3.102.3 \(\int \frac {32-64 x+16 x^2+108 x^4-64 x^5+8 x^6+16 x^8-8 x^9+x^{10}+(64-128 x+32 x^2+108 x^4-64 x^5+8 x^6) \log (5)+(48-96 x+24 x^2+27 x^4-16 x^5+2 x^6) \log ^2(5)+(16-32 x+8 x^2) \log ^3(5)+(2-4 x+x^2) \log ^4(5)+(-28 x^4+8 x^5-8 x^8+2 x^9+(-28 x^4+8 x^5) \log (5)+(-7 x^4+2 x^5) \log ^2(5)) \log (x)+x^8 \log ^2(x)}{64-64 x+16 x^2+64 x^4-48 x^5+8 x^6+16 x^8-8 x^9+x^{10}+(128-128 x+32 x^2+64 x^4-48 x^5+8 x^6) \log (5)+(96-96 x+24 x^2+16 x^4-12 x^5+2 x^6) \log ^2(5)+(32-32 x+8 x^2) \log ^3(5)+(4-4 x+x^2) \log ^4(5)+(-16 x^4+8 x^5-8 x^8+2 x^9+(-16 x^4+8 x^5) \log (5)+(-4 x^4+2 x^5) \log ^2(5)) \log (x)+x^8 \log ^2(x)} \, dx\)

Optimal. Leaf size=24 \[ x+\frac {x}{-2+x+\frac {x^4 (-4+x+\log (x))}{(2+\log (5))^2}} \]

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Rubi [F]  time = 4.39, 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 {32-64 x+16 x^2+108 x^4-64 x^5+8 x^6+16 x^8-8 x^9+x^{10}+\left (64-128 x+32 x^2+108 x^4-64 x^5+8 x^6\right ) \log (5)+\left (48-96 x+24 x^2+27 x^4-16 x^5+2 x^6\right ) \log ^2(5)+\left (16-32 x+8 x^2\right ) \log ^3(5)+\left (2-4 x+x^2\right ) \log ^4(5)+\left (-28 x^4+8 x^5-8 x^8+2 x^9+\left (-28 x^4+8 x^5\right ) \log (5)+\left (-7 x^4+2 x^5\right ) \log ^2(5)\right ) \log (x)+x^8 \log ^2(x)}{64-64 x+16 x^2+64 x^4-48 x^5+8 x^6+16 x^8-8 x^9+x^{10}+\left (128-128 x+32 x^2+64 x^4-48 x^5+8 x^6\right ) \log (5)+\left (96-96 x+24 x^2+16 x^4-12 x^5+2 x^6\right ) \log ^2(5)+\left (32-32 x+8 x^2\right ) \log ^3(5)+\left (4-4 x+x^2\right ) \log ^4(5)+\left (-16 x^4+8 x^5-8 x^8+2 x^9+\left (-16 x^4+8 x^5\right ) \log (5)+\left (-4 x^4+2 x^5\right ) \log ^2(5)\right ) \log (x)+x^8 \log ^2(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(32 - 64*x + 16*x^2 + 108*x^4 - 64*x^5 + 8*x^6 + 16*x^8 - 8*x^9 + x^10 + (64 - 128*x + 32*x^2 + 108*x^4 -
64*x^5 + 8*x^6)*Log[5] + (48 - 96*x + 24*x^2 + 27*x^4 - 16*x^5 + 2*x^6)*Log[5]^2 + (16 - 32*x + 8*x^2)*Log[5]^
3 + (2 - 4*x + x^2)*Log[5]^4 + (-28*x^4 + 8*x^5 - 8*x^8 + 2*x^9 + (-28*x^4 + 8*x^5)*Log[5] + (-7*x^4 + 2*x^5)*
Log[5]^2)*Log[x] + x^8*Log[x]^2)/(64 - 64*x + 16*x^2 + 64*x^4 - 48*x^5 + 8*x^6 + 16*x^8 - 8*x^9 + x^10 + (128
- 128*x + 32*x^2 + 64*x^4 - 48*x^5 + 8*x^6)*Log[5] + (96 - 96*x + 24*x^2 + 16*x^4 - 12*x^5 + 2*x^6)*Log[5]^2 +
(32 - 32*x + 8*x^2)*Log[5]^3 + (4 - 4*x + x^2)*Log[5]^4 + (-16*x^4 + 8*x^5 - 8*x^8 + 2*x^9 + (-16*x^4 + 8*x^5
)*Log[5] + (-4*x^4 + 2*x^5)*Log[5]^2)*Log[x] + x^8*Log[x]^2),x]

