3.96.18 \(\int \frac {-144+420 x^2-1260 x^3+68600 x^4+102900 x^5+34300 x^6+(18-60 x^2+390 x^3-29400 x^4-44100 x^5-14700 x^6) \log ^2(5)+(-30 x^3+4200 x^4+6300 x^5+2100 x^6) \log ^4(5)+(-200 x^4-300 x^5-100 x^6) \log ^6(5)+(-18+60 x^2-390 x^3+29400 x^4+44100 x^5+14700 x^6+(60 x^3-8400 x^4-12600 x^5-4200 x^6) \log ^2(5)+(600 x^4+900 x^5+300 x^6) \log ^4(5)) \log (4 x)+(-30 x^3+4200 x^4+6300 x^5+2100 x^6+(-600 x^4-900 x^5-300 x^6) \log ^2(5)) \log ^2(4 x)+(200 x^4+300 x^5+100 x^6) \log ^3(4 x)}{8575 x^3-3675 x^3 \log ^2(5)+525 x^3 \log ^4(5)-25 x^3 \log ^6(5)+(3675 x^3-1050 x^3 \log ^2(5)+75 x^3 \log ^4(5)) \log (4 x)+(525 x^3-75 x^3 \log ^2(5)) \log ^2(4 x)+25 x^3 \log ^3(4 x)} \, dx\)

Optimal. Leaf size=30 \[ \left (2 x+x^2+\frac {3}{5 x \left (-7+\log ^2(5)-\log (4 x)\right )}\right )^2 \]

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Rubi [F]  time = 2.08, 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 {-144+420 x^2-1260 x^3+68600 x^4+102900 x^5+34300 x^6+\left (18-60 x^2+390 x^3-29400 x^4-44100 x^5-14700 x^6\right ) \log ^2(5)+\left (-30 x^3+4200 x^4+6300 x^5+2100 x^6\right ) \log ^4(5)+\left (-200 x^4-300 x^5-100 x^6\right ) \log ^6(5)+\left (-18+60 x^2-390 x^3+29400 x^4+44100 x^5+14700 x^6+\left (60 x^3-8400 x^4-12600 x^5-4200 x^6\right ) \log ^2(5)+\left (600 x^4+900 x^5+300 x^6\right ) \log ^4(5)\right ) \log (4 x)+\left (-30 x^3+4200 x^4+6300 x^5+2100 x^6+\left (-600 x^4-900 x^5-300 x^6\right ) \log ^2(5)\right ) \log ^2(4 x)+\left (200 x^4+300 x^5+100 x^6\right ) \log ^3(4 x)}{8575 x^3-3675 x^3 \log ^2(5)+525 x^3 \log ^4(5)-25 x^3 \log ^6(5)+\left (3675 x^3-1050 x^3 \log ^2(5)+75 x^3 \log ^4(5)\right ) \log (4 x)+\left (525 x^3-75 x^3 \log ^2(5)\right ) \log ^2(4 x)+25 x^3 \log ^3(4 x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-144 + 420*x^2 - 1260*x^3 + 68600*x^4 + 102900*x^5 + 34300*x^6 + (18 - 60*x^2 + 390*x^3 - 29400*x^4 - 441
00*x^5 - 14700*x^6)*Log[5]^2 + (-30*x^3 + 4200*x^4 + 6300*x^5 + 2100*x^6)*Log[5]^4 + (-200*x^4 - 300*x^5 - 100
*x^6)*Log[5]^6 + (-18 + 60*x^2 - 390*x^3 + 29400*x^4 + 44100*x^5 + 14700*x^6 + (60*x^3 - 8400*x^4 - 12600*x^5
- 4200*x^6)*Log[5]^2 + (600*x^4 + 900*x^5 + 300*x^6)*Log[5]^4)*Log[4*x] + (-30*x^3 + 4200*x^4 + 6300*x^5 + 210
0*x^6 + (-600*x^4 - 900*x^5 - 300*x^6)*Log[5]^2)*Log[4*x]^2 + (200*x^4 + 300*x^5 + 100*x^6)*Log[4*x]^3)/(8575*
