-6 x^2-2 x^3-48 x^5-16 x^6-96 x^8-32 x^9\right ) \log (x)+\left (x^2+8 x^5+16 x^8\right ) \log ^2(x)} \, dx=\frac {-4+3 x+\frac {5 \log (x)}{x+4 x^4}}{-3-x+\log (x)} \]

[Out]

(3*x+5/(4*x^4+x)*ln(x)-4)/(ln(x)-3-x)

Rubi [F]

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

[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{align*} \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{align*}

Mathematica [A] (verified)

Time = 0.07 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.61 \[ \int \frac {-15-x-16 x^2-60 x^3+12 x^4-128 x^5+64 x^7-256 x^8+\left (15+10 x+3 x^2+240 x^3+100 x^4+24 x^5+48 x^8\right ) \log (x)+\left (-5-80 x^3\right ) \log ^2(x)}{9 x^2+6 x^3+x^4+72 x^5+48 x^6+8 x^7+144 x^8+96 x^9+16 x^{10}+\left (-6 x^2-2 x^3-48 x^5-16 x^6-96 x^8-32 x^9\right ) \log (x)+\left (x^2+8 x^5+16 x^8\right ) \log ^2(x)} \, dx=-\frac {x \left (-4+3 x-16 x^3+12 x^4\right )+5 \log (x)}{x \left (1+4 x^3\right ) (3+x-\log (x))} \]

[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])))

Maple [A] (verified)

Time = 0.45 (sec) , antiderivative size = 55, normalized size of antiderivative = 1.96

method	result	size
parallelrisch	\(\frac {16 x -48 x^{5}-20 \ln \left (x \right )+64 x^{4}-12 x^{2}}{4 x \left (-4 x^{3} \ln \left (x \right )+x +12 x^{3}+4 x^{4}-\ln \left (x \right )+3\right )}\)	\(55\)
risch	\(\frac {5}{\left (4 x^{3}+1\right ) x}-\frac {12 x^{5}-16 x^{4}+3 x^{2}+x +15}{\left (4 x^{3}+1\right ) x \left (-\ln \left (x \right )+3+x \right )}\)	\(57\)
default	\(\frac {22 \ln \left (x \right )+88 x^{3} \ln \left (x \right )-\frac {5 \ln \left (x \right )^{2}}{x}-12 x^{3} \ln \left (x \right )^{2}+\frac {15 \ln \left (x \right )}{x}-3 \ln \left (x \right )^{2}-156 x^{3}-39}{\left (\ln \left (x \right )-3\right ) \left (-4 x^{3} \ln \left (x \right )+x +12 x^{3}+4 x^{4}-\ln \left (x \right )+3\right )}\)	\(83\)

[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]

1/4/x*(16*x-48*x^5-20*ln(x)+64*x^4-12*x^2)/(-4*x^3*ln(x)+x+12*x^3+4*x^4-ln(x)+3)

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 55, normalized size of antiderivative = 1.96 \[ \int \frac {-15-x-16 x^2-60 x^3+12 x^4-128 x^5+64 x^7-256 x^8+\left (15+10 x+3 x^2+240 x^3+100 x^4+24 x^5+48 x^8\right ) \log (x)+\left (-5-80 x^3\right ) \log ^2(x)}{9 x^2+6 x^3+x^4+72 x^5+48 x^6+8 x^7+144 x^8+96 x^9+16 x^{10}+\left (-6 x^2-2 x^3-48 x^5-16 x^6-96 x^8-32 x^9\right ) \log (x)+\left (x^2+8 x^5+16 x^8\right ) \log ^2(x)} \, dx=-\frac {12 \, x^{5} - 16 \, x^{4} + 3 \, x^{2} - 4 \, x + 5 \, \log \left (x\right )}{4 \, x^{5} + 12 \, x^{4} + x^{2} - {\left (4 \, x^{4} + x\right )} \log \left (x\right ) + 3 \, x} \]

[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)

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 53 vs. \(2 (22) = 44\).

