3.16.97 \(\int \frac {1+5 x+8 x^2-7 x^3-14 x^4+20 x^5-4 x^6-4 x^7+2 x^8+(3 x+12 x^2-15 x^3-8 x^4+24 x^5-16 x^6+4 x^7) \log (x)}{-5 x-10 x^2+16 x^3+12 x^4-33 x^5+18 x^6+x^7-4 x^8+x^9+(x+5 x^2+6 x^3-11 x^4-8 x^5+24 x^6-16 x^7+4 x^8) \log (x)} \, dx\)

Optimal. Leaf size=28 \[ \log \left (-5+\frac {x \log (x)}{x+\left (-x+x^2\right )^2}+x (x+4 \log (x))\right ) \]

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Rubi [F]  time = 8.30, 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 {1+5 x+8 x^2-7 x^3-14 x^4+20 x^5-4 x^6-4 x^7+2 x^8+\left (3 x+12 x^2-15 x^3-8 x^4+24 x^5-16 x^6+4 x^7\right ) \log (x)}{-5 x-10 x^2+16 x^3+12 x^4-33 x^5+18 x^6+x^7-4 x^8+x^9+\left (x+5 x^2+6 x^3-11 x^4-8 x^5+24 x^6-16 x^7+4 x^8\right ) \log (x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(1 + 5*x + 8*x^2 - 7*x^3 - 14*x^4 + 20*x^5 - 4*x^6 - 4*x^7 + 2*x^8 + (3*x + 12*x^2 - 15*x^3 - 8*x^4 + 24*x
^5 - 16*x^6 + 4*x^7)*Log[x])/(-5*x - 10*x^2 + 16*x^3 + 12*x^4 - 33*x^5 + 18*x^6 + x^7 - 4*x^8 + x^9 + (x + 5*x
^2 + 6*x^3 - 11*x^4 - 8*x^5 + 24*x^6 - 16*x^7 + 4*x^8)*Log[x]),x]

[Out]