x^3 - 3675*x^3*Log[5]^2 + 525*x^3*Log[5]^4 - 25*x^3*Log[5]^6 + (3675*x^3 - 1050*x^3*Log[5]^2 + 75*x^3*Log[5]^4
)*Log[4*x] + (525*x^3 - 75*x^3*Log[5]^2)*Log[4*x]^2 + 25*x^3*Log[4*x]^3),x]

[Out]

4*x^2 + 4*x^3 + x^4 - (576*E^(14 - 2*Log[5]^2)*ExpIntegralEi[-2*(7 - Log[5]^2 + Log[4*x])])/25 - (3*E^(-7 + Lo
g[5]^2)*ExpIntegralEi[7 - Log[5]^2 + Log[4*x]])/10 + 9/(25*x^2*(7 - Log[5]^2 + Log[4*x])^2) - 18/(25*x^2*(7 -
Log[5]^2 + Log[4*x])) + (6*Defer[Int][(-3 + 10*x^2 + 5*x^3)/(x^3*(7*(1 - Log[5]^2/7) + Log[4*x])^2), x])/25

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-144+420 x^2-1260 x^3+68600 x^4+102900 x^5+34300 x^6+\left (18-60 x^2+390 x^3-29400 x^4-44100 x^5-14700 x^6\right ) \log ^2(5)+\left (-30 x^3+4200 x^4+6300 x^5+2100 x^6\right ) \log ^4(5)+\left (-200 x^4-300 x^5-100 x^6\right ) \log ^6(5)+\left (-18+60 x^2-390 x^3+29400 x^4+44100 x^5+14700 x^6+\left (60 x^3-8400 x^4-12600 x^5-4200 x^6\right ) \log ^2(5)+\left (600 x^4+900 x^5+300 x^6\right ) \log ^4(5)\right ) \log (4 x)+\left (-30 x^3+4200 x^4+6300 x^5+2100 x^6+\left (-600 x^4-900 x^5-300 x^6\right ) \log ^2(5)\right ) \log ^2(4 x)+\left (200 x^4+300 x^5+100 x^6\right ) \log ^3(4 x)}{525 x^3 \log ^4(5)-25 x^3 \log ^6(5)+x^3 \left (8575-3675 \log ^2(5)\right )+\left (3675 x^3-1050 x^3 \log ^2(5)+75 x^3 \log ^4(5)\right ) \log (4 x)+\left (525 x^3-75 x^3 \log ^2(5)\right ) \log ^2(4 x)+25 x^3 \log ^3(4 x)} \, dx\\ &=\int \frac {-144+420 x^2-1260 x^3+68600 x^4+102900 x^5+34300 x^6+\left (18-60 x^2+390 x^3-29400 x^4-44100 x^5-14700 x^6\right ) \log ^2(5)+\left (-30 x^3+4200 x^4+6300 x^5+2100 x^6\right ) \log ^4(5)+\left (-200 x^4-300 x^5-100 x^6\right ) \log ^6(5)+\left (-18+60 x^2-390 x^3+29400 x^4+44100 x^5+14700 x^6+\left (60 x^3-8400 x^4-12600 x^5-4200 x^6\right ) \log ^2(5)+\left (600 x^4+900 x^5+300 x^6\right ) \log ^4(5)\right ) \log (4 x)+\left (-30 x^3+4200 x^4+6300 x^5+2100 x^6+\left (-600 x^4-900 x^5-300 x^6\right ) \log ^2(5)\right ) \log ^2(4 x)+\left (200 x^4+300 x^5+100 x^6\right ) \log ^3(4 x)}{x^3 \left (8575-3675 \log ^2(5)\right )+x^3 \left (525 \log ^4(5)-25 \log ^6(5)\right )+\left (3675 x^3-1050 x^3 \log ^2(5)+75 x^3 \log ^4(5)\right ) \log (4 x)+\left (525 x^3-75 x^3 \log ^2(5)\right ) \log ^2(4 x)+25 x^3 \log ^3(4 x)} \, dx\\ &=\int \frac {-144+420 x^2-1260 x^3+68600 x^4+102900 x^5+34300 x^6+\left (18-60 x^2+390 x^3-29400 x^4-44100 x^5-14700 