Integrand size = 143, antiderivative size = 28 \[ \int \frac {1}{9} \left (\left (-168 x+16 x^3\right ) \log ^2(2)+\left (-5376+1536 x^2\right ) \log ^2(2) \log (5)+\left (65024 x-6144 x^3\right ) \log ^2(2) \log ^2(5)+\left (-359424 x^2+10240 x^4\right ) \log ^2(2) \log ^3(5)+\left (1157120 x^3-6144 x^5\right ) \log ^2(2) \log ^4(5)-2293760 x^4 \log ^2(2) \log ^5(5)+2752512 x^5 \log ^2(2) \log ^6(5)-1835008 x^6 \log ^2(2) \log ^7(5)+524288 x^7 \log ^2(2) \log ^8(5)\right ) \, dx=\frac {1}{9} \log ^2(2) \left (-5+2 x^2-(2-4 x \log (5))^4\right )^2 \] Output:
1/9*ln(2)^2*(2*x^2-(2-4*x*ln(5))^4-5)^2
Leaf count is larger than twice the leaf count of optimal. \(118\) vs. \(2(28)=56\).
Time = 0.02 (sec) , antiderivative size = 118, normalized size of antiderivative = 4.21 \[ \int \frac {1}{9} \left (\left (-168 x+16 x^3\right ) \log ^2(2)+\left (-5376+1536 x^2\right ) \log ^2(2) \log (5)+\left (65024 x-6144 x^3\right ) \log ^2(2) \log ^2(5)+\left (-359424 x^2+10240 x^4\right ) \log ^2(2) \log ^3(5)+\left (1157120 x^3-6144 x^5\right ) \log ^2(2) \log ^4(5)-2293760 x^4 \log ^2(2) \log ^5(5)+2752512 x^5 \log ^2(2) \log ^6(5)-1835008 x^6 \log ^2(2) \log ^7(5)+524288 x^7 \log ^2(2) \log ^8(5)\right ) \, dx=\frac {8}{9} \log ^2(2) \left (-\frac {21 x^2}{2}-672 x \log (5)+4064 x^2 \log ^2(5)-32768 x^7 \log ^7(5)+8192 x^8 \log ^8(5)-256 x^5 \log ^3(5) \left (-1+224 \log ^2(5)\right )-64 x^3 \log (5) \left (-1+234 \log ^2(5)\right )+128 x^6 \log ^4(5) \left (-1+448 \log ^2(5)\right )+\frac {1}{2} x^4 \left (1-384 \log ^2(5)+72320 \log ^4(5)\right )\right ) \] Input:
Integrate[((-168*x + 16*x^3)*Log[2]^2 + (-5376 + 1536*x^2)*Log[2]^2*Log[5] + (65024*x - 6144*x^3)*Log[2]^2*Log[5]^2 + (-359424*x^2 + 10240*x^4)*Log[ 2]^2*Log[5]^3 + (1157120*x^3 - 6144*x^5)*Log[2]^2*Log[5]^4 - 2293760*x^4*L og[2]^2*Log[5]^5 + 2752512*x^5*Log[2]^2*Log[5]^6 - 1835008*x^6*Log[2]^2*Lo g[5]^7 + 524288*x^7*Log[2]^2*Log[5]^8)/9,x]
Output:
(8*Log[2]^2*((-21*x^2)/2 - 672*x*Log[5] + 4064*x^2*Log[5]^2 - 32768*x^7*Lo g[5]^7 + 8192*x^8*Log[5]^8 - 256*x^5*Log[5]^3*(-1 + 224*Log[5]^2) - 64*x^3 *Log[5]*(-1 + 234*Log[5]^2) + 128*x^6*Log[5]^4*(-1 + 448*Log[5]^2) + (x^4* (1 - 384*Log[5]^2 + 72320*Log[5]^4))/2))/9
Leaf count is larger than twice the leaf count of optimal. \(173\) vs. \(2(28)=56\).
Time = 0.35 (sec) , antiderivative size = 173, normalized size of antiderivative = 6.18, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.014, 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.
