3.98.37 \(\int \frac {1853 x-7252 x^2+10252 x^3-5952 x^4+1508 x^5+784 x^6-1856 x^7+768 x^8+(2890-7752 x+10312 x^2-10688 x^3+8296 x^4-4448 x^5+1920 x^6-512 x^7) \log (x)+(408 x-3784 x^2+8880 x^3-9488 x^4+6848 x^5-3840 x^6+1024 x^7) \log ^2(x)}{-500 x+200 x^2+940 x^3-464 x^4-448 x^5+256 x^6+(-1000 x+1400 x^2+480 x^3-1408 x^4+512 x^5) \log ^2(x)+(-500 x+1200 x^2-960 x^3+256 x^4) \log ^4(x)} \, dx\)

Optimal. Leaf size=38 \[ \frac {\left (-2+\frac {1}{2 \left (\frac {5-x}{3}-x\right )}-x^2\right )^2}{1+x+\log ^2(x)} \]

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Rubi [F]  time = 6.27, 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 {1853 x-7252 x^2+10252 x^3-5952 x^4+1508 x^5+784 x^6-1856 x^7+768 x^8+\left (2890-7752 x+10312 x^2-10688 x^3+8296 x^4-4448 x^5+1920 x^6-512 x^7\right ) \log (x)+\left (408 x-3784 x^2+8880 x^3-9488 x^4+6848 x^5-3840 x^6+1024 x^7\right ) \log ^2(x)}{-500 x+200 x^2+940 x^3-464 x^4-448 x^5+256 x^6+\left (-1000 x+1400 x^2+480 x^3-1408 x^4+512 x^5\right ) \log ^2(x)+\left (-500 x+1200 x^2-960 x^3+256 x^4\right ) \log ^4(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(1853*x - 7252*x^2 + 10252*x^3 - 5952*x^4 + 1508*x^5 + 784*x^6 - 1856*x^7 + 768*x^8 + (2890 - 7752*x + 103
12*x^2 - 10688*x^3 + 8296*x^4 - 4448*x^5 + 1920*x^6 - 512*x^7)*Log[x] + (408*x - 3784*x^2 + 8880*x^3 - 9488*x^
4 + 6848*x^5 - 3840*x^6 + 1024*x^7)*Log[x]^2)/(-500*x + 200*x^2 + 940*x^3 - 464*x^4 - 448*x^5 + 256*x^6 + (-10
00*x + 1400*x^2 + 480*x^3 - 1408*x^4 + 512*x^5)*Log[x]^2 + (-500*x + 1200*x^2 - 960*x^3 + 256*x^4)*Log[x]^4),x
]

[Out]

289/(100*(1 + x + Log[x]^2)) - (819*Defer[Int][(1 + x + Log[x]^2)^(-2), x])/400 - (3*Defer[Int][x/(1 + x + Log
[x]^2)^2, x])/4 - 4*Defer[Int][x^2/(1 + x + Log[x]^2)^2, x] - Defer[Int][x^4/(1 + x + Log[x]^2)^2, x] - (9*Def
er[Int][1/((-5 + 4*x)^2*(1 + x + Log[x]^2)^2), x])/4 - (171*Defer[Int][1/((-5 + 4*x)*(1 + x + Log[x]^2)^2), x]
)/16 - (3*Defer[Int][Log[x]/(1 + x + Log[x]^2)^2, x])/2 - 8*Defer[Int][(x*Log[x])/(1 + x + Log[x]^2)^2, x] - 2
*Defer[Int][(x^3*Log[x])/(1 + x + Log[x]^2)^2, x] - (18*Defer[Int][Log[x]/((-5 + 4*x)^2*(1 + x + Log[x]^2)^2),
x])/5 - (819*Defer[Int][Log[x]/((-5 + 4*x)*(1 + x + Log[x]^2)^2), x])/50 + (3*Defer[Int][(1 + x + Log[x]^2)^(
-1), x])/4 + 8*Defer[Int][x/(1 + x + Log[x]^2), x] + 4*Defer[Int][x^3/(1 + x + Log[x]^2), x] - 18*Defer[Int][1
/((-5 + 4*x)^3*(1 + x + Log[x]^2)), x] - (171*Defer[Int][1/((-5 + 4*x)^2*(1 + x + Log[x]^2)), x])/4