-Log[1 + x - 2*x^2 + x^3] + Log[1 + 4*x + 4*x^2 - 8*x^3 + 4*x^4] + 10*Defer[Int][(-5 - 5*x + 11*x^2 - 4*x^3 -
2*x^4 + x^5 + Log[x] + 4*x*Log[x] + 4*x^2*Log[x] - 8*x^3*Log[x] + 4*x^4*Log[x])^(-1), x] + Defer[Int][1/(x*(-5
- 5*x + 11*x^2 - 4*x^3 - 2*x^4 + x^5 + Log[x] + 4*x*Log[x] + 4*x^2*Log[x] - 8*x^3*Log[x] + 4*x^4*Log[x])), x]
- 5*Defer[Int][x/(-5 - 5*x + 11*x^2 - 4*x^3 - 2*x^4 + x^5 + Log[x] + 4*x*Log[x] + 4*x^2*Log[x] - 8*x^3*Log[x]
+ 4*x^4*Log[x]), x] - 2*Defer[Int][x^2/(-5 - 5*x + 11*x^2 - 4*x^3 - 2*x^4 + x^5 + Log[x] + 4*x*Log[x] + 4*x^2
*Log[x] - 8*x^3*Log[x] + 4*x^4*Log[x]), x] + 2*Defer[Int][x^3/(-5 - 5*x + 11*x^2 - 4*x^3 - 2*x^4 + x^5 + Log[x
] + 4*x*Log[x] + 4*x^2*Log[x] - 8*x^3*Log[x] + 4*x^4*Log[x]), x] + Defer[Int][x^4/(-5 - 5*x + 11*x^2 - 4*x^3 -
2*x^4 + x^5 + Log[x] + 4*x*Log[x] + 4*x^2*Log[x] - 8*x^3*Log[x] + 4*x^4*Log[x]), x] + 9*Defer[Int][1/((1 + 4*
x + 4*x^2 - 8*x^3 + 4*x^4)*(-5 - 5*x + 11*x^2 - 4*x^3 - 2*x^4 + x^5 + Log[x] + 4*x*Log[x] + 4*x^2*Log[x] - 8*x
^3*Log[x] + 4*x^4*Log[x])), x] + 47*Defer[Int][x/((1 + 4*x + 4*x^2 - 8*x^3 + 4*x^4)*(-5 - 5*x + 11*x^2 - 4*x^3
- 2*x^4 + x^5 + Log[x] + 4*x*Log[x] + 4*x^2*Log[x] - 8*x^3*Log[x] + 4*x^4*Log[x])), x] - 62*Defer[Int][x^2/((
1 + 4*x + 4*x^2 - 8*x^3 + 4*x^4)*(-5 - 5*x + 11*x^2 - 4*x^3 - 2*x^4 + x^5 + Log[x] + 4*x*Log[x] + 4*x^2*Log[x]
- 8*x^3*Log[x] + 4*x^4*Log[x])), x] + 22*Defer[Int][x^3/((1 + 4*x + 4*x^2 - 8*x^3 + 4*x^4)*(-5 - 5*x + 11*x^2
- 4*x^3 - 2*x^4 + x^5 + Log[x] + 4*x*Log[x] + 4*x^2*Log[x] - 8*x^3*Log[x] + 4*x^4*Log[x])), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-1-5 x-8 x^2+7 x^3+14 x^4-20 x^5+4 x^6+4 x^7-2 x^8-\left (3 x+12 x^2-15 x^3-8 x^4+24 x^5-16 x^6+4 x^7\right ) \log (x)}{x \left (1+x-2 x^2+x^3\right ) \left (5+5 x-11 x^2+4 x^3+2 x^4-x^5-\log (x)-4 x \log (x)-4 x^2 \log (x)+8 x^3 \log (x)-4 x^4 \log (x)\right )} \, dx\\ &=\int \left (\frac {3+12 x-15 x^2-8 x^3+24 x^4-16 x^5+4 x^6}{\left (1+x-2 x^2+x^3\right ) \left (1+4 x+4 x^2-8 x^3+4 x^4\right )}+\frac {1+23 x+86 x^2-52 x^3-80 x^4+81 x^5+8 x^6-20 x^7+4 x^9}{x \left (1+4 x+4 x^2-8 x^3+4 x^4\right ) \left (-5-5 x+11 x^2-4 x^3-2 x^4+x^5+\log (x)+4 x \log (x)+4 x^2 \log (x)-8 x^3 \log (x)+4 x^4 \log (x)\right )}\right ) \, dx\\ &=\int \frac {3+12 x-15 x^2-8 x^3+24 x^4-16 x^5+4 x^6}{\left (1+x-2 x^2+x^3\right ) \left (1+4 x+4 x^2-8 x^3+4 x^4\right )} \, dx+\int \frac {1+23 x+86 x^2-52 x^3-80 x^4+81 x^5+8 x^6-20 x^7+4 x^9}{x \left (1+4 x+4 x^2-8 x^3+4 x^4\right ) \left (-5-5 x+11 x^2-4 x^3-2 x^4+x^5+\log (x)+4 x \log (x)+4 x^2 \log (x)-8 x^3 \log (x)+4 x^4 \log (x)\right )} \, dx\\ &=\int \left (\frac {-1+4 x-3 x^2}{1+x-2 x^2+x^3}+\frac {4 \left (1+2 x-6 x^2+4 x^3\right )}{1+4 x+4 x^2-8 x^3+4 x^4}\right ) \, dx+\int \left (\frac {10}{-5-5 x+11 x^2-4 x^3-2 x^4+x^5+\log (x)+4 x \log (x)+4 x^2 \log (x)-8 x^3 \log (x)+4 x^4 \log (x)}+\frac {1}{x \left (-5-5 x+11 x^2-4 x^3-2 x^4+x^5+\log (x)+4 x \log (x)+4 x^2 \log (x)-8 x^3 \log (x)+4 x^4 \log (x)\right )}-\frac {5 x}{-5-5 x+11 x^2-4 x^3-2 x^4+x^5+\log (x)+4 x \log (x)+4 x^2 \log (x)-8 x^3 \log (x)+4 x^4 \log (x)}-\frac {2 x^2}{-5-5 x+11 x^2-4 x^3-2 x^4+x^5+\log (x)+4 x \log (x)+4 x^2 \log (x)-8 x^3 \log (x)+4 x^4 \log (x)}+\frac {2 x^3}{-5-5 x+11 x^2-4 x^3-2 x^4+x^5+\log (x)+4 x \log (x)+4 x^2 \log (x)-8 x^3 \log (x)+4 x^4 \log (x)}+\frac {x^4}{-5-5 x+11 x^2-4 x^3-2 x^4+x^5+\log (x)+4 x \log (x)+4 x^2 \log (x)-8 x^3 \log (x)+4 x^4 \log (x)}+\frac {9+47 x-62 x^2+22 x^3}{\left (1+4 x+4 x^2-8 x^3+4 x^4\right ) \left (-5-5 x+11 x^2-4 x^3-2 x^4+x^5+\log (x)+4 x \log (x)+4 x^2 \log (x)-8 x^3 \log (x)+4 x^4 \log (x)\right )}\right ) \, dx\\ &=-\left (2 \int \frac {x^2}{-5-5 x+11 x^2-4 x^3-2 x^4+x^5+\log (x)+4 x \log (x)+4 x^2 \log (x)-8 x^3 \log (x)+4 x^4 \log (x)} \, dx\right )+2 \int \frac {x^3}{-5-5 x+11 x^2-4 x^3-2 x^4+x^5+\log (x)+4 x \log (x)+4 x^2 \log (x)-8 x^3 \log (x)+4 x^4 \log (x)} \, dx+4 \int \frac {1+2 x-6 x^2+4 x^3}{1+4 x+4 x^2-8 x^3+4 x^4} \, dx-5 \int \frac {x}{-5-5 x+11 x^2-4 x^3-2 x^4+x^5+\log (x)+4 x \log (x)+4 x^2 \log (x)-8 x^3 \log (x)+4 x^4 \log (x)} \, dx+10 \int \frac {1}{-5-5 x+11 x^2-4 x^3-2 x^4+x^5+\log (x)+4 x \log (x)+4 x^2 \log (x)-8 x^3 \log (x)+4 x^4 \log (x)} \, dx+\int \frac {-1+4 x-3 x^2}{1+x-2 x^2+x^3} \, dx+\int \frac {1}{x \left (-5-5 x+11 x^2-4 x^3-2 x^4+x^5+\log (x)+4 x \log (x)+4 x^2 \log (x)-8 x^3 \log (x)+4 x^4 \log (x)\right )} \, dx+\int \frac {x^4}{-5-5 x+11 x^2-4 x^3-2 x^4+x^5+\log (x)+4 x \log (x)+4 x^2 \log (x)-8 x^3 \log (x)+4 x^4 \log (x)} \, dx+\int \frac {9+47 x-62 x^2+22 x^3}{\left (1+4 x+4 x^2-8 x^3+4 x^4\right ) \left (-5-5 x+11 x^2-4 x^3-2 x^4+x^5+\log (x)+4 x \log (x)+4 x^2 \log (x)-8 x^3 \log (x)+4 x^4 \log (x)\right )} \, dx\\ &=-\log \left (1+x-2 x^2+x^3\right )+\log \left (1+4 x+4 x^2-8 x^3+4 x^4\right )-2 \int \frac {x^2}{-5-5 x+11 x^2-4 x^3-2 x^4+x^5+\log (x)+4 x \log (x)+4 x^2 \log (x)-8 x^3 \log (x)+4 x^4 \log (x)} \, dx+2 \int \frac {x^3}{-5-5 x+11 x^2-4 x^3-2 x^4+x^5+\log (x)+4 x \log (x)+4 x^2 \log (x)-8 x^3 \log (x)+4 x^4 \log (x)} \, dx-5 \int \frac {x}{-5-5 x+11 x^2-4 x^3-2 x^4+x^5+\log (x)+4 x \log (x)+4 x^2 \log (x)-8 x^3 \log (x)+4 x^4 \log (x)} \, dx+10 \int \frac {1}{-5-5 x+11 x^2-4 x^3-2 x^4+x^5+\log (x)+4 x \log (x)+4 x^2 \log (x)-8 x^3 \log (x)+4 x^4 \log (x)} \, dx+\int \frac {1}{x \left (-5-5 x+11 x^2-4 x^3-2 x^4+x^5+\log (x)+4 x \log (x)+4 x^2 \log (x)-8 x^3 \log (x)+4 x^4 \log (x)\right )} \, dx+\int \frac {x^4}{-5-5 x+11 x^2-4 x^3-2 x^4+x^5+\log (x)+4 x \log (x)+4 x^2 \log (x)-8 x^3 \log (x)+4 x^4 \log (x)} \, dx+\int \left (\frac {9}{\left (1+4 x+4 