| \(\displaystyle \int \frac {1}{9} \left (524288 x^7 \log ^2(2) \log ^8(5)-1835008 x^6 \log ^2(2) \log ^7(5)+2752512 x^5 \log ^2(2) \log ^6(5)-2293760 x^4 \log ^2(2) \log ^5(5)+\left (65024 x-6144 x^3\right ) \log ^2(2) \log ^2(5)+\left (16 x^3-168 x\right ) \log ^2(2)+\left (1536 x^2-5376\right ) \log ^2(2) \log (5)+\left (1157120 x^3-6144 x^5\right ) \log ^2(2) \log ^4(5)+\left (10240 x^4-359424 x^2\right ) \log ^2(2) \log ^3(5)\right ) \, dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{9} \int \left (524288 \log ^2(2) \log ^8(5) x^7-1835008 \log ^2(2) \log ^7(5) x^6+2752512 \log ^2(2) \log ^6(5) x^5-2293760 \log ^2(2) \log ^5(5) x^4+2048 \left (565 x^3-3 x^5\right ) \log ^2(2) \log ^4(5)-1024 \left (351 x^2-10 x^4\right ) \log ^2(2) \log ^3(5)+512 \left (127 x-12 x^3\right ) \log ^2(2) \log ^2(5)-768 \left (7-2 x^2\right ) \log ^2(2) \log (5)-8 \left (21 x-2 x^3\right ) \log ^2(2)\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {1}{9} \left (65536 x^8 \log ^2(2) \log ^8(5)-262144 x^7 \log ^2(2) \log ^7(5)+458752 x^6 \log ^2(2) \log ^6(5)-1024 x^6 \log ^2(2) \log ^4(5)-458752 x^5 \log ^2(2) \log ^5(5)+2048 x^5 \log ^2(2) \log ^3(5)-1536 x^4 \log ^2(2) \log ^2(5)+4 x^4 \log ^2(2)+289280 x^4 \log ^2(2) \log ^4(5)+512 x^3 \log ^2(2) \log (5)-119808 x^3 \log ^2(2) \log ^3(5)+32512 x^2 \log ^2(2) \log ^2(5)-84 x^2 \log ^2(2)-5376 x \log ^2(2) \log (5)\right )\) |
Input:
Int[((-168*x + 16*x^3)*Log[2]^2 + (-5376 + 1536*x^2)*Log[2]^2*Log[5] + (65 024*x - 6144*x^3)*Log[2]^2*Log[5]^2 + (-359424*x^2 + 10240*x^4)*Log[2]^2*L og[5]^3 + (1157120*x^3 - 6144*x^5)*Log[2]^2*Log[5]^4 - 2293760*x^4*Log[2]^ 2*Log[5]^5 + 2752512*x^5*Log[2]^2*Log[5]^6 - 1835008*x^6*Log[2]^2*Log[5]^7 + 524288*x^7*Log[2]^2*Log[5]^8)/9,x]
Output:
(-84*x^2*Log[2]^2 + 4*x^4*Log[2]^2 - 5376*x*Log[2]^2*Log[5] + 512*x^3*Log[ 2]^2*Log[5] + 32512*x^2*Log[2]^2*Log[5]^2 - 1536*x^4*Log[2]^2*Log[5]^2 - 1 19808*x^3*Log[2]^2*Log[5]^3 + 2048*x^5*Log[2]^2*Log[5]^3 + 289280*x^4*Log[ 2]^2*Log[5]^4 - 1024*x^6*Log[2]^2*Log[5]^4 - 458752*x^5*Log[2]^2*Log[5]^5 + 458752*x^6*Log[2]^2*Log[5]^6 - 262144*x^7*Log[2]^2*Log[5]^7 + 65536*x^8* Log[2]^2*Log[5]^8)/9
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Time = 0.42 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.71
| method | result | size |
| default | \(\frac {\ln \left (2\right )^{2} \left (256 x^{4} \ln \left (5\right )^{4}-512 x^{3} \ln \left (5\right )^{3}+384 x^{2} \ln \left (5\right )^{2}-128 x \ln \left (5\right )-2 x^{2}+21\right )^{2}}{9}\) | \(48\) |
| gosper | \(\frac {4 \ln \left (2\right )^{2} x \left (16384 \ln \left (5\right )^{8} x^{7}-65536 \ln \left (5\right )^{7} x^{6}+114688 \ln \left (5\right )^{6} x^{5}-114688 x^{4} \ln \left (5\right )^{5}-256 \ln \left (5\right )^{4} x^{5}+72320 \ln \left (5\right )^{4} x^{3}+512 x^{4} \ln \left (5\right )^{3}-29952 \ln \left (5\right )^{3} x^{2}-384 \ln \left (5\right )^{2} x^{3}+8128 x \ln \left (5\right )^{2}+128 x^{2} \ln \left (5\right )+x^{3}-1344 \ln \left (5\right )-21 x \right )}{9}\) | \(114\) |