[Out]

x - 8*(2 + Log[5])^4*Defer[Int][(4*x^4 - x^5 + 8*(1 + (Log[5]*(4 + Log[5]))/4) - 4*x*(1 + (Log[5]*(4 + Log[5])
)/4) - x^4*Log[x])^(-2), x] + 3*(2 + Log[5])^4*Defer[Int][x/(4*x^4 - x^5 + 8*(1 + (Log[5]*(4 + Log[5]))/4) - 4
*x*(1 + (Log[5]*(4 + Log[5]))/4) - x^4*Log[x])^2, x] - (2 + Log[5])^2*Defer[Int][x^4/(4*x^4 - x^5 + 8*(1 + (Lo
g[5]*(4 + Log[5]))/4) - 4*x*(1 + (Log[5]*(4 + Log[5]))/4) - x^4*Log[x])^2, x] - (2 + Log[5])^2*Defer[Int][x^5/
(4*x^4 - x^5 + 8*(1 + (Log[5]*(4 + Log[5]))/4) - 4*x*(1 + (Log[5]*(4 + Log[5]))/4) - x^4*Log[x])^2, x] + 3*(2
+ Log[5])^2*Defer[Int][(4*x^4 - x^5 + 8*(1 + (Log[5]*(4 + Log[5]))/4) - 4*x*(1 + (Log[5]*(4 + Log[5]))/4) - x^
4*Log[x])^(-1), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {16 x^8-8 x^9+x^{10}+27 x^4 (2+\log (5))^2-16 x^5 (2+\log (5))^2+2 x^6 (2+\log (5))^2+2 (2+\log (5))^4-4 x (2+\log (5))^4+x^2 (2+\log (5))^4+x^4 \left (-8 x^4+2 x^5-7 (2+\log (5))^2+2 x (2+\log (5))^2\right ) \log (x)+x^8 \log ^2(x)}{\left (4 x^4-x^5+2 (2+\log (5))^2-x (2+\log (5))^2-x^4 \log (x)\right )^2} \, dx\\ &=\int \left (1+\frac {(2+\log (5))^2 \left (-x^4-x^5-32 \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )+12 x \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )\right )}{\left (4 x^4-x^5+8 \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )-4 x \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )-x^4 \log (x)\right )^2}+\frac {3 (2+\log (5))^2}{4 x^4-x^5+8 \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )-4 x \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )-x^4 \log (x)}\right ) \, dx\\ &=x+(2+\log (5))^2 \int \frac {-x^4-x^5-32 \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )+12 x \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )}{\left (4 x^4-x^5+8 \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )-4 x \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )-x^4 \log (x)\right )^2} \, dx+\left (3 (2+\log (5))^2\right ) \int \frac {1}{4 x^4-x^5+8 \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )-4 x \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )-x^4 \log (x)} \, dx\\ &=x+(2+\log (5))^2 \int \frac {-x^4-x^5-8 (2+\log (5))^2+3 x (2+\log (5))^2}{\left (4 x^4-x^5+2 (2+\log (5))^2-x (2+\log (5))^2-x^4 \log (x)\right )^2} \, dx+\left (3 (2+\log (5))^2\right ) \int \frac {1}{4 x^4-x^5+8 \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )-4 x \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )-x^4 \log (x)} \, dx\\ &=x+(2+\log (5))^2 \int \left (-\frac {x^4}{\left (4 x^4-x^5+8 \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )-4 x \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )-x^4 \log (x)\right )^2}-\frac {x^5}{\left (4 x^4-x^5+8 \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )-4 x \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )-x^4 \log (x)\right )^2}-\frac {8 (2+\log (5))^2}{\left (4 x^4-x^5+8 \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )-4 x \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )-x^4 \log (x)\right )^2}+\frac {3 x (2+\log (5))^2}{\left (4 x^4-x^5+8 \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )-4 x \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )-x^4 \log (x)\right )^2}\right ) \, dx+\left (3 (2+\log (5))^2\right ) \int \frac {1}{4 x^4-x^5+8 \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )-4 x \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )-x^4 \log (x)} \, dx\\ &=x-(2+\log (5))^2 \int \frac {x^4}{\left (4 x^4-x^5+8 \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )-4 x \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )-x^4 \log (x)\right )^2} \, dx-(2+\log (5))^2 \int \frac {x^5}{\left (4 x^4-x^5+8 \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )-4 x \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )-x^4 \log (x)\right )^2} \, dx+\left (3 (2+\log (5))^2\right ) \int \frac {1}{4 x^4-x^5+8 \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )-4 x \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )-x^4 \log (x)} \, dx+\left (3 (2+\log (5))^4\right ) \int \frac {x}{\left (4 x^4-x^5+8 \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )-4 x \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )-x^4 \log (x)\right )^2} \, dx-\left (8 (2+\log (5))^4\right ) \int \frac {1}{\left (4 x^4-x^5+8 \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )-4 x \left (1+\frac {1}{4} \log (5) (4+\log (5))\right )-x^4 \log (x)\right )^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.10, size = 43, normalized size = 1.79 \begin {gather*} x+\frac {x (2+\log (5))^2}{-4 x^4+x^5-2 (2+\log (5))^2+x (2+\log (5))^2+x^4 \log (x)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(32 - 64*x + 16*x^2 + 108*x^4 - 64*x^5 + 8*x^6 + 16*x^8 - 8*x^9 + x^10 + (64 - 128*x + 32*x^2 + 108*
x^4 - 64*x^5 + 8*x^6)*Log[5] + (48 - 96*x + 24*x^2 + 27*x^4 - 16*x^5 + 2*x^6)*Log[5]^2 + (16 - 32*x + 8*x^2)*L
og[5]^3 + (2 - 4*x + x^2)*Log[5]^4 + (-28*x^4 + 8*x^5 - 8*x^8 + 2*x^9 + (-28*x^4 + 8*x^5)*Log[5] + (-7*x^4 + 2
*x^5)*Log[5]^2)*Log[x] + x^8*Log[x]^2)/(64 - 64*x + 16*x^2 + 64*x^4 - 48*x^5 + 8*x^6 + 16*x^8 - 8*x^9 + x^10 +
(128 - 128*x + 32*x^2 + 64*x^4 - 48*x^5 + 8*x^6)*Log[5] + (96 - 96*x + 24*x^2 + 16*x^4 - 12*x^5 + 2*x^6)*Log[
5]^2 + (32 - 32*x + 8*x^2)*Log[5]^3 + (4 - 4*x + x^2)*Log[5]^4 + (-16*x^4 + 8*x^5 - 8*x^8 + 2*x^9 + (-16*x^4 +
8*x^5)*Log[5] + (-4*x^4 + 2*x^5)*Log[5]^2)*Log[x] + x^8*Log[x]^2),x]

