\(\int \frac {1}{625} (625+3000 x+8775 x^2+12400 x^3+12960 x^4+7936 x^5+1792 x^6+(1100 x+3000 x^2+5280 x^3+4992 x^4+1536 x^5) \log (x)+(100 x+510 x^2+1008 x^3+480 x^4) \log ^2(x)+(64 x^2+64 x^3) \log ^3(x)+3 x^2 \log ^4(x)) \, dx\) [655]

Optimal result

Integrand size = 110, antiderivative size = 23 \[ \int \frac {1}{625} \left (625+3000 x+8775 x^2+12400 x^3+12960 x^4+7936 x^5+1792 x^6+\left (1100 x+3000 x^2+5280 x^3+4992 x^4+1536 x^5\right ) \log (x)+\left (100 x+510 x^2+1008 x^3+480 x^4\right ) \log ^2(x)+\left (64 x^2+64 x^3\right ) \log ^3(x)+3 x^2 \log ^4(x)\right ) \, dx=\frac {\left (x+\left (x+\frac {1}{5} x (4 x+\log (x))\right )^2\right )^2}{x} \] Output:

(x+(x+1/5*(4*x+ln(x))*x)^2)^2/x
 

Mathematica [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(164\) vs. \(2(23)=46\).

Time = 0.03 (sec) , antiderivative size = 164, normalized size of antiderivative = 7.13 \[ \int \frac {1}{625} \left (625+3000 x+8775 x^2+12400 x^3+12960 x^4+7936 x^5+1792 x^6+\left (1100 x+3000 x^2+5280 x^3+4992 x^4+1536 x^5\right ) \log (x)+\left (100 x+510 x^2+1008 x^3+480 x^4\right ) \log ^2(x)+\left (64 x^2+64 x^3\right ) \log ^3(x)+3 x^2 \log ^4(x)\right ) \, dx=x+2 x^2+\frac {21 x^3}{5}+\frac {112 x^4}{25}+\frac {96 x^5}{25}+\frac {256 x^6}{125}+\frac {256 x^7}{625}+\frac {4}{5} x^2 \log (x)+\frac {36}{25} x^3 \log (x)+\frac {48}{25} x^4 \log (x)+\frac {192}{125} x^5 \log (x)+\frac {256}{625} x^6 \log (x)+\frac {2}{25} x^2 \log ^2(x)+\frac {6}{25} x^3 \log ^2(x)+\frac {48}{125} x^4 \log ^2(x)+\frac {96}{625} x^5 \log ^2(x)+\frac {4}{125} x^3 \log ^3(x)+\frac {16}{625} x^4 \log ^3(x)+\frac {1}{625} x^3 \log ^4(x) \] Input:

Integrate[(625 + 3000*x + 8775*x^2 + 12400*x^3 + 12960*x^4 + 7936*x^5 + 17 
92*x^6 + (1100*x + 3000*x^2 + 5280*x^3 + 4992*x^4 + 1536*x^5)*Log[x] + (10 
0*x + 510*x^2 + 1008*x^3 + 480*x^4)*Log[x]^2 + (64*x^2 + 64*x^3)*Log[x]^3 
+ 3*x^2*Log[x]^4)/625,x]
 

Output:

x + 2*x^2 + (21*x^3)/5 + (112*x^4)/25 + (96*x^5)/25 + (256*x^6)/125 + (256 
*x^7)/625 + (4*x^2*Log[x])/5 + (36*x^3*Log[x])/25 + (48*x^4*Log[x])/25 + ( 
192*x^5*Log[x])/125 + (256*x^6*Log[x])/625 + (2*x^2*Log[x]^2)/25 + (6*x^3* 
Log[x]^2)/25 + (48*x^4*Log[x]^2)/125 + (96*x^5*Log[x]^2)/625 + (4*x^3*Log[ 
x]^3)/125 + (16*x^4*Log[x]^3)/625 + (x^3*Log[x]^4)/625
 

Rubi [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(135\) vs. \(2(23)=46\).

Time = 0.58 (sec) , antiderivative size = 135, normalized size of antiderivative = 5.87, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.018, Rules used = {27, 2009}

Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.