| norman | \(\left (\frac {32512 \ln \left (2\right )^{2} \ln \left (5\right )^{2}}{9}-\frac {28 \ln \left (2\right )^{2}}{3}\right ) x^{2}+\left (-13312 \ln \left (2\right )^{2} \ln \left (5\right )^{3}+\frac {512 \ln \left (2\right )^{2} \ln \left (5\right )}{9}\right ) x^{3}+\left (-\frac {458752 \ln \left (2\right )^{2} \ln \left (5\right )^{5}}{9}+\frac {2048 \ln \left (2\right )^{2} \ln \left (5\right )^{3}}{9}\right ) x^{5}+\left (\frac {458752 \ln \left (2\right )^{2} \ln \left (5\right )^{6}}{9}-\frac {1024 \ln \left (2\right )^{2} \ln \left (5\right )^{4}}{9}\right ) x^{6}+\left (\frac {289280 \ln \left (2\right )^{2} \ln \left (5\right )^{4}}{9}-\frac {512 \ln \left (2\right )^{2} \ln \left (5\right )^{2}}{3}+\frac {4 \ln \left (2\right )^{2}}{9}\right ) x^{4}-\frac {1792 x \ln \left (2\right )^{2} \ln \left (5\right )}{3}-\frac {262144 \ln \left (2\right )^{2} \ln \left (5\right )^{7} x^{7}}{9}+\frac {65536 \ln \left (2\right )^{2} \ln \left (5\right )^{8} x^{8}}{9}\) | \(162\) |
| parallelrisch | \(\frac {65536 \ln \left (2\right )^{2} \ln \left (5\right )^{8} x^{8}}{9}-\frac {262144 \ln \left (2\right )^{2} \ln \left (5\right )^{7} x^{7}}{9}+\frac {458752 \ln \left (2\right )^{2} \ln \left (5\right )^{6} x^{6}}{9}-\frac {1024 \ln \left (2\right )^{2} \ln \left (5\right )^{4} x^{6}}{9}-\frac {458752 \ln \left (2\right )^{2} \ln \left (5\right )^{5} x^{5}}{9}+\frac {2048 \ln \left (2\right )^{2} \ln \left (5\right )^{3} x^{5}}{9}+\frac {289280 \ln \left (2\right )^{2} \ln \left (5\right )^{4} x^{4}}{9}-\frac {512 \ln \left (5\right )^{2} \ln \left (2\right )^{2} x^{4}}{3}+\frac {4 x^{4} \ln \left (2\right )^{2}}{9}-13312 \ln \left (2\right )^{2} \ln \left (5\right )^{3} x^{3}+\frac {512 \ln \left (2\right )^{2} \ln \left (5\right ) x^{3}}{9}+\frac {32512 \ln \left (5\right )^{2} \ln \left (2\right )^{2} x^{2}}{9}-\frac {28 x^{2} \ln \left (2\right )^{2}}{3}-\frac {1792 x \ln \left (2\right )^{2} \ln \left (5\right )}{3}\) | \(170\) |
| parts | \(\frac {65536 \ln \left (2\right )^{2} \ln \left (5\right )^{8} x^{8}}{9}-\frac {262144 \ln \left (2\right )^{2} \ln \left (5\right )^{7} x^{7}}{9}+\frac {458752 \ln \left (2\right )^{2} \ln \left (5\right )^{6} x^{6}}{9}-\frac {1024 \ln \left (2\right )^{2} \ln \left (5\right )^{4} x^{6}}{9}-\frac {458752 \ln \left (2\right )^{2} \ln \left (5\right )^{5} x^{5}}{9}+\frac {2048 \ln \left (2\right )^{2} \ln \left (5\right )^{3} x^{5}}{9}+\frac {289280 \ln \left (2\right )^{2} \ln \left (5\right )^{4} x^{4}}{9}-\frac {512 \ln \left (5\right )^{2} \ln \left (2\right )^{2} x^{4}}{3}+\frac {4 x^{4} \ln \left (2\right )^{2}}{9}-13312 \ln \left (2\right )^{2} \ln \left (5\right )^{3} x^{3}+\frac {512 \ln \left (2\right )^{2} \ln \left (5\right ) x^{3}}{9}+\frac {32512 \ln \left (5\right )^{2} \ln \left (2\right )^{2} x^{2}}{9}-\frac {28 x^{2} \ln \left (2\right )^{2}}{3}-\frac {1792 x \ln \left (2\right )^{2} \ln \left (5\right )}{3}\) | \(170\) |
| risch | \(\frac {65536 \ln \left (2\right )^{2} \ln \left (5\right )^{8} x^{8}}{9}-\frac {262144 \ln \left (2\right )^{2} \ln \left (5\right )^{7} x^{7}}{9}+\frac {458752 \ln \left (2\right )^{2} \ln \left (5\right )^{6} x^{6}}{9}-\frac {458752 \ln \left (2\right )^{2} \ln \left (5\right )^{5} x^{5}}{9}-\frac {1024 \ln \left (2\right )^{2} \ln \left (5\right )^{4} x^{6}}{9}+\frac {289280 \ln \left (2\right )^{2} \ln \left (5\right )^{4} x^{4}}{9}+\frac {2048 \ln \left (2\right )^{2} \ln \left (5\right )^{3} x^{5}}{9}-13312 \ln \left (2\right )^{2} \ln \left (5\right )^{3} x^{3}-\frac {512 \ln \left (5\right )^{2} \ln \left (2\right )^{2} x^{4}}{3}+\frac {32512 \ln \left (5\right )^{2} \ln \left (2\right )^{2} x^{2}}{9}-\frac {516128 \ln \left (2\right )^{2} \ln \left (5\right )^{2}}{27}+\frac {512 \ln \left (2\right )^{2} \ln \left (5\right ) x^{3}}{9}-\frac {1792 x \ln \left (2\right )^{2} \ln \left (5\right )}{3}+\frac {4 x^{4} \ln \left (2\right )^{2}}{9}-\frac {28 x^{2} \ln \left (2\right )^{2}}{3}+49 \ln \left (2\right )^{2}\) | \(186\) |
Input:
int(524288/9*x^7*ln(2)^2*ln(5)^8-1835008/9*x^6*ln(2)^2*ln(5)^7+917504/3*x^ 5*ln(2)^2*ln(5)^6-2293760/9*x^4*ln(2)^2*ln(5)^5+1/9*(-6144*x^5+1157120*x^3 )*ln(2)^2*ln(5)^4+1/9*(10240*x^4-359424*x^2)*ln(2)^2*ln(5)^3+1/9*(-6144*x^ 3+65024*x)*ln(2)^2*ln(5)^2+1/9*(1536*x^2-5376)*ln(2)^2*ln(5)+1/9*(16*x^3-1 68*x)*ln(2)^2,x,method=_RETURNVERBOSE)
Output:
1/9*ln(2)^2*(256*x^4*ln(5)^4-512*x^3*ln(5)^3+384*x^2*ln(5)^2-128*x*ln(5)-2 *x^2+21)^2
Leaf count of result is larger than twice the leaf count of optimal. 148 vs. \(2 (26) = 52\).
Time = 0.07 (sec) , antiderivative size = 148, normalized size of antiderivative = 5.29 \[ \int \frac {1}{9} \left (\left (-168 x+16 x^3\right ) \log ^2(2)+\left (-5376+1536 x^2\right ) \log ^2(2) \log (5)+\left (65024 x-6144 x^3\right ) \log ^2(2) \log ^2(5)+\left (-359424 x^2+10240 x^4\right ) \log ^2(2) \log ^3(5)+\left (1157120 x^3-6144 x^5\right ) \log ^2(2) \log ^4(5)-2293760 x^4 \log ^2(2) \log ^5(5)+2752512 x^5 \log ^2(2) \log ^6(5)-1835008 x^6 \log ^2(2) \log ^7(5)+524288 x^7 \log ^2(2) \log ^8(5)\right ) \, dx=\frac {65536}{9} \, x^{8} \log \left (5\right )^{8} \log \left (2\right )^{2} - \frac {262144}{9} \, x^{7} \log \left (5\right )^{7} \log \left (2\right )^{2} + \frac {458752}{9} \, x^{6} \log \left (5\right )^{6} \log \left (2\right )^{2} - \frac {458752}{9} \, x^{5} \log \left (5\right )^{5} \log \left (2\right )^{2} - \frac {512}{9} \, {\left (2 \, x^{6} - 565 \, x^{4}\right )} \log \left (5\right )^{4} \log \left (2\right )^{2} + \frac {1024}{9} \, {\left (2 \, x^{5} - 117 \, x^{3}\right )} \log \left (5\right )^{3} \log \left (2\right )^{2} - \frac {256}{9} \, {\left (6 \, x^{4} - 127 \, x^{2}\right )} \log \left (5\right )^{2} \log \left (2\right )^{2} + \frac {256}{9} \, {\left (2 \, x^{3} - 21 \, x\right )} \log \left (5\right ) \log \left (2\right )^{2} + \frac {4}{9} \, {\left (x^{4} - 21 \, x^{2}\right )} \log \left (2\right )^{2} \] Input:
integrate(524288/9*x^7*log(2)^2*log(5)^8-1835008/9*x^6*log(2)^2*log(5)^7+9 17504/3*x^5*log(2)^2*log(5)^6-2293760/9*x^4*log(2)^2*log(5)^5+1/9*(-6144*x ^5+1157120*x^3)*log(2)^2*log(5)^4+1/9*(10240*x^4-359424*x^2)*log(2)^2*log( 5)^3+1/9*(-6144*x^3+65024*x)*log(2)^2*log(5)^2+1/9*(1536*x^2-5376)*log(2)^ 2*log(5)+1/9*(16*x^3-168*x)*log(2)^2,x, algorithm="fricas")
Output:
65536/9*x^8*log(5)^8*log(2)^2 - 262144/9*x^7*log(5)^7*log(2)^2 + 458752/9* x^6*log(5)^6*log(2)^2 - 458752/9*x^5*log(5)^5*log(2)^2 - 512/9*(2*x^6 - 56 5*x^4)*log(5)^4*log(2)^2 + 1024/9*(2*x^5 - 117*x^3)*log(5)^3*log(2)^2 - 25 6/9*(6*x^4 - 127*x^2)*log(5)^2*log(2)^2 + 256/9*(2*x^3 - 21*x)*log(5)*log( 2)^2 + 4/9*(x^4 - 21*x^2)*log(2)^2
Leaf count of result is larger than twice the leaf count of optimal. 199 vs. \(2 (24) = 48\).