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\left (17-16 x+10 x^2-8 x^3\right ) \left (x \left (-109+324 x-234 x^2-112 x^3+96 x^4\right )-2 \left (85-148 x+114 x^2-80 x^3+32 x^4\right ) \log (x)+8 x \left (-3+25 x-40 x^2+16 x^3\right ) \log ^2(x)\right )}{4 (5-4 x)^3 x \left (1+x+\log ^2(x)\right )^2} \, dx\\ &=\frac {1}{4} \int \frac {\left (17-16 x+10 x^2-8 x^3\right ) \left (x \left (-109+324 x-234 x^2-112 x^3+96 x^4\right )-2 \left (85-148 x+114 x^2-80 x^3+32 x^4\right ) \log (x)+8 x \left (-3+25 x-40 x^2+16 x^3\right ) \log ^2(x)\right )}{(5-4 x)^3 x \left (1+x+\log ^2(x)\right )^2} \, dx\\ &=\frac {1}{4} \int \left (-\frac {\left (-17+16 x-10 x^2+8 x^3\right )^2 (x+2 \log (x))}{x (-5+4 x)^2 \left (1+x+\log ^2(x)\right )^2}+\frac {8 \left (51-473 x+1110 x^2-1186 x^3+856 x^4-480 x^5+128 x^6\right )}{(-5+4 x)^3 \left (1+x+\log ^2(x)\right )}\right ) \, dx\\ &=-\left (\frac {1}{4} \int \frac {\left (-17+16 x-10 x^2+8 x^3\right )^2 (x+2 \log (x))}{x (-5+4 x)^2 \left (1+x+\log ^2(x)\right )^2} \, dx\right )+2 \int \frac {51-473 x+1110 x^2-1186 x^3+856 x^4-480 x^5+128 x^6}{(-5+4 x)^3 \left (1+x+\log ^2(x)\right )} \, dx\\ &=-\left (\frac {1}{4} \int \left (\frac {3 (x+2 \log (x))}{\left (1+x+\log ^2(x)\right )^2}+\frac {289 (x+2 \log (x))}{25 x \left (1+x+\log ^2(x)\right )^2}+\frac {16 x (x+2 \log (x))}{\left (1+x+\log ^2(x)\right )^2}+\frac {4 x^3 (x+2 \log (x))}{\left (1+x+\log ^2(x)\right )^2}+\frac {36 (x+2 \log (x))}{5 (-5+4 x)^2 \left (1+x+\log ^2(x)\right )^2}+\frac {819 (x+2 \log (x))}{25 (-5+4 x) \left (1+x+\log ^2(x)\right )^2}\right ) \, dx\right )+2 \int \left (\frac {3}{8 \left (1+x+\log ^2(x)\right )}+\frac {4 x}{1+x+\log ^2(x)}+\frac {2 x^3}{1+x+\log ^2(x)}-\frac {9}{(-5+4 x)^3 \left (1+x+\log ^2(x)\right )}-\frac {171}{8 (-5+4 x)^2 \left (1+x+\log ^2(x)\right )}\right ) \, dx\\ &=-\left (\frac {3}{4} \int \frac {x+2 \log (x)}{\left (1+x+\log ^2(x)\right )^2} \, dx\right )+\frac {3}{4} \int \frac {1}{1+x+\log ^2(x)} \, dx-\frac {9}{5} \int \frac {x+2 \log (x)}{(-5+4 x)^2 \left (1+x+\log ^2(x)\right )^2} \, dx-\frac {289}{100} \int \frac {x+2 \log (x)}{x \left (1+x+\log ^2(x)\right )^2} \, dx-4 \int \frac {x (x+2 \log (x))}{\left (1+x+\log ^2(x)\right )^2} \, dx+4 \int \frac {x^3}{1+x+\log ^2(x)} \, dx+8 \int \frac {x}{1+x+\log ^2(x)} \, dx-\frac {819}{100} \int \frac {x+2 \log (x)}{(-5+4 x) \left (1+x+\log ^2(x)\right )^2} \, dx-18 \int \frac {1}{(-5+4 x)^3 \left (1+x+\log ^2(x)\right )} \, dx-\frac {171}{4} \int \frac {1}{(-5+4 x)^2 \left (1+x+\log ^2(x)\right )} \, dx-\int \frac {x^3 (x+2 \log (x))}{\left (1+x+\log ^2(x)\right )^2} \, dx\\ &=\frac {289}{100 \left (1+x+\log ^2(x)\right )}+\frac {3}{4} \int \frac {1}{1+x+\log ^2(x)} \, dx-\frac {3}{4} \int \left (\frac {x}{\left (1+x+\log ^2(x)\right )^2}+\frac {2 \log (x)}{\left (1+x+\log ^2(x)\right )^2}\right ) \, dx-\frac {9}{5} \int \left (\frac {x}{(-5+4 x)^2 \left (1+x+\log ^2(x)\right )^2}+\frac {2 \log (x)}{(-5+4 x)^2 \left (1+x+\log ^2(x)\right )^2}\right ) \, dx+4 \int \frac {x^3}{1+x+\log ^2(x)} \, dx-4 \int \left (\frac {x^2}{\left (1+x+\log ^2(x)\right )^2}+\frac {2 x \log (x)}{\left (1+x+\log ^2(x)\right )^2}\right ) \, dx+8 \int \frac {x}{1+x+\log ^2(x)} \, dx-\frac {819}{100} \int \left (\frac {x}{(-5+4 x) \left (1+x+\log ^2(x)\right )^2}+\frac {2 \log (x)}{(-5+4 x) \left (1+x+\log ^2(x)\right )^2}\right ) \, dx-18 \int \frac {1}{(-5+4 x)^3 \left (1+x+\log ^2(x)\right )} \, dx-\frac {171}{4} \int \frac {1}{(-5+4 x)^2 \left (1+x+\log ^2(x)\right )} \, dx-\int \left (\frac {x^4}{\left (1+x+\log ^2(x)\right )^2}+\frac {2 x^3 \log (x)}{\left (1+x+\log ^2(x)\right )^2}\right ) \, dx\\ &=\frac {289}{100 \left (1+x+\log ^2(x)\right )}-\frac {3}{4} \int \frac {x}{\left (1+x+\log ^2(x)\right )^2} \, dx+\frac {3}{4} \int \frac {1}{1+x+\log ^2(x)} \, dx-\frac {3}{2} \int \frac {\log (x)}{\left (1+x+\log ^2(x)\right )^2} \, dx-\frac {9}{5} \int \frac {x}{(-5+4 x)^2 \left (1+x+\log ^2(x)\right )^2} \, dx-2 \int \frac {x^3 \log (x)}{\left (1+x+\log ^2(x)\right )^2} \, dx-\frac {18}{5} \int \frac {\log (x)}{(-5+4 x)^2 \left (1+x+\log ^2(x)\right )^2} \, dx-4 \int \frac {x^2}{\left (1+x+\log ^2(x)\right )^2} \, dx+4 \int \frac {x^3}{1+x+\log ^2(x)} \, dx-8 \int \frac {x \log (x)}{\left (1+x+\log ^2(x)\right )^2} \, dx+8 \int \frac {x}{1+x+\log ^2(x)} \, dx-\frac {819}{100} \int \frac {x}{(-5+4 x) \left (1+x+\log ^2(x)\right )^2} \, dx-\frac {819}{50} \int \frac {\log (x)}{(-5+4 x) \left (1+x+\log ^2(x)\right )^2} \, dx-18 \int \frac {1}{(-5+4 x)^3 \left (1+x+\log ^2(x)\right )} \, dx-\frac {171}{4} \int \frac {1}{(-5+4 x)^2 \left (1+x+\log ^2(x)\right )} \, dx-\int \frac {x^4}{\left (1+x+\log ^2(x)\right )^2} \, dx\\ &=\frac {289}{100 \left (1+x+\log ^2(x)\right )}-\frac {3}{4} \int \frac {x}{\left (1+x+\log ^2(x)\right )^2} \, dx+\frac {3}{4} \int \frac {1}{1+x+\log ^2(x)} \, dx-\frac {3}{2} \int \frac {\log (x)}{\left (1+x+\log ^2(x)\right )^2} \, dx-\frac {9}{5} \int \left (\frac {5}{4 (-5+4 x)^2 \left (1+x+\log ^2(x)\right )^2}+\frac {1}{4 (-5+4 x) \left (1+x+\log ^2(x)\right )^2}\right ) \, dx-2 \int \frac {x^3 \log (x)}{\left (1+x+\log ^2(x)\right )^2} \, dx-\frac {18}{5} \int \frac {\log (x)}{(-5+4 x)^2 \left (1+x+\log ^2(x)\right )^2} \, dx-4 \int \frac {x^2}{\left (1+x+\log ^2(x)\right )^2} \, dx+4 \int \frac {x^3}{1+x+\log ^2(x)} \, dx-8 \int \frac {x \log (x)}{\left (1+x+\log ^2(x)\right )^2} \, dx+8 \int \frac {x}{1+x+\log ^2(x)} \, dx-\frac {819}{100} \int \left (\frac {1}{4 \left (1+x+\log ^2(x)\right )^2}+\frac {5}{4 (-5+4 x) \left (1+x+\log ^2(x)\right )^2}\right ) \, dx-\frac {819}{50} \int \frac {\log (x)}{(-5+4 x) \left (1+x+\log ^2(x)\right )^2} \, dx-18 \int \frac {1}{(-5+4 x)^3 \left (1+x+\log ^2(x)\right )} \, dx-\frac {171}{4} \int \frac {1}{(-5+4 x)^2 \left (1+x+\log ^2(x)\right )} \, dx-\int \frac {x^4}{\left (1+x+\log ^2(x)\right )^2} \, dx\\ &=\frac {289}{100 \left (1+x+\log ^2(x)\right )}-\frac {9}{20} \int \frac {1}{(-5+4 x) \left (1+x+\log ^2(x)\right )^2} \, dx-\frac {3}{4} \int \frac {x}{\left (1+x+\log ^2(x)\right )^2} \, dx+\frac {3}{4} \int \frac {1}{1+x+\log ^2(x)} \, dx-\frac {3}{2} \int \frac {\log (x)}{\left (1+x+\log ^2(x)\right )^2} \, dx-2 \int \frac {x^3 \log (x)}{\left (1+x+\log ^2(x)\right )^2} \, dx-\frac {819}{400} \int \frac {1}{\left (1+x+\log ^2(x)\right )^2} \, dx-\frac {9}{4} \int \frac {1}{(-5+4 x)^2 \left (1+x+\log ^2(x)\right )^2} \, dx-\frac {18}{5} \int \frac {\log (x)}{(-5+4 x)^2 \left (1+x+\log ^2(x)\right )^2} \, dx-4 \int \frac {x^2}{\left (1+x+\log ^2(x)\right )^2} \, dx+4 \int \frac {x^3}{1+x+\log ^2(x)} \, dx-8 \int \frac {x \log (x)}{\left (1+x+\log ^2(x)\right )^2} \, dx+8 \int \frac {x}{1+x+\log ^2(x)} \, dx-\frac {819}{80} \int \frac {1}{(-5+4 x) \left (1+x+\log ^2(x)\right )^2} \, dx-\frac {819}{50} \int \frac {\log (x)}{(-5+4 x) \left (1+x+\log ^2(x)\right )^2} \, dx-18 \int \frac {1}{(-5+4 x)^3 \left (1+x+\log ^2(x)\right )} \, dx-\frac {171}{4} \int \frac {1}{(-5+4 x)^2 \left (1+x+\log ^2(x)\right )} \, dx-\int \frac {x^4}{\left (1+x+\log ^2(x)\right )^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.07, size = 37, normalized size = 0.97 \begin {gather*} \frac {\left (17-16 x+10 x^2-8 x^3\right )^2}{4 (5-4 x)^2 \left (1+x+\log ^2(x)\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(1853*x - 7252*x^2 + 10252*x^3 - 5952*x^4 + 1508*x^5 + 784*x^6 - 1856*x^7 + 768*x^8 + (2890 - 7752*x
+ 10312*x^2 - 10688*x^3 + 8296*x^4 - 4448*x^5 + 1920*x^6 - 512*x^7)*Log[x] + (408*x - 3784*x^2 + 8880*x^3 - 9
488*x^4 + 6848*x^5 - 3840*x^6 + 1024*x^7)*Log[x]^2)/(-500*x + 200*x^2 + 940*x^3 - 464*x^4 - 448*x^5 + 256*x^6
+ (-1000*x + 1400*x^2 + 480*x^3 - 1408*x^4 + 512*x^5)*Log[x]^2 + (-500*x + 1200*x^2 - 960*x^3 + 256*x^4)*Log[x
]^4),x]