\(\displaystyle \int \frac {1}{625} \left (1792 x^6+7936 x^5+12960 x^4+12400 x^3+8775 x^2+3 x^2 \log ^4(x)+\left (64 x^3+64 x^2\right ) \log ^3(x)+\left (480 x^4+1008 x^3+510 x^2+100 x\right ) \log ^2(x)+\left (1536 x^5+4992 x^4+5280 x^3+3000 x^2+1100 x\right ) \log (x)+3000 x+625\right ) \, dx\)

\(\Big \downarrow \) 27

\(\displaystyle \frac {1}{625} \int \left (1792 x^6+7936 x^5+12960 x^4+12400 x^3+3 \log ^4(x) x^2+8775 x^2+3000 x+64 \left (x^3+x^2\right ) \log ^3(x)+2 \left (240 x^4+504 x^3+255 x^2+50 x\right ) \log ^2(x)+4 \left (384 x^5+1248 x^4+1320 x^3+750 x^2+275 x\right ) \log (x)+625\right )dx\)

\(\Big \downarrow \) 2009

\(\displaystyle \frac {1}{625} \left (256 x^7+1280 x^6+256 x^6 \log (x)+2400 x^5+96 x^5 \log ^2(x)+960 x^5 \log (x)+2800 x^4+16 x^4 \log ^3(x)+240 x^4 \log ^2(x)+1200 x^4 \log (x)+2625 x^3+x^3 \log ^4(x)+20 x^3 \log ^3(x)+150 x^3 \log ^2(x)+900 x^3 \log (x)+1250 x^2+50 x^2 \log ^2(x)+500 x^2 \log (x)+625 x\right )\)

Input:

Int[(625 + 3000*x + 8775*x^2 + 12400*x^3 + 12960*x^4 + 7936*x^5 + 1792*x^6 
 + (1100*x + 3000*x^2 + 5280*x^3 + 4992*x^4 + 1536*x^5)*Log[x] + (100*x + 
510*x^2 + 1008*x^3 + 480*x^4)*Log[x]^2 + (64*x^2 + 64*x^3)*Log[x]^3 + 3*x^ 
2*Log[x]^4)/625,x]
 

Output:

(625*x + 1250*x^2 + 2625*x^3 + 2800*x^4 + 2400*x^5 + 1280*x^6 + 256*x^7 + 
500*x^2*Log[x] + 900*x^3*Log[x] + 1200*x^4*Log[x] + 960*x^5*Log[x] + 256*x 
^6*Log[x] + 50*x^2*Log[x]^2 + 150*x^3*Log[x]^2 + 240*x^4*Log[x]^2 + 96*x^5 
*Log[x]^2 + 20*x^3*Log[x]^3 + 16*x^4*Log[x]^3 + x^3*Log[x]^4)/625
 

Defintions of rubi rules used

rule 27

Int[(a_)*(Fx_), x_Symbol] :> Simp[a   Int[Fx, x], x] /; FreeQ[a, x] &&  !Ma 
tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
 

rule 2009

Int[u_, x_Symbol] :> Simp[IntSum[u, x], x] /; SumQ[u]
 

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(130\) vs. \(2(21)=42\).

Time = 9.27 (sec) , antiderivative size = 131, normalized size of antiderivative = 5.70