x^2-8 x^3+4 x^4\right ) \left (-5-5 x+11 x^2-4 x^3-2 x^4+x^5+\log (x)+4 x \log (x)+4 x^2 \log (x)-8 x^3 \log (x)+4 x^4 \log (x)\right )}+\frac {47 x}{\left (1+4 x+4 x^2-8 x^3+4 x^4\right ) \left (-5-5 x+11 x^2-4 x^3-2 x^4+x^5+\log (x)+4 x \log (x)+4 x^2 \log (x)-8 x^3 \log (x)+4 x^4 \log (x)\right )}-\frac {62 x^2}{\left (1+4 x+4 x^2-8 x^3+4 x^4\right ) \left (-5-5 x+11 x^2-4 x^3-2 x^4+x^5+\log (x)+4 x \log (x)+4 x^2 \log (x)-8 x^3 \log (x)+4 x^4 \log (x)\right )}+\frac {22 x^3}{\left (1+4 x+4 x^2-8 x^3+4 x^4\right ) \left (-5-5 x+11 x^2-4 x^3-2 x^4+x^5+\log (x)+4 x \log (x)+4 x^2 \log (x)-8 x^3 \log (x)+4 x^4 \log (x)\right )}\right ) \, dx\\ &=-\log \left (1+x-2 x^2+x^3\right )+\log \left (1+4 x+4 x^2-8 x^3+4 x^4\right )-2 \int \frac {x^2}{-5-5 x+11 x^2-4 x^3-2 x^4+x^5+\log (x)+4 x \log (x)+4 x^2 \log (x)-8 x^3 \log (x)+4 x^4 \log (x)} \, dx+2 \int \frac {x^3}{-5-5 x+11 x^2-4 x^3-2 x^4+x^5+\log (x)+4 x \log (x)+4 x^2 \log (x)-8 x^3 \log (x)+4 x^4 \log (x)} \, dx-5 \int \frac {x}{-5-5 x+11 x^2-4 x^3-2 x^4+x^5+\log (x)+4 x \log (x)+4 x^2 \log (x)-8 x^3 \log (x)+4 x^4 \log (x)} \, dx+9 \int \frac {1}{\left (1+4 x+4 x^2-8 x^3+4 x^4\right ) \left (-5-5 x+11 x^2-4 x^3-2 x^4+x^5+\log (x)+4 x \log (x)+4 x^2 \log (x)-8 x^3 \log (x)+4 x^4 \log (x)\right )} \, dx+10 \int \frac {1}{-5-5 x+11 x^2-4 x^3-2 x^4+x^5+\log (x)+4 x \log (x)+4 x^2 \log (x)-8 x^3 \log (x)+4 x^4 \log (x)} \, dx+22 \int \frac {x^3}{\left (1+4 x+4 x^2-8 x^3+4 x^4\right ) \left (-5-5 x+11 x^2-4 x^3-2 x^4+x^5+\log (x)+4 x \log (x)+4 x^2 \log (x)-8 x^3 \log (x)+4 x^4 \log (x)\right )} \, dx+47 \int \frac {x}{\left (1+4 x+4 x^2-8 x^3+4 x^4\right ) \left (-5-5 x+11 x^2-4 x^3-2 x^4+x^5+\log (x)+4 x \log (x)+4 x^2 \log (x)-8 x^3 \log (x)+4 x^4 \log (x)\right )} \, dx-62 \int \frac {x^2}{\left (1+4 x+4 x^2-8 x^3+4 x^4\right ) \left (-5-5 x+11 x^2-4 x^3-2 x^4+x^5+\log (x)+4 x \log (x)+4 x^2 \log (x)-8 x^3 \log (x)+4 x^4 \log (x)\right )} \, dx+\int \frac {1}{x \left (-5-5 x+11 x^2-4 x^3-2 x^4+x^5+\log (x)+4 x \log (x)+4 x^2 \log (x)-8 x^3 \log (x)+4 x^4 \log (x)\right )} \, dx+\int \frac {x^4}{-5-5 x+11 x^2-4 x^3-2 x^4+x^5+\log (x)+4 x \log (x)+4 x^2 \log (x)-8 x^3 \log (x)+4 x^4 \log (x)} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.09, size = 71, normalized size = 2.54 \begin {gather*} -\log \left (1+x-2 x^2+x^3\right )+\log \left (5+5 x-11 x^2+4 x^3+2 x^4-x^5-\log (x)-4 x \log (x)-4 x^2 \log (x)+8 x^3 \log (x)-4 x^4 \log (x)\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(1 + 5*x + 8*x^2 - 7*x^3 - 14*x^4 + 20*x^5 - 4*x^6 - 4*x^7 + 2*x^8 + (3*x + 12*x^2 - 15*x^3 - 8*x^4
+ 24*x^5 - 16*x^6 + 4*x^7)*Log[x])/(-5*x - 10*x^2 + 16*x^3 + 12*x^4 - 33*x^5 + 18*x^6 + x^7 - 4*x^8 + x^9 + (x
+ 5*x^2 + 6*x^3 - 11*x^4 - 8*x^5 + 24*x^6 - 16*x^7 + 4*x^8)*Log[x]),x]