[Out]

x + (x*(2 + Log[5])^2)/(-4*x^4 + x^5 - 2*(2 + Log[5])^2 + x*(2 + Log[5])^2 + x^4*Log[x])

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fricas [B]  time = 0.92, size = 83, normalized size = 3.46 \begin {gather*} \frac {x^{6} + x^{5} \log \relax (x) - 4 \, x^{5} + {\left (x^{2} - x\right )} \log \relax (5)^{2} + 4 \, x^{2} + 4 \, {\left (x^{2} - x\right )} \log \relax (5) - 4 \, x}{x^{5} + x^{4} \log \relax (x) - 4 \, x^{4} + {\left (x - 2\right )} \log \relax (5)^{2} + 4 \, {\left (x - 2\right )} \log \relax (5) + 4 \, x - 8} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x^8*log(x)^2+((2*x^5-7*x^4)*log(5)^2+(8*x^5-28*x^4)*log(5)+2*x^9-8*x^8+8*x^5-28*x^4)*log(x)+(x^2-4*
x+2)*log(5)^4+(8*x^2-32*x+16)*log(5)^3+(2*x^6-16*x^5+27*x^4+24*x^2-96*x+48)*log(5)^2+(8*x^6-64*x^5+108*x^4+32*
x^2-128*x+64)*log(5)+x^10-8*x^9+16*x^8+8*x^6-64*x^5+108*x^4+16*x^2-64*x+32)/(x^8*log(x)^2+((2*x^5-4*x^4)*log(5
)^2+(8*x^5-16*x^4)*log(5)+2*x^9-8*x^8+8*x^5-16*x^4)*log(x)+(x^2-4*x+4)*log(5)^4+(8*x^2-32*x+32)*log(5)^3+(2*x^
6-12*x^5+16*x^4+24*x^2-96*x+96)*log(5)^2+(8*x^6-48*x^5+64*x^4+32*x^2-128*x+128)*log(5)+x^10-8*x^9+16*x^8+8*x^6
-48*x^5+64*x^4+16*x^2-64*x+64),x, algorithm="fricas")