method	result	size
default	\(x +\frac {48 x^{4} \ln \left (x \right )^{2}}{125}+\frac {192 x^{5} \ln \left (x \right )}{125}+\frac {256 x^{6} \ln \left (x \right )}{625}+\frac {96 x^{5} \ln \left (x \right )^{2}}{625}+\frac {48 x^{4} \ln \left (x \right )}{25}+\frac {6 x^{3} \ln \left (x \right )^{2}}{25}+\frac {4 x^{3} \ln \left (x \right )^{3}}{125}+\frac {2 x^{2} \ln \left (x \right )^{2}}{25}+\frac {16 x^{4} \ln \left (x \right )^{3}}{625}+\frac {36 x^{3} \ln \left (x \right )}{25}+\frac {4 x^{2} \ln \left (x \right )}{5}+\frac {256 x^{6}}{125}+2 x^{2}+\frac {21 x^{3}}{5}+\frac {112 x^{4}}{25}+\frac {96 x^{5}}{25}+\frac {256 x^{7}}{625}+\frac {x^{3} \ln \left (x \right )^{4}}{625}\)	\(131\)
risch	\(x +\frac {48 x^{4} \ln \left (x \right )^{2}}{125}+\frac {192 x^{5} \ln \left (x \right )}{125}+\frac {256 x^{6} \ln \left (x \right )}{625}+\frac {96 x^{5} \ln \left (x \right )^{2}}{625}+\frac {48 x^{4} \ln \left (x \right )}{25}+\frac {6 x^{3} \ln \left (x \right )^{2}}{25}+\frac {4 x^{3} \ln \left (x \right )^{3}}{125}+\frac {2 x^{2} \ln \left (x \right )^{2}}{25}+\frac {16 x^{4} \ln \left (x \right )^{3}}{625}+\frac {36 x^{3} \ln \left (x \right )}{25}+\frac {4 x^{2} \ln \left (x \right )}{5}+\frac {256 x^{6}}{125}+2 x^{2}+\frac {21 x^{3}}{5}+\frac {112 x^{4}}{25}+\frac {96 x^{5}}{25}+\frac {256 x^{7}}{625}+\frac {x^{3} \ln \left (x \right )^{4}}{625}\)	\(131\)
parallelrisch	\(x +\frac {48 x^{4} \ln \left (x \right )^{2}}{125}+\frac {192 x^{5} \ln \left (x \right )}{125}+\frac {256 x^{6} \ln \left (x \right )}{625}+\frac {96 x^{5} \ln \left (x \right )^{2}}{625}+\frac {48 x^{4} \ln \left (x \right )}{25}+\frac {6 x^{3} \ln \left (x \right )^{2}}{25}+\frac {4 x^{3} \ln \left (x \right )^{3}}{125}+\frac {2 x^{2} \ln \left (x \right )^{2}}{25}+\frac {16 x^{4} \ln \left (x \right )^{3}}{625}+\frac {36 x^{3} \ln \left (x \right )}{25}+\frac {4 x^{2} \ln \left (x \right )}{5}+\frac {256 x^{6}}{125}+2 x^{2}+\frac {21 x^{3}}{5}+\frac {112 x^{4}}{25}+\frac {96 x^{5}}{25}+\frac {256 x^{7}}{625}+\frac {x^{3} \ln \left (x \right )^{4}}{625}\)	\(131\)
parts	\(x +\frac {48 x^{4} \ln \left (x \right )^{2}}{125}+\frac {192 x^{5} \ln \left (x \right )}{125}+\frac {256 x^{6} \ln \left (x \right )}{625}+\frac {96 x^{5} \ln \left (x \right )^{2}}{625}+\frac {48 x^{4} \ln \left (x \right )}{25}+\frac {6 x^{3} \ln \left (x \right )^{2}}{25}+\frac {4 x^{3} \ln \left (x \right )^{3}}{125}+\frac {2 x^{2} \ln \left (x \right )^{2}}{25}+\frac {16 x^{4} \ln \left (x \right )^{3}}{625}+\frac {36 x^{3} \ln \left (x \right )}{25}+\frac {4 x^{2} \ln \left (x \right )}{5}+\frac {256 x^{6}}{125}+2 x^{2}+\frac {21 x^{3}}{5}+\frac {112 x^{4}}{25}+\frac {96 x^{5}}{25}+\frac {256 x^{7}}{625}+\frac {x^{3} \ln \left (x \right )^{4}}{625}\)	\(131\)
orering	\(\text {Expression too large to display}\)	\(2064\)

Input:

int(3/625*x^2*ln(x)^4+1/625*(64*x^3+64*x^2)*ln(x)^3+1/625*(480*x^4+1008*x^ 
3+510*x^2+100*x)*ln(x)^2+1/625*(1536*x^5+4992*x^4+5280*x^3+3000*x^2+1100*x 
)*ln(x)+1792/625*x^6+7936/625*x^5+2592/125*x^4+496/25*x^3+351/25*x^2+24/5* 
x+1,x,method=_RETURNVERBOSE)
 

Output:

x+48/125*x^4*ln(x)^2+192/125*x^5*ln(x)+256/625*x^6*ln(x)+96/625*x^5*ln(x)^ 
2+48/25*x^4*ln(x)+6/25*x^3*ln(x)^2+4/125*x^3*ln(x)^3+2/25*x^2*ln(x)^2+16/6 
25*x^4*ln(x)^3+36/25*x^3*ln(x)+4/5*x^2*ln(x)+256/125*x^6+2*x^2+21/5*x^3+11 
2/25*x^4+96/25*x^5+256/625*x^7+1/625*x^3*ln(x)^4
 

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 115 vs. \(2 (25) = 50\).

