3.9.67 \(\int \frac {1}{9} ((-168 x+16 x^3) \log ^2(2)+(-5376+1536 x^2) \log ^2(2) \log (5)+(65024 x-6144 x^3) \log ^2(2) \log ^2(5)+(-359424 x^2+10240 x^4) \log ^2(2) \log ^3(5)+(1157120 x^3-6144 x^5) \log ^2(2) \log ^4(5)-2293760 x^4 \log ^2(2) \log ^5(5)+2752512 x^5 \log ^2(2) \log ^6(5)-1835008 x^6 \log ^2(2) \log ^7(5)+524288 x^7 \log ^2(2) \log ^8(5)) \, dx\) [867]

Optimal. Leaf size=28 \[ \frac {1}{9} \log ^2(2) \left (-5+2 x^2-(2-4 x \log (5))^4\right )^2 \]

[Out]

1/9*ln(2)^2*(2*x^2-(2-4*x*ln(5))^4-5)^2

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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(195\) vs. \(2(28)=56\).
time = 0.05, antiderivative size = 195, normalized size of antiderivative = 6.96, number of steps used = 7, number of rules used = 1, integrand size = 143, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.007, Rules used = {12} \begin {gather*} \frac {65536}{9} x^8 \log ^2(2) \log ^8(5)-\frac {262144}{9} x^7 \log ^2(2) \log ^7(5)+\frac {458752}{9} x^6 \log ^2(2) \log ^6(5)-\frac {1024}{9} x^6 \log ^2(2) \log ^4(5)-\frac {458752}{9} x^5 \log ^2(2) \log ^5(5)+\frac {2048}{9} x^5 \log ^2(2) \log ^3(5)-\frac {512}{3} x^4 \log ^2(2) \log ^2(5)+\frac {4}{9} x^4 \log ^2(2)+\frac {289280}{9} x^4 \log ^2(2) \log ^4(5)+\frac {512}{9} x^3 \log ^2(2) \log (5)-13312 x^3 \log ^2(2) \log ^3(5)+\frac {32512}{9} x^2 \log ^2(2) \log ^2(5)-\frac {28}{3} x^2 \log ^2(2)-\frac {1792}{3} x \log ^2(2) \log (5) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[((-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*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]

[Out]

(-28*x^2*Log[2]^2)/3 + (4*x^4*Log[2]^2)/9 - (1792*x*Log[2]^2*Log[5])/3 + (512*x^3*Log[2]^2*Log[5])/9 + (32512*
x^2*Log[2]^2*Log[5]^2)/9 - (512*x^4*Log[2]^2*Log[5]^2)/3 - 13312*x^3*Log[2]^2*Log[5]^3 + (2048*x^5*Log[2]^2*Lo
g[5]^3)/9 + (289280*x^4*Log[2]^2*Log[5]^4)/9 - (1024*x^6*Log[2]^2*Log[5]^4)/9 - (458752*x^5*Log[2]^2*Log[5]^5)
/9 + (458752*x^6*Log[2]^2*Log[5]^6)/9 - (262144*x^7*Log[2]^2*Log[5]^7)/9 + (65536*x^8*Log[2]^2*Log[5]^8)/9