[Out]

-Log[1 + x - 2*x^2 + x^3] + Log[5 + 5*x - 11*x^2 + 4*x^3 + 2*x^4 - x^5 - Log[x] - 4*x*Log[x] - 4*x^2*Log[x] +
8*x^3*Log[x] - 4*x^4*Log[x]]

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fricas [B]  time = 0.87, size = 106, normalized size = 3.79 \begin {gather*} \log \left (4 \, x^{4} - 8 \, x^{3} + 4 \, x^{2} + 4 \, x + 1\right ) - \log \left (x^{3} - 2 \, x^{2} + x + 1\right ) + \log \left (\frac {x^{5} - 2 \, x^{4} - 4 \, x^{3} + 11 \, x^{2} + {\left (4 \, x^{4} - 8 \, x^{3} + 4 \, x^{2} + 4 \, x + 1\right )} \log \relax (x) - 5 \, x - 5}{4 \, x^{4} - 8 \, x^{3} + 4 \, x^{2} + 4 \, x + 1}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^7-16*x^6+24*x^5-8*x^4-15*x^3+12*x^2+3*x)*log(x)+2*x^8-4*x^7-4*x^6+20*x^5-14*x^4-7*x^3+8*x^2+5*
x+1)/((4*x^8-16*x^7+24*x^6-8*x^5-11*x^4+6*x^3+5*x^2+x)*log(x)+x^9-4*x^8+x^7+18*x^6-33*x^5+12*x^4+16*x^3-10*x^2
-5*x),x, algorithm="fricas")

[Out]

log(4*x^4 - 8*x^3 + 4*x^2 + 4*x + 1) - log(x^3 - 2*x^2 + x + 1) + log((x^5 - 2*x^4 - 4*x^3 + 11*x^2 + (4*x^4 -
8*x^3 + 4*x^2 + 4*x + 1)*log(x) - 5*x - 5)/(4*x^4 - 8*x^3 + 4*x^2 + 4*x + 1))