Time = 0.09 (sec) , antiderivative size = 115, normalized size of antiderivative = 5.00 \[ \int \frac {1}{625} \left (625+3000 x+8775 x^2+12400 x^3+12960 x^4+7936 x^5+1792 x^6+\left (1100 x+3000 x^2+5280 x^3+4992 x^4+1536 x^5\right ) \log (x)+\left (100 x+510 x^2+1008 x^3+480 x^4\right ) \log ^2(x)+\left (64 x^2+64 x^3\right ) \log ^3(x)+3 x^2 \log ^4(x)\right ) \, dx=\frac {256}{625} \, x^{7} + \frac {1}{625} \, x^{3} \log \left (x\right )^{4} + \frac {256}{125} \, x^{6} + \frac {96}{25} \, x^{5} + \frac {112}{25} \, x^{4} + \frac {4}{625} \, {\left (4 \, x^{4} + 5 \, x^{3}\right )} \log \left (x\right )^{3} + \frac {21}{5} \, x^{3} + \frac {2}{625} \, {\left (48 \, x^{5} + 120 \, x^{4} + 75 \, x^{3} + 25 \, x^{2}\right )} \log \left (x\right )^{2} + 2 \, x^{2} + \frac {4}{625} \, {\left (64 \, x^{6} + 240 \, x^{5} + 300 \, x^{4} + 225 \, x^{3} + 125 \, x^{2}\right )} \log \left (x\right ) + x \] Input:

integrate(3/625*x^2*log(x)^4+1/625*(64*x^3+64*x^2)*log(x)^3+1/625*(480*x^4 
+1008*x^3+510*x^2+100*x)*log(x)^2+1/625*(1536*x^5+4992*x^4+5280*x^3+3000*x 
^2+1100*x)*log(x)+1792/625*x^6+7936/625*x^5+2592/125*x^4+496/25*x^3+351/25 
*x^2+24/5*x+1,x, algorithm="fricas")
 

Output:

256/625*x^7 + 1/625*x^3*log(x)^4 + 256/125*x^6 + 96/25*x^5 + 112/25*x^4 + 
4/625*(4*x^4 + 5*x^3)*log(x)^3 + 21/5*x^3 + 2/625*(48*x^5 + 120*x^4 + 75*x 
^3 + 25*x^2)*log(x)^2 + 2*x^2 + 4/625*(64*x^6 + 240*x^5 + 300*x^4 + 225*x^ 
3 + 125*x^2)*log(x) + x
 

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 138 vs. \(2 (19) = 38\).

Time = 0.15 (sec) , antiderivative size = 138, normalized size of antiderivative = 6.00 \[ \int \frac {1}{625} \left (625+3000 x+8775 x^2+12400 x^3+12960 x^4+7936 x^5+1792 x^6+\left (1100 x+3000 x^2+5280 x^3+4992 x^4+1536 x^5\right ) \log (x)+\left (100 x+510 x^2+1008 x^3+480 x^4\right ) \log ^2(x)+\left (64 x^2+64 x^3\right ) \log ^3(x)+3 x^2 \log ^4(x)\right ) \, dx=\frac {256 x^{7}}{625} + \frac {256 x^{6}}{125} + \frac {96 x^{5}}{25} + \frac {112 x^{4}}{25} + \frac {x^{3} \log {\left (x \right )}^{4}}{625} + \frac {21 x^{3}}{5} + 2 x^{2} + x + \left (\frac {16 x^{4}}{625} + \frac {4 x^{3}}{125}\right ) \log {\left (x \right )}^{3} + \left (\frac {96 x^{5}}{625} + \frac {48 x^{4}}{125} + \frac {6 x^{3}}{25} + \frac {2 x^{2}}{25}\right ) \log {\left (x \right )}^{2} + \left (\frac {256 x^{6}}{625} + \frac {192 x^{5}}{125} + \frac {48 x^{4}}{25} + \frac {36 x^{3}}{25} + \frac {4 x^{2}}{5}\right ) \log {\left (x \right )} \] Input:

integrate(3/625*x**2*ln(x)**4+1/625*(64*x**3+64*x**2)*ln(x)**3+1/625*(480* 
x**4+1008*x**3+510*x**2+100*x)*ln(x)**2+1/625*(1536*x**5+4992*x**4+5280*x* 
*3+3000*x**2+1100*x)*ln(x)+1792/625*x**6+7936/625*x**5+2592/125*x**4+496/2 
5*x**3+351/25*x**2+24/5*x+1,x)
 

Output:

256*x**7/625 + 256*x**6/125 + 96*x**5/25 + 112*x**4/25 + x**3*log(x)**4/62 
5 + 21*x**3/5 + 2*x**2 + x + (16*x**4/625 + 4*x**3/125)*log(x)**3 + (96*x* 
*5/625 + 48*x**4/125 + 6*x**3/25 + 2*x**2/25)*log(x)**2 + (256*x**6/625 + 
192*x**5/125 + 48*x**4/25 + 36*x**3/25 + 4*x**2/5)*log(x)
 

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 205 vs. \(2 (25) = 50\).

Time = 0.04 (sec) , antiderivative size = 205, normalized size of antiderivative = 8.91 \[ \int \frac {1}{625} \left (625+3000 x+8775 x^2+12400 x^3+12960 x^4+7936 x^5+1792 x^6+\left (1100 x+3000 x^2+5280 x^3+4992 x^4+1536 x^5\right ) \log (x)+\left (100 x+510 x^2+1008 x^3+480 x^4\right ) \log ^2(x)+\left (64 x^2+64 x^3\right ) \log ^3(x)+3 x^2 \log ^4(x)\right ) \, dx=\frac {256}{625} \, x^{7} + \frac {96}{15625} \, {\left (25 \, \log \left (x\right )^{2} - 10 \, \log \left (x\right ) + 2\right )} x^{5} + \frac {256}{125} \, x^{6} + \frac {1}{1250} \, {\left (32 \, \log \left (x\right )^{3} - 24 \, \log \left (x\right )^{2} + 12 \, \log \left (x\right ) - 3\right )} x^{4} + \frac {63}{1250} \, {\left (8 \, \log \left (x\right )^{2} - 4 \, \log \left (x\right ) + 1\right )} x^{4} + \frac {59808}{15625} \, x^{5} + \frac {1}{16875} \, {\left (27 \, \log \left (x\right )^{4} - 36 \, \log \left (x\right )^{3} + 36 \, \log \left (x\right )^{2} - 24 \, \log \left (x\right ) + 8\right )} x^{3} + \frac {64}{16875} \, {\left (9 \, \log \left (x\right )^{3} - 9 \, \log \left (x\right )^{2} + 6 \, \log \left (x\right ) - 2\right )} x^{3} + \frac {34}{1125} \, {\left (9 \, \log \left (x\right )^{2} - 6 \, \log \left (x\right ) + 2\right )} x^{3} + \frac {554}{125} \, x^{4} + \frac {1}{25} \, {\left (2 \, \log \left (x\right )^{2} - 2 \, \log \left (x\right ) + 1\right )} x^{2} + \frac {311}{75} \, x^{3} + \frac {49}{25} \, x^{2} + \frac {2}{3125} \, {\left (640 \, x^{6} + 2496 \, x^{5} + 3300 \, x^{4} + 2500 \, x^{3} + 1375 \, x^{2}\right )} \log \left (x\right ) + x \] Input:

integrate(3/625*x^2*log(x)^4+1/625*(64*x^3+64*x^2)*log(x)^3+1/625*(480*x^4 
+1008*x^3+510*x^2+100*x)*log(x)^2+1/625*(1536*x^5+4992*x^4+5280*x^3+3000*x 
^2+1100*x)*log(x)+1792/625*x^6+7936/625*x^5+2592/125*x^4+496/25*x^3+351/25 
*x^2+24/5*x+1,x, algorithm="maxima")
 