[Out]

(x^6 + x^5*log(x) - 4*x^5 + (x^2 - x)*log(5)^2 + 4*x^2 + 4*(x^2 - x)*log(5) - 4*x)/(x^5 + x^4*log(x) - 4*x^4 +
(x - 2)*log(5)^2 + 4*(x - 2)*log(5) + 4*x - 8)

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giac [B]  time = 0.26, size = 60, normalized size = 2.50 \begin {gather*} x + \frac {x \log \relax (5)^{2} + 4 \, x \log \relax (5) + 4 \, x}{x^{5} + x^{4} \log \relax (x) - 4 \, x^{4} + x \log \relax (5)^{2} + 4 \, x \log \relax (5) - 2 \, \log \relax (5)^{2} + 4 \, x - 8 \, \log \relax (5) - 8} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x^8*log(x)^2+((2*x^5-7*x^4)*log(5)^2+(8*x^5-28*x^4)*log(5)+2*x^9-8*x^8+8*x^5-28*x^4)*log(x)+(x^2-4*
x+2)*log(5)^4+(8*x^2-32*x+16)*log(5)^3+(2*x^6-16*x^5+27*x^4+24*x^2-96*x+48)*log(5)^2+(8*x^6-64*x^5+108*x^4+32*
x^2-128*x+64)*log(5)+x^10-8*x^9+16*x^8+8*x^6-64*x^5+108*x^4+16*x^2-64*x+32)/(x^8*log(x)^2+((2*x^5-4*x^4)*log(5
)^2+(8*x^5-16*x^4)*log(5)+2*x^9-8*x^8+8*x^5-16*x^4)*log(x)+(x^2-4*x+4)*log(5)^4+(8*x^2-32*x+32)*log(5)^3+(2*x^
6-12*x^5+16*x^4+24*x^2-96*x+96)*log(5)^2+(8*x^6-48*x^5+64*x^4+32*x^2-128*x+128)*log(5)+x^10-8*x^9+16*x^8+8*x^6
-48*x^5+64*x^4+16*x^2-64*x+64),x, algorithm="giac")

[Out]

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

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maple [B]  time = 0.04, size = 57, normalized size = 2.38

method	result	size
risch	\(x +\frac {\left (\ln \relax (5)^{2}+4 \ln \relax (5)+4\right ) x}{x^{4} \ln \relax (x )+x^{5}-4 x^{4}+x \ln \relax (5)^{2}-2 \ln \relax (5)^{2}+4 x \ln \relax (5)-8 \ln \relax (5)+4 x -8}\)	\(57\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((x^8*ln(x)^2+((2*x^5-7*x^4)*ln(5)^2+(8*x^5-28*x^4)*ln(5)+2*x^9-8*x^8+8*x^5-28*x^4)*ln(x)+(x^2-4*x+2)*ln(5)
^4+(8*x^2-32*x+16)*ln(5)^3+(2*x^6-16*x^5+27*x^4+24*x^2-96*x+48)*ln(5)^2+(8*x^6-64*x^5+108*x^4+32*x^2-128*x+64)
*ln(5)+x^10-8*x^9+16*x^8+8*x^6-64*x^5+108*x^4+16*x^2-64*x+32)/(x^8*ln(x)^2+((2*x^5-4*x^4)*ln(5)^2+(8*x^5-16*x^
4)*ln(5)+2*x^9-8*x^8+8*x^5-16*x^4)*ln(x)+(x^2-4*x+4)*ln(5)^4+(8*x^2-32*x+32)*ln(5)^3+(2*x^6-12*x^5+16*x^4+24*x
^2-96*x+96)*ln(5)^2+(8*x^6-48*x^5+64*x^4+32*x^2-128*x+128)*ln(5)+x^10-8*x^9+16*x^8+8*x^6-48*x^5+64*x^4+16*x^2-
64*x+64),x,method=_RETURNVERBOSE)

[Out]

x+(ln(5)^2+4*ln(5)+4)*x/(x^4*ln(x)+x^5-4*x^4+x*ln(5)^2-2*ln(5)^2+4*x*ln(5)-8*ln(5)+4*x-8)