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{9} \int \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 {458752}{9} x^5 \log ^2(2) \log ^5(5)+\frac {458752}{9} x^6 \log ^2(2) \log ^6(5)-\frac {262144}{9} x^7 \log ^2(2) \log ^7(5)+\frac {65536}{9} x^8 \log ^2(2) \log ^8(5)+\frac {1}{9} \log ^2(2) \int \left (-168 x+16 x^3\right ) \, dx+\frac {1}{9} \left (\log ^2(2) \log (5)\right ) \int \left (-5376+1536 x^2\right ) \, dx+\frac {1}{9} \left (\log ^2(2) \log ^2(5)\right ) \int \left (65024 x-6144 x^3\right ) \, dx+\frac {1}{9} \left (\log ^2(2) \log ^3(5)\right ) \int \left (-359424 x^2+10240 x^4\right ) \, dx+\frac {1}{9} \left (\log ^2(2) \log ^4(5)\right ) \int \left (1157120 x^3-6144 x^5\right ) \, dx\\ &=-\frac {28}{3} x^2 \log ^2(2)+\frac {4}{9} x^4 \log ^2(2)-\frac {1792}{3} x \log ^2(2) \log (5)+\frac {512}{9} x^3 \log ^2(2) \log (5)+\frac {32512}{9} x^2 \log ^2(2) \log ^2(5)-\frac {512}{3} x^4 \log ^2(2) \log ^2(5)-13312 x^3 \log ^2(2) \log ^3(5)+\frac {2048}{9} x^5 \log ^2(2) \log ^3(5)+\frac {289280}{9} x^4 \log ^2(2) \log ^4(5)-\frac {1024}{9} x^6 \log ^2(2) \log ^4(5)-\frac {458752}{9} x^5 \log ^2(2) \log ^5(5)+\frac {458752}{9} x^6 \log ^2(2) \log ^6(5)-\frac {262144}{9} x^7 \log ^2(2) \log ^7(5)+\frac {65536}{9} x^8 \log ^2(2) \log ^8(5)\\ \end {aligned} \end {gather*}

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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(118\) vs. \(2(28)=56\).
time = 0.02, size = 118, normalized size = 4.21 \begin {gather*} \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 ) \end {gather*}

Antiderivative was successfully verified.

[In]

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
*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]

[Out]

(8*Log[2]^2*((-21*x^2)/2 - 672*x*Log[5] + 4064*x^2*Log[5]^2 - 32768*x^7*Log[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

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Maple [A]
time = 0.33, size = 48, normalized size = 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	\(\frac {4 \ln \left (2\right )^{2} x \left (16384 x^{7} \ln \left (5\right )^{8}-65536 x^{6} \ln \left (5\right )^{7}+114688 x^{5} \ln \left (5\right )^{6}-114688 x^{4} \ln \left (5\right )^{5}-256 \ln \left (5\right )^{4} x^{5}+72320 x^{3} \ln \left (5\right )^{4}+512 x^{4} \ln \left (5\right )^{3}-29952 x^{2} \ln \left (5\right )^{3}-384 x^{3} \ln \left (5\right )^{2}+8128 x \ln \left (5\right )^{2}+128 x^{2} \ln \left (5\right )+x^{3}-1344 \ln \left (5\right )-21 x \right )}{9}\)	\(114\)
norman	\(\left (\frac {32512 \ln \left (2\right )^{2} \ln \left (5\right )^{2}}{9}-\frac {28 \ln \left (2\right )^{2}}{3}\right ) x^{2}+\left (-13312 \ln \left (2\right )^{2} \ln \left (5\right )^{3}+\frac {512 \ln \left (2\right )^{2} \ln \left (5\right )}{9}\right ) x^{3}+\left (-\frac {458752 \ln \left (2\right )^{2} \ln \left (5\right )^{5}}{9}+\frac {2048 \ln \left (2\right )^{2} \ln \left (5\right )^{3}}{9}\right ) x^{5}+\left (\frac {458752 \ln \left (2\right )^{2} \ln \left (5\right )^{6}}{9}-\frac {1024 \ln \left (2\right )^{2} \ln \left (5\right )^{4}}{9}\right ) x^{6}+\left (\frac {289280 \ln \left (2\right )^{2} \ln \left (5\right )^{4}}{9}-\frac {512 \ln \left (2\right )^{2} \ln \left (5\right )^{2}}{3}+\frac {4 \ln \left (2\right )^{2}}{9}\right ) x^{4}-\frac {1792 x \ln \left (2\right )^{2} \ln \left (5\right )}{3}-\frac {262144 \ln \left (2\right )^{2} \ln \left (5\right )^{7} x^{7}}{9}+\frac {65536 \ln \left (2\right )^{2} \ln \left (5\right )^{8} x^{8}}{9}\)	\(162\)
risch	\(\frac {65536 \ln \left (2\right )^{2} \ln \left (5\right )^{8} x^{8}}{9}-\frac {262144 \ln \left (2\right )^{2} \ln \left (5\right )^{7} x^{7}}{9}+\frac {458752 \ln \left (2\right )^{2} \ln \left (5\right )^{6} x^{6}}{9}-\frac {458752 \ln \left (2\right )^{2} \ln \left (5\right )^{5} x^{5}}{9}-\frac {1024 \ln \left (2\right )^{2} \ln \left (5\right )^{4} x^{6}}{9}+\frac {289280 \ln \left (2\right )^{2} \ln \left (5\right )^{4} x^{4}}{9}+\frac {2048 \ln \left (2\right )^{2} \ln \left (5\right )^{3} x^{5}}{9}-13312 \ln \left (2\right )^{2} \ln \left (5\right )^{3} x^{3}-\frac {512 \ln \left (2\right )^{2} \ln \left (5\right )^{2} x^{4}}{3}+\frac {32512 x^{2} \ln \left (2\right )^{2} \ln \left (5\right )^{2}}{9}-\frac {516128 \ln \left (2\right )^{2} \ln \left (5\right )^{2}}{27}+\frac {512 \ln \left (2\right )^{2} \ln \left (5\right ) x^{3}}{9}-\frac {1792 x \ln \left (2\right )^{2} \ln \left (5\right )}{3}+\frac {4 x^{4} \ln \left (2\right )^{2}}{9}-\frac {28 x^{2} \ln \left (2\right )^{2}}{3}+49 \ln \left (2\right )^{2}\)	\(186\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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^3-168*x)*ln(2)^2,x,method=_RETURNVERB
OSE)