Time = 0.05 (sec) , antiderivative size = 199, normalized size of antiderivative = 7.11 \[ \int \frac {1}{9} \left (\left (-168 x+16 x^3\right ) \log ^2(2)+\left (-5376+1536 x^2\right ) \log ^2(2) \log (5)+\left (65024 x-6144 x^3\right ) \log ^2(2) \log ^2(5)+\left (-359424 x^2+10240 x^4\right ) \log ^2(2) \log ^3(5)+\left (1157120 x^3-6144 x^5\right ) \log ^2(2) \log ^4(5)-2293760 x^4 \log ^2(2) \log ^5(5)+2752512 x^5 \log ^2(2) \log ^6(5)-1835008 x^6 \log ^2(2) \log ^7(5)+524288 x^7 \log ^2(2) \log ^8(5)\right ) \, dx=\frac {65536 x^{8} \log {\left (2 \right )}^{2} \log {\left (5 \right )}^{8}}{9} - \frac {262144 x^{7} \log {\left (2 \right )}^{2} \log {\left (5 \right )}^{7}}{9} + x^{6} \left (- \frac {1024 \log {\left (2 \right )}^{2} \log {\left (5 \right )}^{4}}{9} + \frac {458752 \log {\left (2 \right )}^{2} \log {\left (5 \right )}^{6}}{9}\right ) + x^{5} \left (- \frac {458752 \log {\left (2 \right )}^{2} \log {\left (5 \right )}^{5}}{9} + \frac {2048 \log {\left (2 \right )}^{2} \log {\left (5 \right )}^{3}}{9}\right ) + x^{4} \left (- \frac {512 \log {\left (2 \right )}^{2} \log {\left (5 \right )}^{2}}{3} + \frac {4 \log {\left (2 \right )}^{2}}{9} + \frac {289280 \log {\left (2 \right )}^{2} \log {\left (5 \right )}^{4}}{9}\right ) + x^{3} \left (- 13312 \log {\left (2 \right )}^{2} \log {\left (5 \right )}^{3} + \frac {512 \log {\left (2 \right )}^{2} \log {\left (5 \right )}}{9}\right ) + x^{2} \left (- \frac {28 \log {\left (2 \right )}^{2}}{3} + \frac {32512 \log {\left (2 \right )}^{2} \log {\left (5 \right )}^{2}}{9}\right ) - \frac {1792 x \log {\left (2 \right )}^{2} \log {\left (5 \right )}}{3} \] Input:
integrate(524288/9*x**7*ln(2)**2*ln(5)**8-1835008/9*x**6*ln(2)**2*ln(5)**7 +917504/3*x**5*ln(2)**2*ln(5)**6-2293760/9*x**4*ln(2)**2*ln(5)**5+1/9*(-61 44*x**5+1157120*x**3)*ln(2)**2*ln(5)**4+1/9*(10240*x**4-359424*x**2)*ln(2) **2*ln(5)**3+1/9*(-6144*x**3+65024*x)*ln(2)**2*ln(5)**2+1/9*(1536*x**2-537 6)*ln(2)**2*ln(5)+1/9*(16*x**3-168*x)*ln(2)**2,x)
Output:
65536*x**8*log(2)**2*log(5)**8/9 - 262144*x**7*log(2)**2*log(5)**7/9 + x** 6*(-1024*log(2)**2*log(5)**4/9 + 458752*log(2)**2*log(5)**6/9) + x**5*(-45 8752*log(2)**2*log(5)**5/9 + 2048*log(2)**2*log(5)**3/9) + x**4*(-512*log( 2)**2*log(5)**2/3 + 4*log(2)**2/9 + 289280*log(2)**2*log(5)**4/9) + x**3*( -13312*log(2)**2*log(5)**3 + 512*log(2)**2*log(5)/9) + x**2*(-28*log(2)**2 /3 + 32512*log(2)**2*log(5)**2/9) - 1792*x*log(2)**2*log(5)/3
Leaf count of result is larger than twice the leaf count of optimal. 148 vs. \(2 (26) = 52\).