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maxima [B]  time = 0.49, size = 83, normalized size = 3.46 \begin {gather*} \frac {x^{6} + x^{5} \log \relax (x) - 4 \, x^{5} + {\left (\log \relax (5)^{2} + 4 \, \log \relax (5) + 4\right )} x^{2} - {\left (\log \relax (5)^{2} + 4 \, \log \relax (5) + 4\right )} x}{x^{5} + x^{4} \log \relax (x) - 4 \, x^{4} + {\left (\log \relax (5)^{2} + 4 \, \log \relax (5) + 4\right )} x - 2 \, \log \relax (5)^{2} - 8 \, \log \relax (5) - 8} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x^8*log(x)^2+((2*x^5-7*x^4)*log(5)^2+(8*x^5-28*x^4)*log(5)+2*x^9-8*x^8+8*x^5-28*x^4)*log(x)+(x^2-4*
x+2)*log(5)^4+(8*x^2-32*x+16)*log(5)^3+(2*x^6-16*x^5+27*x^4+24*x^2-96*x+48)*log(5)^2+(8*x^6-64*x^5+108*x^4+32*
x^2-128*x+64)*log(5)+x^10-8*x^9+16*x^8+8*x^6-64*x^5+108*x^4+16*x^2-64*x+32)/(x^8*log(x)^2+((2*x^5-4*x^4)*log(5
)^2+(8*x^5-16*x^4)*log(5)+2*x^9-8*x^8+8*x^5-16*x^4)*log(x)+(x^2-4*x+4)*log(5)^4+(8*x^2-32*x+32)*log(5)^3+(2*x^
6-12*x^5+16*x^4+24*x^2-96*x+96)*log(5)^2+(8*x^6-48*x^5+64*x^4+32*x^2-128*x+128)*log(5)+x^10-8*x^9+16*x^8+8*x^6
-48*x^5+64*x^4+16*x^2-64*x+64),x, algorithm="maxima")

[Out]

(x^6 + x^5*log(x) - 4*x^5 + (log(5)^2 + 4*log(5) + 4)*x^2 - (log(5)^2 + 4*log(5) + 4)*x)/(x^5 + x^4*log(x) - 4
*x^4 + (log(5)^2 + 4*log(5) + 4)*x - 2*log(5)^2 - 8*log(5) - 8)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {{\ln \relax (5)}^4\,\left (x^2-4\,x+2\right )-\ln \relax (x)\,\left (\ln \relax (5)\,\left (28\,x^4-8\,x^5\right )+28\,x^4-8\,x^5+8\,x^8-2\,x^9+{\ln \relax (5)}^2\,\left (7\,x^4-2\,x^5\right )\right )-64\,x+{\ln \relax (5)}^2\,\left (2\,x^6-16\,x^5+27\,x^4+24\,x^2-96\,x+48\right )+x^8\,{\ln \relax (x)}^2+{\ln \relax (5)}^3\,\left (8\,x^2-32\,x+16\right )+16\,x^2+108\,x^4-64\,x^5+8\,x^6+16\,x^8-8\,x^9+x^{10}+\ln \relax (5)\,\left (8\,x^6-64\,x^5+108\,x^4+32\,x^2-128\,x+64\right )+32}{{\ln \relax (5)}^4\,\left (x^2-4\,x+4\right )-\ln \relax (x)\,\left (\ln \relax (5)\,\left (16\,x^4-8\,x^5\right )+16\,x^4-8\,x^5+8\,x^8-2\,x^9+{\ln \relax (5)}^2\,\left (4\,x^4-2\,x^5\right )\right )-64\,x+{\ln \relax (5)}^2\,\left (2\,x^6-12\,x^5+16\,x^4+24\,x^2-96\,x+96\right )+x^8\,{\ln \relax (x)}^2+{\ln \relax (5)}^3\,\left (8\,x^2-32\,x+32\right )+16\,x^2+64\,x^4-48\,x^5+8\,x^6+16\,x^8-8\,x^9+x^{10}+\ln \relax (5)\,\left (8\,x^6-48\,x^5+64\,x^4+32\,x^2-128\,x+128\right )+64} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(5)^4*(x^2 - 4*x + 2) - log(x)*(log(5)*(28*x^4 - 8*x^5) + 28*x^4 - 8*x^5 + 8*x^8 - 2*x^9 + log(5)^2*(7
*x^4 - 2*x^5)) - 64*x + log(5)^2*(24*x^2 - 96*x + 27*x^4 - 16*x^5 + 2*x^6 + 48) + x^8*log(x)^2 + log(5)^3*(8*x
^2 - 32*x + 16) + 16*x^2 + 108*x^4 - 64*x^5 + 8*x^6 + 16*x^8 - 8*x^9 + x^10 + log(5)*(32*x^2 - 128*x + 108*x^4
- 64*x^5 + 8*x^6 + 64) + 32)/(log(5)^4*(x^2 - 4*x + 4) - log(x)*(log(5)*(16*x^4 - 8*x^5) + 16*x^4 - 8*x^5 + 8
*x^8 - 2*x^9 + log(5)^2*(4*x^4 - 2*x^5)) - 64*x + log(5)^2*(24*x^2 - 96*x + 16*x^4 - 12*x^5 + 2*x^6 + 96) + x^
8*log(x)^2 + log(5)^3*(8*x^2 - 32*x + 32) + 16*x^2 + 64*x^4 - 48*x^5 + 8*x^6 + 16*x^8 - 8*x^9 + x^10 + log(5)*
(32*x^2 - 128*x + 64*x^4 - 48*x^5 + 8*x^6 + 128) + 64),x)