[Out]

(17 - 16*x + 10*x^2 - 8*x^3)^2/(4*(5 - 4*x)^2*(1 + x + Log[x]^2))

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fricas [B]  time = 0.51, size = 64, normalized size = 1.68 \begin {gather*} \frac {64 \, x^{6} - 160 \, x^{5} + 356 \, x^{4} - 592 \, x^{3} + 596 \, x^{2} - 544 \, x + 289}{4 \, {\left (16 \, x^{3} + {\left (16 \, x^{2} - 40 \, x + 25\right )} \log \relax (x)^{2} - 24 \, x^{2} - 15 \, x + 25\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((1024*x^7-3840*x^6+6848*x^5-9488*x^4+8880*x^3-3784*x^2+408*x)*log(x)^2+(-512*x^7+1920*x^6-4448*x^5+
8296*x^4-10688*x^3+10312*x^2-7752*x+2890)*log(x)+768*x^8-1856*x^7+784*x^6+1508*x^5-5952*x^4+10252*x^3-7252*x^2
+1853*x)/((256*x^4-960*x^3+1200*x^2-500*x)*log(x)^4+(512*x^5-1408*x^4+480*x^3+1400*x^2-1000*x)*log(x)^2+256*x^
6-448*x^5-464*x^4+940*x^3+200*x^2-500*x),x, algorithm="fricas")

[Out]

1/4*(64*x^6 - 160*x^5 + 356*x^4 - 592*x^3 + 596*x^2 - 544*x + 289)/(16*x^3 + (16*x^2 - 40*x + 25)*log(x)^2 - 2
4*x^2 - 15*x + 25)

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giac [B]  time = 0.22, size = 71, normalized size = 1.87 \begin {gather*} \frac {64 \, x^{6} - 160 \, x^{5} + 356 \, x^{4} - 592 \, x^{3} + 596 \, x^{2} - 544 \, x + 289}{4 \, {\left (16 \, x^{2} \log \relax (x)^{2} + 16 \, x^{3} - 40 \, x \log \relax (x)^{2} - 24 \, x^{2} + 25 \, \log \relax (x)^{2} - 15 \, x + 25\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((1024*x^7-3840*x^6+6848*x^5-9488*x^4+8880*x^3-3784*x^2+408*x)*log(x)^2+(-512*x^7+1920*x^6-4448*x^5+
8296*x^4-10688*x^3+10312*x^2-7752*x+2890)*log(x)+768*x^8-1856*x^7+784*x^6+1508*x^5-5952*x^4+10252*x^3-7252*x^2
+1853*x)/((256*x^4-960*x^3+1200*x^2-500*x)*log(x)^4+(512*x^5-1408*x^4+480*x^3+1400*x^2-1000*x)*log(x)^2+256*x^
6-448*x^5-464*x^4+940*x^3+200*x^2-500*x),x, algorithm="giac")

[Out]

1/4*(64*x^6 - 160*x^5 + 356*x^4 - 592*x^3 + 596*x^2 - 544*x + 289)/(16*x^2*log(x)^2 + 16*x^3 - 40*x*log(x)^2 -
24*x^2 + 25*log(x)^2 - 15*x + 25)

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maple [B]  time = 0.04, size = 54, normalized size = 1.42

method	result	size
risch	\(\frac {64 x^{6}-160 x^{5}+356 x^{4}-592 x^{3}+596 x^{2}-544 x +289}{4 \left (16 x^{2}-40 x +25\right ) \left (x +\ln \relax (x )^{2}+1\right )}\)	\(54\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((1024*x^7-3840*x^6+6848*x^5-9488*x^4+8880*x^3-3784*x^2+408*x)*ln(x)^2+(-512*x^7+1920*x^6-4448*x^5+8296*x^
4-10688*x^3+10312*x^2-7752*x+2890)*ln(x)+768*x^8-1856*x^7+784*x^6+1508*x^5-5952*x^4+10252*x^3-7252*x^2+1853*x)
/((256*x^4-960*x^3+1200*x^2-500*x)*ln(x)^4+(512*x^5-1408*x^4+480*x^3+1400*x^2-1000*x)*ln(x)^2+256*x^6-448*x^5-
464*x^4+940*x^3+200*x^2-500*x),x,method=_RETURNVERBOSE)

[Out]

1/4*(64*x^6-160*x^5+356*x^4-592*x^3+596*x^2-544*x+289)/(16*x^2-40*x+25)/(x+ln(x)^2+1)