Output:

256/625*x^7 + 96/15625*(25*log(x)^2 - 10*log(x) + 2)*x^5 + 256/125*x^6 + 1 
/1250*(32*log(x)^3 - 24*log(x)^2 + 12*log(x) - 3)*x^4 + 63/1250*(8*log(x)^ 
2 - 4*log(x) + 1)*x^4 + 59808/15625*x^5 + 1/16875*(27*log(x)^4 - 36*log(x) 
^3 + 36*log(x)^2 - 24*log(x) + 8)*x^3 + 64/16875*(9*log(x)^3 - 9*log(x)^2 
+ 6*log(x) - 2)*x^3 + 34/1125*(9*log(x)^2 - 6*log(x) + 2)*x^3 + 554/125*x^ 
4 + 1/25*(2*log(x)^2 - 2*log(x) + 1)*x^2 + 311/75*x^3 + 49/25*x^2 + 2/3125 
*(640*x^6 + 2496*x^5 + 3300*x^4 + 2500*x^3 + 1375*x^2)*log(x) + x
 

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 130 vs. \(2 (25) = 50\).

Time = 0.12 (sec) , antiderivative size = 130, normalized size of antiderivative = 5.65 \[ \int \frac {1}{625} \left (625+3000 x+8775 x^2+12400 x^3+12960 x^4+7936 x^5+1792 x^6+\left (1100 x+3000 x^2+5280 x^3+4992 x^4+1536 x^5\right ) \log (x)+\left (100 x+510 x^2+1008 x^3+480 x^4\right ) \log ^2(x)+\left (64 x^2+64 x^3\right ) \log ^3(x)+3 x^2 \log ^4(x)\right ) \, dx=\frac {256}{625} \, x^{7} + \frac {256}{625} \, x^{6} \log \left (x\right ) + \frac {96}{625} \, x^{5} \log \left (x\right )^{2} + \frac {16}{625} \, x^{4} \log \left (x\right )^{3} + \frac {1}{625} \, x^{3} \log \left (x\right )^{4} + \frac {256}{125} \, x^{6} + \frac {192}{125} \, x^{5} \log \left (x\right ) + \frac {48}{125} \, x^{4} \log \left (x\right )^{2} + \frac {4}{125} \, x^{3} \log \left (x\right )^{3} + \frac {96}{25} \, x^{5} + \frac {48}{25} \, x^{4} \log \left (x\right ) + \frac {6}{25} \, x^{3} \log \left (x\right )^{2} + \frac {112}{25} \, x^{4} + \frac {36}{25} \, x^{3} \log \left (x\right ) + \frac {2}{25} \, x^{2} \log \left (x\right )^{2} + \frac {21}{5} \, x^{3} + \frac {4}{5} \, x^{2} \log \left (x\right ) + 2 \, x^{2} + x \] Input:

integrate(3/625*x^2*log(x)^4+1/625*(64*x^3+64*x^2)*log(x)^3+1/625*(480*x^4 
+1008*x^3+510*x^2+100*x)*log(x)^2+1/625*(1536*x^5+4992*x^4+5280*x^3+3000*x 
^2+1100*x)*log(x)+1792/625*x^6+7936/625*x^5+2592/125*x^4+496/25*x^3+351/25 
*x^2+24/5*x+1,x, algorithm="giac")
 

Output:

256/625*x^7 + 256/625*x^6*log(x) + 96/625*x^5*log(x)^2 + 16/625*x^4*log(x) 
^3 + 1/625*x^3*log(x)^4 + 256/125*x^6 + 192/125*x^5*log(x) + 48/125*x^4*lo 
g(x)^2 + 4/125*x^3*log(x)^3 + 96/25*x^5 + 48/25*x^4*log(x) + 6/25*x^3*log( 
x)^2 + 112/25*x^4 + 36/25*x^3*log(x) + 2/25*x^2*log(x)^2 + 21/5*x^3 + 4/5* 
x^2*log(x) + 2*x^2 + x
 