[Out]

int((log(5)^4*(x^2 - 4*x + 2) - log(x)*(log(5)*(28*x^4 - 8*x^5) + 28*x^4 - 8*x^5 + 8*x^8 - 2*x^9 + log(5)^2*(7
*x^4 - 2*x^5)) - 64*x + log(5)^2*(24*x^2 - 96*x + 27*x^4 - 16*x^5 + 2*x^6 + 48) + x^8*log(x)^2 + log(5)^3*(8*x
^2 - 32*x + 16) + 16*x^2 + 108*x^4 - 64*x^5 + 8*x^6 + 16*x^8 - 8*x^9 + x^10 + log(5)*(32*x^2 - 128*x + 108*x^4
- 64*x^5 + 8*x^6 + 64) + 32)/(log(5)^4*(x^2 - 4*x + 4) - log(x)*(log(5)*(16*x^4 - 8*x^5) + 16*x^4 - 8*x^5 + 8
*x^8 - 2*x^9 + log(5)^2*(4*x^4 - 2*x^5)) - 64*x + log(5)^2*(24*x^2 - 96*x + 16*x^4 - 12*x^5 + 2*x^6 + 96) + x^
8*log(x)^2 + log(5)^3*(8*x^2 - 32*x + 32) + 16*x^2 + 64*x^4 - 48*x^5 + 8*x^6 + 16*x^8 - 8*x^9 + x^10 + log(5)*
(32*x^2 - 128*x + 64*x^4 - 48*x^5 + 8*x^6 + 128) + 64), x)

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sympy [B]  time = 0.49, size = 63, normalized size = 2.62 \begin {gather*} x + \frac {x \log {\relax (5 )}^{2} + 4 x + 4 x \log {\relax (5 )}}{x^{5} + x^{4} \log {\relax (x )} - 4 x^{4} + x \log {\relax (5 )}^{2} + 4 x + 4 x \log {\relax (5 )} - 8 \log {\relax (5 )} - 8 - 2 \log {\relax (5 )}^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x**8*ln(x)**2+((2*x**5-7*x**4)*ln(5)**2+(8*x**5-28*x**4)*ln(5)+2*x**9-8*x**8+8*x**5-28*x**4)*ln(x)+
(x**2-4*x+2)*ln(5)**4+(8*x**2-32*x+16)*ln(5)**3+(2*x**6-16*x**5+27*x**4+24*x**2-96*x+48)*ln(5)**2+(8*x**6-64*x
**5+108*x**4+32*x**2-128*x+64)*ln(5)+x**10-8*x**9+16*x**8+8*x**6-64*x**5+108*x**4+16*x**2-64*x+32)/(x**8*ln(x)
**2+((2*x**5-4*x**4)*ln(5)**2+(8*x**5-16*x**4)*ln(5)+2*x**9-8*x**8+8*x**5-16*x**4)*ln(x)+(x**2-4*x+4)*ln(5)**4
+(8*x**2-32*x+32)*ln(5)**3+(2*x**6-12*x**5+16*x**4+24*x**2-96*x+96)*ln(5)**2+(8*x**6-48*x**5+64*x**4+32*x**2-1
28*x+128)*ln(5)+x**10-8*x**9+16*x**8+8*x**6-48*x**5+64*x**4+16*x**2-64*x+64),x)

[Out]

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

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