Time = 0.03 (sec) , antiderivative size = 148, normalized size of antiderivative = 5.29 \[ \int \frac {1}{9} \left (\left (-168 x+16 x^3\right ) \log ^2(2)+\left (-5376+1536 x^2\right ) \log ^2(2) \log (5)+\left (65024 x-6144 x^3\right ) \log ^2(2) \log ^2(5)+\left (-359424 x^2+10240 x^4\right ) \log ^2(2) \log ^3(5)+\left (1157120 x^3-6144 x^5\right ) \log ^2(2) \log ^4(5)-2293760 x^4 \log ^2(2) \log ^5(5)+2752512 x^5 \log ^2(2) \log ^6(5)-1835008 x^6 \log ^2(2) \log ^7(5)+524288 x^7 \log ^2(2) \log ^8(5)\right ) \, dx=\frac {65536}{9} \, x^{8} \log \left (5\right )^{8} \log \left (2\right )^{2} - \frac {262144}{9} \, x^{7} \log \left (5\right )^{7} \log \left (2\right )^{2} + \frac {458752}{9} \, x^{6} \log \left (5\right )^{6} \log \left (2\right )^{2} - \frac {458752}{9} \, x^{5} \log \left (5\right )^{5} \log \left (2\right )^{2} - \frac {512}{9} \, {\left (2 \, x^{6} - 565 \, x^{4}\right )} \log \left (5\right )^{4} \log \left (2\right )^{2} + \frac {1024}{9} \, {\left (2 \, x^{5} - 117 \, x^{3}\right )} \log \left (5\right )^{3} \log \left (2\right )^{2} - \frac {256}{9} \, {\left (6 \, x^{4} - 127 \, x^{2}\right )} \log \left (5\right )^{2} \log \left (2\right )^{2} + \frac {256}{9} \, {\left (2 \, x^{3} - 21 \, x\right )} \log \left (5\right ) \log \left (2\right )^{2} + \frac {4}{9} \, {\left (x^{4} - 21 \, x^{2}\right )} \log \left (2\right )^{2} \] Input:
integrate(524288/9*x^7*log(2)^2*log(5)^8-1835008/9*x^6*log(2)^2*log(5)^7+9 17504/3*x^5*log(2)^2*log(5)^6-2293760/9*x^4*log(2)^2*log(5)^5+1/9*(-6144*x ^5+1157120*x^3)*log(2)^2*log(5)^4+1/9*(10240*x^4-359424*x^2)*log(2)^2*log( 5)^3+1/9*(-6144*x^3+65024*x)*log(2)^2*log(5)^2+1/9*(1536*x^2-5376)*log(2)^ 2*log(5)+1/9*(16*x^3-168*x)*log(2)^2,x, algorithm="maxima")
Output:
65536/9*x^8*log(5)^8*log(2)^2 - 262144/9*x^7*log(5)^7*log(2)^2 + 458752/9* x^6*log(5)^6*log(2)^2 - 458752/9*x^5*log(5)^5*log(2)^2 - 512/9*(2*x^6 - 56 5*x^4)*log(5)^4*log(2)^2 + 1024/9*(2*x^5 - 117*x^3)*log(5)^3*log(2)^2 - 25 6/9*(6*x^4 - 127*x^2)*log(5)^2*log(2)^2 + 256/9*(2*x^3 - 21*x)*log(5)*log( 2)^2 + 4/9*(x^4 - 21*x^2)*log(2)^2
Leaf count of result is larger than twice the leaf count of optimal. 148 vs. \(2 (26) = 52\).