Mupad [B] (verification not implemented)

Time = 3.06 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.65 \[ \int \frac {1}{625} \left (625+3000 x+8775 x^2+12400 x^3+12960 x^4+7936 x^5+1792 x^6+\left (1100 x+3000 x^2+5280 x^3+4992 x^4+1536 x^5\right ) \log (x)+\left (100 x+510 x^2+1008 x^3+480 x^4\right ) \log ^2(x)+\left (64 x^2+64 x^3\right ) \log ^3(x)+3 x^2 \log ^4(x)\right ) \, dx=\frac {x\,{\left (16\,x^3+8\,x^2\,\ln \left (x\right )+40\,x^2+x\,{\ln \left (x\right )}^2+10\,x\,\ln \left (x\right )+25\,x+25\right )}^2}{625} \] Input:

int((24*x)/5 + (log(x)*(1100*x + 3000*x^2 + 5280*x^3 + 4992*x^4 + 1536*x^5 
))/625 + (log(x)^3*(64*x^2 + 64*x^3))/625 + (3*x^2*log(x)^4)/625 + (log(x) 
^2*(100*x + 510*x^2 + 1008*x^3 + 480*x^4))/625 + (351*x^2)/25 + (496*x^3)/ 
25 + (2592*x^4)/125 + (7936*x^5)/625 + (1792*x^6)/625 + 1,x)
 

Output:

(x*(25*x + x*log(x)^2 + 8*x^2*log(x) + 10*x*log(x) + 40*x^2 + 16*x^3 + 25) 
^2)/625
 

Reduce [B] (verification not implemented)

Time = 0.18 (sec) , antiderivative size = 126, normalized size of antiderivative = 5.48 \[ \int \frac {1}{625} \left (625+3000 x+8775 x^2+12400 x^3+12960 x^4+7936 x^5+1792 x^6+\left (1100 x+3000 x^2+5280 x^3+4992 x^4+1536 x^5\right ) \log (x)+\left (100 x+510 x^2+1008 x^3+480 x^4\right ) \log ^2(x)+\left (64 x^2+64 x^3\right ) \log ^3(x)+3 x^2 \log ^4(x)\right ) \, dx=\frac {x \left (\mathrm {log}\left (x \right )^{4} x^{2}+16 \mathrm {log}\left (x \right )^{3} x^{3}+20 \mathrm {log}\left (x \right )^{3} x^{2}+96 \mathrm {log}\left (x \right )^{2} x^{4}+240 \mathrm {log}\left (x \right )^{2} x^{3}+150 \mathrm {log}\left (x \right )^{2} x^{2}+50 \mathrm {log}\left (x \right )^{2} x +256 \,\mathrm {log}\left (x \right ) x^{5}+960 \,\mathrm {log}\left (x \right ) x^{4}+1200 \,\mathrm {log}\left (x \right ) x^{3}+900 \,\mathrm {log}\left (x \right ) x^{2}+500 \,\mathrm {log}\left (x \right ) x +256 x^{6}+1280 x^{5}+2400 x^{4}+2800 x^{3}+2625 x^{2}+1250 x +625\right )}{625} \] Input:

int(3/625*x^2*log(x)^4+1/625*(64*x^3+64*x^2)*log(x)^3+1/625*(480*x^4+1008* 
x^3+510*x^2+100*x)*log(x)^2+1/625*(1536*x^5+4992*x^4+5280*x^3+3000*x^2+110 
0*x)*log(x)+1792/625*x^6+7936/625*x^5+2592/125*x^4+496/25*x^3+351/25*x^2+2 
4/5*x+1,x)
 

Output:

(x*(log(x)**4*x**2 + 16*log(x)**3*x**3 + 20*log(x)**3*x**2 + 96*log(x)**2* 
x**4 + 240*log(x)**2*x**3 + 150*log(x)**2*x**2 + 50*log(x)**2*x + 256*log( 
x)*x**5 + 960*log(x)*x**4 + 1200*log(x)*x**3 + 900*log(x)*x**2 + 500*log(x 
)*x + 256*x**6 + 1280*x**5 + 2400*x**4 + 2800*x**3 + 2625*x**2 + 1250*x + 
625))/625