Time = 0.12 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.89 \[ \int \frac {-15-x-16 x^2-60 x^3+12 x^4-128 x^5+64 x^7-256 x^8+\left (15+10 x+3 x^2+240 x^3+100 x^4+24 x^5+48 x^8\right ) \log (x)+\left (-5-80 x^3\right ) \log ^2(x)}{9 x^2+6 x^3+x^4+72 x^5+48 x^6+8 x^7+144 x^8+96 x^9+16 x^{10}+\left (-6 x^2-2 x^3-48 x^5-16 x^6-96 x^8-32 x^9\right ) \log (x)+\left (x^2+8 x^5+16 x^8\right ) \log ^2(x)} \, dx=\frac {12 x^{5} - 16 x^{4} + 3 x^{2} + x + 15}{- 4 x^{5} - 12 x^{4} - x^{2} - 3 x + \left (4 x^{4} + x\right ) \log {\left (x \right )}} + \frac {5}{4 x^{4} + x} \]

[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)

Maxima [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 55, normalized size of antiderivative = 1.96 \[ \int \frac {-15-x-16 x^2-60 x^3+12 x^4-128 x^5+64 x^7-256 x^8+\left (15+10 x+3 x^2+240 x^3+100 x^4+24 x^5+48 x^8\right ) \log (x)+\left (-5-80 x^3\right ) \log ^2(x)}{9 x^2+6 x^3+x^4+72 x^5+48 x^6+8 x^7+144 x^8+96 x^9+16 x^{10}+\left (-6 x^2-2 x^3-48 x^5-16 x^6-96 x^8-32 x^9\right ) \log (x)+\left (x^2+8 x^5+16 x^8\right ) \log ^2(x)} \, dx=-\frac {12 \, x^{5} - 16 \, x^{4} + 3 \, x^{2} - 4 \, x + 5 \, \log \left (x\right )}{4 \, x^{5} + 12 \, x^{4} + x^{2} - {\left (4 \, x^{4} + x\right )} \log \left (x\right ) + 3 \, x} \]

[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)

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 71 vs. \(2 (29) = 58\).

Time = 0.32 (sec) , antiderivative size = 71, normalized size of antiderivative = 2.54 \[ \int \frac {-15-x-16 x^2-60 x^3+12 x^4-128 x^5+64 x^7-256 x^8+\left (15+10 x+3 x^2+240 x^3+100 x^4+24 x^5+48 x^8\right ) \log (x)+\left (-5-80 x^3\right ) \log ^2(x)}{9 x^2+6 x^3+x^4+72 x^5+48 x^6+8 x^7+144 x^8+96 x^9+16 x^{10}+\left (-6 x^2-2 x^3-48 x^5-16 x^6-96 x^8-32 x^9\right ) \log (x)+\left (x^2+8 x^5+16 x^8\right ) \log ^2(x)} \, dx=-\frac {20 \, x^{2}}{4 \, x^{3} + 1} - \frac {12 \, x^{5} - 16 \, x^{4} + 3 \, x^{2} + x + 15}{4 \, x^{5} - 4 \, x^{4} \log \left (x\right ) + 12 \, x^{4} + x^{2} - x \log \left (x\right ) + 3 \, x} + \frac {5}{x} \]

[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

Mupad [B] (verification not implemented)

Time = 12.37 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.64 \[ \int \frac {-15-x-16 x^2-60 x^3+12 x^4-128 x^5+64 x^7-256 x^8+\left (15+10 x+3 x^2+240 x^3+100 x^4+24 x^5+48 x^8\right ) \log (x)+\left (-5-80 x^3\right ) \log ^2(x)}{9 x^2+6 x^3+x^4+72 x^5+48 x^6+8 x^7+144 x^8+96 x^9+16 x^{10}+\left (-6 x^2-2 x^3-48 x^5-16 x^6-96 x^8-32 x^9\right ) \log (x)+\left (x^2+8 x^5+16 x^8\right ) \log ^2(x)} \, dx=-\frac {5\,\ln \left (x\right )+x\,\left (3\,\ln \left (x\right )-13\right )+x^4\,\left (12\,\ln \left (x\right )-52\right )}{x\,\left (4\,x^3+1\right )\,\left (x-\ln \left (x\right )+3\right )} \]

[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))