Time = 0.11 (sec) , antiderivative size = 148, normalized size of antiderivative = 5.29 \[ \int \frac {1}{9} \left (\left (-168 x+16 x^3\right ) \log ^2(2)+\left (-5376+1536 x^2\right ) \log ^2(2) \log (5)+\left (65024 x-6144 x^3\right ) \log ^2(2) \log ^2(5)+\left (-359424 x^2+10240 x^4\right ) \log ^2(2) \log ^3(5)+\left (1157120 x^3-6144 x^5\right ) \log ^2(2) \log ^4(5)-2293760 x^4 \log ^2(2) \log ^5(5)+2752512 x^5 \log ^2(2) \log ^6(5)-1835008 x^6 \log ^2(2) \log ^7(5)+524288 x^7 \log ^2(2) \log ^8(5)\right ) \, dx=\frac {65536}{9} \, x^{8} \log \left (5\right )^{8} \log \left (2\right )^{2} - \frac {262144}{9} \, x^{7} \log \left (5\right )^{7} \log \left (2\right )^{2} + \frac {458752}{9} \, x^{6} \log \left (5\right )^{6} \log \left (2\right )^{2} - \frac {458752}{9} \, x^{5} \log \left (5\right )^{5} \log \left (2\right )^{2} - \frac {512}{9} \, {\left (2 \, x^{6} - 565 \, x^{4}\right )} \log \left (5\right )^{4} \log \left (2\right )^{2} + \frac {1024}{9} \, {\left (2 \, x^{5} - 117 \, x^{3}\right )} \log \left (5\right )^{3} \log \left (2\right )^{2} - \frac {256}{9} \, {\left (6 \, x^{4} - 127 \, x^{2}\right )} \log \left (5\right )^{2} \log \left (2\right )^{2} + \frac {256}{9} \, {\left (2 \, x^{3} - 21 \, x\right )} \log \left (5\right ) \log \left (2\right )^{2} + \frac {4}{9} \, {\left (x^{4} - 21 \, x^{2}\right )} \log \left (2\right )^{2} \] Input:
integrate(524288/9*x^7*log(2)^2*log(5)^8-1835008/9*x^6*log(2)^2*log(5)^7+9 17504/3*x^5*log(2)^2*log(5)^6-2293760/9*x^4*log(2)^2*log(5)^5+1/9*(-6144*x ^5+1157120*x^3)*log(2)^2*log(5)^4+1/9*(10240*x^4-359424*x^2)*log(2)^2*log( 5)^3+1/9*(-6144*x^3+65024*x)*log(2)^2*log(5)^2+1/9*(1536*x^2-5376)*log(2)^ 2*log(5)+1/9*(16*x^3-168*x)*log(2)^2,x, algorithm="giac")
Output:
65536/9*x^8*log(5)^8*log(2)^2 - 262144/9*x^7*log(5)^7*log(2)^2 + 458752/9* x^6*log(5)^6*log(2)^2 - 458752/9*x^5*log(5)^5*log(2)^2 - 512/9*(2*x^6 - 56 5*x^4)*log(5)^4*log(2)^2 + 1024/9*(2*x^5 - 117*x^3)*log(5)^3*log(2)^2 - 25 6/9*(6*x^4 - 127*x^2)*log(5)^2*log(2)^2 + 256/9*(2*x^3 - 21*x)*log(5)*log( 2)^2 + 4/9*(x^4 - 21*x^2)*log(2)^2
Time = 0.07 (sec) , antiderivative size = 163, normalized size of antiderivative = 5.82 \[ \int \frac {1}{9} \left (\left (-168 x+16 x^3\right ) \log ^2(2)+\left (-5376+1536 x^2\right ) \log ^2(2) \log (5)+\left (65024 x-6144 x^3\right ) \log ^2(2) \log ^2(5)+\left (-359424 x^2+10240 x^4\right ) \log ^2(2) \log ^3(5)+\left (1157120 x^3-6144 x^5\right ) \log ^2(2) \log ^4(5)-2293760 x^4 \log ^2(2) \log ^5(5)+2752512 x^5 \log ^2(2) \log ^6(5)-1835008 x^6 \log ^2(2) \log ^7(5)+524288 x^7 \log ^2(2) \log ^8(5)\right ) \, dx=\frac {65536\,{\ln \left (2\right )}^2\,{\ln \left (5\right )}^8\,x^8}{9}-\frac {262144\,{\ln \left (2\right )}^2\,{\ln \left (5\right )}^7\,x^7}{9}+\left (\frac {458752\,{\ln \left (2\right )}^2\,{\ln \left (5\right )}^6}{9}-\frac {1024\,{\ln \left (2\right )}^2\,{\ln \left (5\right )}^4}{9}\right )\,x^6+\left (\frac {2048\,{\ln \left (2\right )}^2\,{\ln \left (5\right )}^3}{9}-\frac {458752\,{\ln \left (2\right )}^2\,{\ln \left (5\right )}^5}{9}\right )\,x^5+\left (\frac {4\,{\ln \left (2\right )}^2}{9}-\frac {512\,{\ln \left (2\right )}^2\,{\ln \left (5\right )}^2}{3}+\frac {289280\,{\ln \left (2\right )}^2\,{\ln \left (5\right )}^4}{9}\right )\,x^4+\left (\frac {512\,{\ln \left (2\right )}^2\,\ln \left (5\right )}{9}-13312\,{\ln \left (2\right )}^2\,{\ln \left (5\right )}^3\right )\,x^3+\left (\frac {32512\,{\ln \left (2\right )}^2\,{\ln \left (5\right )}^2}{9}-\frac {28\,{\ln \left (2\right )}^2}{3}\right )\,x^2-\frac {1792\,{\ln \left (2\right )}^2\,\ln \left (5\right )\,x}{3} \] Input:
int((log(2)^2*log(5)*(1536*x^2 - 5376))/9 - (log(2)^2*(168*x - 16*x^3))/9 + (log(2)^2*log(5)^2*(65024*x - 6144*x^3))/9 - (log(2)^2*log(5)^3*(359424* x^2 - 10240*x^4))/9 + (log(2)^2*log(5)^4*(1157120*x^3 - 6144*x^5))/9 - (22 93760*x^4*log(2)^2*log(5)^5)/9 + (917504*x^5*log(2)^2*log(5)^6)/3 - (18350 08*x^6*log(2)^2*log(5)^7)/9 + (524288*x^7*log(2)^2*log(5)^8)/9,x)
Output:
x^3*((512*log(2)^2*log(5))/9 - 13312*log(2)^2*log(5)^3) - x^6*((1024*log(2 )^2*log(5)^4)/9 - (458752*log(2)^2*log(5)^6)/9) + x^5*((2048*log(2)^2*log( 5)^3)/9 - (458752*log(2)^2*log(5)^5)/9) + x^4*((4*log(2)^2)/9 - (512*log(2 )^2*log(5)^2)/3 + (289280*log(2)^2*log(5)^4)/9) - x^2*((28*log(2)^2)/3 - ( 32512*log(2)^2*log(5)^2)/9) - (1792*x*log(2)^2*log(5))/3 - (262144*x^7*log (2)^2*log(5)^7)/9 + (65536*x^8*log(2)^2*log(5)^8)/9
Time = 0.30 (sec) , antiderivative size = 113, normalized size of antiderivative = 4.04 \[ \int \frac {1}{9} \left (\left (-168 x+16 x^3\right ) \log ^2(2)+\left (-5376+1536 x^2\right ) \log ^2(2) \log (5)+\left (65024 x-6144 x^3\right ) \log ^2(2) \log ^2(5)+\left (-359424 x^2+10240 x^4\right ) \log ^2(2) \log ^3(5)+\left (1157120 x^3-6144 x^5\right ) \log ^2(2) \log ^4(5)-2293760 x^4 \log ^2(2) \log ^5(5)+2752512 x^5 \log ^2(2) \log ^6(5)-1835008 x^6 \log ^2(2) \log ^7(5)+524288 x^7 \log ^2(2) \log ^8(5)\right ) \, dx=\frac {4 \mathrm {log}\left (2\right )^{2} x \left (16384 \mathrm {log}\left (5\right )^{8} x^{7}-65536 \mathrm {log}\left (5\right )^{7} x^{6}+114688 \mathrm {log}\left (5\right )^{6} x^{5}-114688 \mathrm {log}\left (5\right )^{5} x^{4}-256 \mathrm {log}\left (5\right )^{4} x^{5}+72320 \mathrm {log}\left (5\right )^{4} x^{3}+512 \mathrm {log}\left (5\right )^{3} x^{4}-29952 \mathrm {log}\left (5\right )^{3} x^{2}-384 \mathrm {log}\left (5\right )^{2} x^{3}+8128 \mathrm {log}\left (5\right )^{2} x +128 \,\mathrm {log}\left (5\right ) x^{2}-1344 \,\mathrm {log}\left (5\right )+x^{3}-21 x \right )}{9} \] Input:
int(524288/9*x^7*log(2)^2*log(5)^8-1835008/9*x^6*log(2)^2*log(5)^7+917504/ 3*x^5*log(2)^2*log(5)^6-2293760/9*x^4*log(2)^2*log(5)^5+1/9*(-6144*x^5+115 7120*x^3)*log(2)^2*log(5)^4+1/9*(10240*x^4-359424*x^2)*log(2)^2*log(5)^3+1 /9*(-6144*x^3+65024*x)*log(2)^2*log(5)^2+1/9*(1536*x^2-5376)*log(2)^2*log( 5)+1/9*(16*x^3-168*x)*log(2)^2,x)
Output:
(4*log(2)**2*x*(16384*log(5)**8*x**7 - 65536*log(5)**7*x**6 + 114688*log(5 )**6*x**5 - 114688*log(5)**5*x**4 - 256*log(5)**4*x**5 + 72320*log(5)**4*x **3 + 512*log(5)**3*x**4 - 29952*log(5)**3*x**2 - 384*log(5)**2*x**3 + 812 8*log(5)**2*x + 128*log(5)*x**2 - 1344*log(5) + x**3 - 21*x))/9