[Out]

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

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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 148 vs. \(2 (26) = 52\).
time = 0.26, size = 148, normalized size = 5.29 \begin {gather*} \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} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(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)^6-229376
0/9*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*lo
g(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")

[Out]

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 - 565*x^4)*log(5)^4*log(2)^2 + 1024/9*(2*x^5 - 117*x^3)*log(5)^3*log(2)^2 -
256/9*(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

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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 148 vs. \(2 (26) = 52\).
time = 0.36, size = 148, normalized size = 5.29 \begin {gather*} \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} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(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)^6-229376
0/9*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*lo
g(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")

[Out]

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 - 565*x^4)*log(5)^4*log(2)^2 + 1024/9*(2*x^5 - 117*x^3)*log(5)^3*log(2)^2 -
256/9*(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

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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 199 vs. \(2 (24) = 48\).
time = 0.03, size = 199, normalized size = 7.11 \begin {gather*} \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} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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)**6-229
3760/9*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**3-168
*x)*ln(2)**2,x)

[Out]

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 + 458
752*log(2)**2*log(5)**6/9) + x**5*(-458752*log(2)**2*log(5)**5/9 + 2048*log(2)**2*log(5)**3/9) + x**4*(-512*lo
g(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*l
og(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

________________________________________________________________________________________

Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 148 vs. \(2 (26) = 52\).
time = 0.40, size = 148, normalized size = 5.29 \begin {gather*} \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} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(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)^6-229376
0/9*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*lo
g(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")

[Out]

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 - 565*x^4)*log(5)^4*log(2)^2 + 1024/9*(2*x^5 - 117*x^3)*log(5)^3*log(2)^2 -
256/9*(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

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Mupad [B]
time = 0.09, size = 163, normalized size = 5.82 \begin {gather*} \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} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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 - (
2293760*x^4*log(2)^2*log(5)^5)/9 + (917504*x^5*log(2)^2*log(5)^6)/3 - (1835008*x^6*log(2)^2*log(5)^7)/9 + (524
288*x^7*log(2)^2*log(5)^8)/9,x)

[Out]

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*l
og(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) - (179
2*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

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