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giac [B]  time = 0.52, size = 67, normalized size = 2.39 \begin {gather*} \log \left (x^{5} + 4 \, x^{4} \log \relax (x) - 2 \, x^{4} - 8 \, x^{3} \log \relax (x) - 4 \, x^{3} + 4 \, x^{2} \log \relax (x) + 11 \, x^{2} + 4 \, x \log \relax (x) - 5 \, x + \log \relax (x) - 5\right ) - \log \left (x^{3} - 2 \, x^{2} + x + 1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^7-16*x^6+24*x^5-8*x^4-15*x^3+12*x^2+3*x)*log(x)+2*x^8-4*x^7-4*x^6+20*x^5-14*x^4-7*x^3+8*x^2+5*
x+1)/((4*x^8-16*x^7+24*x^6-8*x^5-11*x^4+6*x^3+5*x^2+x)*log(x)+x^9-4*x^8+x^7+18*x^6-33*x^5+12*x^4+16*x^3-10*x^2
-5*x),x, algorithm="giac")

[Out]

log(x^5 + 4*x^4*log(x) - 2*x^4 - 8*x^3*log(x) - 4*x^3 + 4*x^2*log(x) + 11*x^2 + 4*x*log(x) - 5*x + log(x) - 5)
- log(x^3 - 2*x^2 + x + 1)

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maple [B]  time = 0.11, size = 68, normalized size = 2.43

method	result	size
norman	\(-\ln \left (x^{3}-2 x^{2}+x +1\right )+\ln \left (x^{5}+4 x^{4} \ln \relax (x )-2 x^{4}-8 x^{3} \ln \relax (x )-4 x^{3}+4 x^{2} \ln \relax (x )+11 x^{2}+4 x \ln \relax (x )-5 x +\ln \relax (x )-5\right )\)	\(68\)
risch	\(-\ln \left (x^{3}-2 x^{2}+x +1\right )+\ln \left (4 x^{4}-8 x^{3}+4 x^{2}+4 x +1\right )+\ln \left (\ln \relax (x )+\frac {x^{5}-2 x^{4}-4 x^{3}+11 x^{2}-5 x -5}{4 x^{4}-8 x^{3}+4 x^{2}+4 x +1}\right )\)	\(87\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((4*x^7-16*x^6+24*x^5-8*x^4-15*x^3+12*x^2+3*x)*ln(x)+2*x^8-4*x^7-4*x^6+20*x^5-14*x^4-7*x^3+8*x^2+5*x+1)/((
4*x^8-16*x^7+24*x^6-8*x^5-11*x^4+6*x^3+5*x^2+x)*ln(x)+x^9-4*x^8+x^7+18*x^6-33*x^5+12*x^4+16*x^3-10*x^2-5*x),x,
method=_RETURNVERBOSE)

[Out]

-ln(x^3-2*x^2+x+1)+ln(x^5+4*x^4*ln(x)-2*x^4-8*x^3*ln(x)-4*x^3+4*x^2*ln(x)+11*x^2+4*x*ln(x)-5*x+ln(x)-5)

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maxima [B]  time = 0.45, size = 106, normalized size = 3.79 \begin {gather*} \log \left (4 \, x^{4} - 8 \, x^{3} + 4 \, x^{2} + 4 \, x + 1\right ) - \log \left (x^{3} - 2 \, x^{2} + x + 1\right ) + \log \left (\frac {x^{5} - 2 \, x^{4} - 4 \, x^{3} + 11 \, x^{2} + {\left (4 \, x^{4} - 8 \, x^{3} + 4 \, x^{2} + 4 \, x + 1\right )} \log \relax (x) - 5 \, x - 5}{4 \, x^{4} - 8 \, x^{3} + 4 \, x^{2} + 4 \, x + 1}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^7-16*x^6+24*x^5-8*x^4-15*x^3+12*x^2+3*x)*log(x)+2*x^8-4*x^7-4*x^6+20*x^5-14*x^4-7*x^3+8*x^2+5*
x+1)/((4*x^8-16*x^7+24*x^6-8*x^5-11*x^4+6*x^3+5*x^2+x)*log(x)+x^9-4*x^8+x^7+18*x^6-33*x^5+12*x^4+16*x^3-10*x^2
-5*x),x, algorithm="maxima")