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maxima [B]  time = 0.40, size = 64, normalized size = 1.68 \begin {gather*} \frac {64 \, x^{6} - 160 \, x^{5} + 356 \, x^{4} - 592 \, x^{3} + 596 \, x^{2} - 544 \, x + 289}{4 \, {\left (16 \, x^{3} + {\left (16 \, x^{2} - 40 \, x + 25\right )} \log \relax (x)^{2} - 24 \, x^{2} - 15 \, x + 25\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((1024*x^7-3840*x^6+6848*x^5-9488*x^4+8880*x^3-3784*x^2+408*x)*log(x)^2+(-512*x^7+1920*x^6-4448*x^5+
8296*x^4-10688*x^3+10312*x^2-7752*x+2890)*log(x)+768*x^8-1856*x^7+784*x^6+1508*x^5-5952*x^4+10252*x^3-7252*x^2
+1853*x)/((256*x^4-960*x^3+1200*x^2-500*x)*log(x)^4+(512*x^5-1408*x^4+480*x^3+1400*x^2-1000*x)*log(x)^2+256*x^
6-448*x^5-464*x^4+940*x^3+200*x^2-500*x),x, algorithm="maxima")

[Out]

1/4*(64*x^6 - 160*x^5 + 356*x^4 - 592*x^3 + 596*x^2 - 544*x + 289)/(16*x^3 + (16*x^2 - 40*x + 25)*log(x)^2 - 2
4*x^2 - 15*x + 25)

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mupad [B]  time = 6.14, size = 81, normalized size = 2.13 \begin {gather*} -\frac {-64\,x^{10}-16\,x^9+148\,x^8-227\,x^7+588\,x^6+93\,x^5-1157\,x^4+\frac {6565\,x^3}{4}-2431\,x^2+1445\,x}{{\left (4\,x-5\right )}^3\,\left ({\ln \relax (x)}^2+x+1\right )\,\left (x^3+4\,x^2+4\,x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(1853*x + log(x)^2*(408*x - 3784*x^2 + 8880*x^3 - 9488*x^4 + 6848*x^5 - 3840*x^6 + 1024*x^7) - log(x)*(77
52*x - 10312*x^2 + 10688*x^3 - 8296*x^4 + 4448*x^5 - 1920*x^6 + 512*x^7 - 2890) - 7252*x^2 + 10252*x^3 - 5952*
x^4 + 1508*x^5 + 784*x^6 - 1856*x^7 + 768*x^8)/(500*x + log(x)^4*(500*x - 1200*x^2 + 960*x^3 - 256*x^4) - log(
x)^2*(1400*x^2 - 1000*x + 480*x^3 - 1408*x^4 + 512*x^5) - 200*x^2 - 940*x^3 + 464*x^4 + 448*x^5 - 256*x^6),x)

[Out]

-(1445*x - 2431*x^2 + (6565*x^3)/4 - 1157*x^4 + 93*x^5 + 588*x^6 - 227*x^7 + 148*x^8 - 16*x^9 - 64*x^10)/((4*x
- 5)^3*(x + log(x)^2 + 1)*(4*x + 4*x^2 + x^3))

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sympy [B]  time = 0.30, size = 60, normalized size = 1.58 \begin {gather*} \frac {64 x^{6} - 160 x^{5} + 356 x^{4} - 592 x^{3} + 596 x^{2} - 544 x + 289}{64 x^{3} - 96 x^{2} - 60 x + \left (64 x^{2} - 160 x + 100\right ) \log {\relax (x )}^{2} + 100} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((1024*x**7-3840*x**6+6848*x**5-9488*x**4+8880*x**3-3784*x**2+408*x)*ln(x)**2+(-512*x**7+1920*x**6-4
448*x**5+8296*x**4-10688*x**3+10312*x**2-7752*x+2890)*ln(x)+768*x**8-1856*x**7+784*x**6+1508*x**5-5952*x**4+10
252*x**3-7252*x**2+1853*x)/((256*x**4-960*x**3+1200*x**2-500*x)*ln(x)**4+(512*x**5-1408*x**4+480*x**3+1400*x**
2-1000*x)*ln(x)**2+256*x**6-448*x**5-464*x**4+940*x**3+200*x**2-500*x),x)

[Out]

(64*x**6 - 160*x**5 + 356*x**4 - 592*x**3 + 596*x**2 - 544*x + 289)/(64*x**3 - 96*x**2 - 60*x + (64*x**2 - 160
*x + 100)*log(x)**2 + 100)

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