[Out]

log(4*x^4 - 8*x^3 + 4*x^2 + 4*x + 1) - log(x^3 - 2*x^2 + x + 1) + log((x^5 - 2*x^4 - 4*x^3 + 11*x^2 + (4*x^4 -
8*x^3 + 4*x^2 + 4*x + 1)*log(x) - 5*x - 5)/(4*x^4 - 8*x^3 + 4*x^2 + 4*x + 1))

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {5\,x+\ln \relax (x)\,\left (4\,x^7-16\,x^6+24\,x^5-8\,x^4-15\,x^3+12\,x^2+3\,x\right )+8\,x^2-7\,x^3-14\,x^4+20\,x^5-4\,x^6-4\,x^7+2\,x^8+1}{\ln \relax (x)\,\left (4\,x^8-16\,x^7+24\,x^6-8\,x^5-11\,x^4+6\,x^3+5\,x^2+x\right )-5\,x-10\,x^2+16\,x^3+12\,x^4-33\,x^5+18\,x^6+x^7-4\,x^8+x^9} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((5*x + log(x)*(3*x + 12*x^2 - 15*x^3 - 8*x^4 + 24*x^5 - 16*x^6 + 4*x^7) + 8*x^2 - 7*x^3 - 14*x^4 + 20*x^5
- 4*x^6 - 4*x^7 + 2*x^8 + 1)/(log(x)*(x + 5*x^2 + 6*x^3 - 11*x^4 - 8*x^5 + 24*x^6 - 16*x^7 + 4*x^8) - 5*x - 10
*x^2 + 16*x^3 + 12*x^4 - 33*x^5 + 18*x^6 + x^7 - 4*x^8 + x^9),x)

[Out]

int((5*x + log(x)*(3*x + 12*x^2 - 15*x^3 - 8*x^4 + 24*x^5 - 16*x^6 + 4*x^7) + 8*x^2 - 7*x^3 - 14*x^4 + 20*x^5
- 4*x^6 - 4*x^7 + 2*x^8 + 1)/(log(x)*(x + 5*x^2 + 6*x^3 - 11*x^4 - 8*x^5 + 24*x^6 - 16*x^7 + 4*x^8) - 5*x - 10
*x^2 + 16*x^3 + 12*x^4 - 33*x^5 + 18*x^6 + x^7 - 4*x^8 + x^9), x)

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sympy [B]  time = 1.25, size = 83, normalized size = 2.96 \begin {gather*} \log {\left (\log {\relax (x )} + \frac {x^{5} - 2 x^{4} - 4 x^{3} + 11 x^{2} - 5 x - 5}{4 x^{4} - 8 x^{3} + 4 x^{2} + 4 x + 1} \right )} - \log {\left (x^{3} - 2 x^{2} + x + 1 \right )} + \log {\left (4 x^{4} - 8 x^{3} + 4 x^{2} + 4 x + 1 \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x**7-16*x**6+24*x**5-8*x**4-15*x**3+12*x**2+3*x)*ln(x)+2*x**8-4*x**7-4*x**6+20*x**5-14*x**4-7*x*
*3+8*x**2+5*x+1)/((4*x**8-16*x**7+24*x**6-8*x**5-11*x**4+6*x**3+5*x**2+x)*ln(x)+x**9-4*x**8+x**7+18*x**6-33*x*
*5+12*x**4+16*x**3-10*x**2-5*x),x)

[Out]

log(log(x) + (x**5 - 2*x**4 - 4*x**3 + 11*x**2 - 5*x - 5)/(4*x**4 - 8*x**3 + 4*x**2 + 4*x + 1)) - log(x**3 - 2
*x**2 + x + 1) + log(4*x**4 - 8*x**3 + 4*x**2 + 4*x + 1)

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