x^6\right ) \log ^2(5)+\left (-30 x^3+4200 x^4+6300 x^5+2100 x^6\right ) \log ^4(5)+\left (-200 x^4-300 x^5-100 x^6\right ) \log ^6(5)+\left (-18+60 x^2-390 x^3+29400 x^4+44100 x^5+14700 x^6+\left (60 x^3-8400 x^4-12600 x^5-4200 x^6\right ) \log ^2(5)+\left (600 x^4+900 x^5+300 x^6\right ) \log ^4(5)\right ) \log (4 x)+\left (-30 x^3+4200 x^4+6300 x^5+2100 x^6+\left (-600 x^4-900 x^5-300 x^6\right ) \log ^2(5)\right ) \log ^2(4 x)+\left (200 x^4+300 x^5+100 x^6\right ) \log ^3(4 x)}{x^3 \left (8575-3675 \log ^2(5)+525 \log ^4(5)-25 \log ^6(5)\right )+\left (3675 x^3-1050 x^3 \log ^2(5)+75 x^3 \log ^4(5)\right ) \log (4 x)+\left (525 x^3-75 x^3 \log ^2(5)\right ) \log ^2(4 x)+25 x^3 \log ^3(4 x)} \, dx\\ &=\int \frac {2 \left (9 \left (-8+\log ^2(5)\right )-30 x^2 \left (-7+\log ^2(5)\right )-100 x^4 \left (-7+\log ^2(5)\right )^3-150 x^5 \left (-7+\log ^2(5)\right )^3-50 x^6 \left (-7+\log ^2(5)\right )^3-15 x^3 \left (42-13 \log ^2(5)+\log ^4(5)\right )+3 \left (-3+10 x^2+100 x^4 \left (-7+\log ^2(5)\right )^2+150 x^5 \left (-7+\log ^2(5)\right )^2+50 x^6 \left (-7+\log ^2(5)\right )^2+5 x^3 \left (-13+2 \log ^2(5)\right )\right ) \log (4 x)-15 x^3 \left (1+20 x \left (-7+\log ^2(5)\right )+30 x^2 \left (-7+\log ^2(5)\right )+10 x^3 \left (-7+\log ^2(5)\right )\right ) \log ^2(4 x)+50 x^4 \left (2+3 x+x^2\right ) \log ^3(4 x)\right )}{25 x^3 \left (7 \left (1-\frac {\log ^2(5)}{7}\right )+\log (4 x)\right )^3} \, dx\\ &=\frac {2}{25} \int \frac {9 \left (-8+\log ^2(5)\right )-30 x^2 \left (-7+\log ^2(5)\right )-100 x^4 \left (-7+\log ^2(5)\right )^3-150 x^5 \left (-7+\log ^2(5)\right )^3-50 x^6 \left (-7+\log ^2(5)\right )^3-15 x^3 \left (42-13 \log ^2(5)+\log ^4(5)\right )+3 \left (-3+10 x^2+100 x^4 \left (-7+\log ^2(5)\right )^2+150 x^5 \left (-7+\log ^2(5)\right )^2+50 x^6 \left (-7+\log ^2(5)\right )^2+5 x^3 \left (-13+2 \log ^2(5)\right )\right ) \log (4 x)-15 x^3 \left (1+20 x \left (-7+\log ^2(5)\right )+30 x^2 \left (-7+\log ^2(5)\right )+10 x^3 \left (-7+\log ^2(5)\right )\right ) \log ^2(4 x)+50 x^4 \left (2+3 x+x^2\right ) \log ^3(4 x)}{x^3 \left (7 \left (1-\frac {\log ^2(5)}{7}\right )+\log (4 x)\right )^3} \, dx\\ &=\frac {2}{25} \int \left (50 x \left (2+3 x+x^2\right )+\frac {9}{x^3 \left (-7 \left (1-\frac {\log ^2(5)}{7}\right )-\log (4 x)\right )^3}+\frac {15}{-7 \left (1-\frac {\log ^2(5)}{7}\right )-\log (4 x)}+\frac {3 \left (-3+10 x^2+5 x^3\right )}{x^3 \left (7 \left (1-\frac {\log ^2(5)}{7}\right )+\log (4 x)\right )^2}\right ) \, dx\\ &=\frac {6}{25} \int \frac {-3+10 x^2+5 x^3}{x^3 \left (7 \left (1-\frac {\log ^2(5)}{7}\right )+\log (4 x)\right )^2} \, dx+\frac {18}{25} \int \frac {1}{x^3 \left (-7 \left (1-\frac {\log ^2(5)}{7}\right )-\log (4 x)\right )^3} \, dx+\frac {6}{5} \int \frac {1}{-7 \left (1-\frac {\log ^2(5)}{7}\right )-\log (4 x)} \, dx+4 \int x \left (2+3 x+x^2\right ) \, dx\\ &=\frac {9}{25 x^2 \left (7-\log ^2(5)+\log (4 x)\right )^2}+\frac {6}{25} \int \frac {-3+10 x^2+5 x^3}{x^3 \left (7 \left (1-\frac {\log ^2(5)}{7}\right )+\log (4 x)\right )^2} \, dx+\frac {3}{10} \operatorname {Subst}\left (\int \frac {e^x}{-x-7 \left (1-\frac {\log ^2(5)}{7}\right )} \, dx,x,\log (4 x)\right )+\frac {18}{25} \int \frac {1}{x^3 \left (-7 \left (1-\frac {\log ^2(5)}{7}\right )-\log (4 x)\right )^2} \, dx+4 \int \left (2 x+3 x^2+x^3\right ) \, dx\\ &=4 x^2+4 x^3+x^4-\frac {3}{10} e^{-7+\log ^2(5)} \text {Ei}\left (7-\log ^2(5)+\log (4 x)\right )+\frac {9}{25 x^2 \left (7-\log ^2(5)+\log (4 x)\right )^2}-\frac {18}{25 x^2 \left (7-\log ^2(5)+\log (4 x)\right )}+\frac {6}{25} \int \frac {-3+10 x^2+5 x^3}{x^3 \left (7 \left (1-\frac {\log ^2(5)}{7}\right )+\log (4 x)\right )^2} \, dx+\frac {36}{25} \int \frac {1}{x^3 \left (-7 \left (1-\frac {\log ^2(5)}{7}\right )-\log (4 x)\right )} \, dx\\ &=4 x^2+4 x^3+x^4-\frac {3}{10} e^{-7+\log ^2(5)} \text {Ei}\left (7-\log ^2(5)+\log (4 x)\right )+\frac {9}{25 x^2 \left (7-\log ^2(5)+\log (4 x)\right )^2}-\frac {18}{25 x^2 \left (7-\log ^2(5)+\log (4 x)\right )}+\frac {6}{25} \int \frac {-3+10 x^2+5 x^3}{x^3 \left (7 \left (1-\frac {\log ^2(5)}{7}\right )+\log (4 x)\right )^2} \, dx+\frac {576}{25} \operatorname {Subst}\left (\int \frac {e^{-2 x}}{-x-7 \left (1-\frac {\log ^2(5)}{7}\right )} \, dx,x,\log (4 x)\right )\\ &=4 x^2+4 x^3+x^4-\frac {576}{25} e^{14-2 \log ^2(5)} \text {Ei}\left (-2 \left (7-\log ^2(5)+\log (4 x)\right )\right )-\frac {3}{10} e^{-7+\log ^2(5)} \text {Ei}\left (7-\log ^2(5)+\log (4 x)\right )+\frac {9}{25 x^2 \left (7-\log ^2(5)+\log (4 x)\right )^2}-\frac {18}{25 x^2 \left (7-\log ^2(5)+\log (4 x)\right )}+\frac {6}{25} \int \frac {-3+10 x^2+5 x^3}{x^3 \left (7 \left (1-\frac {\log ^2(5)}{7}\right )+\log (4 x)\right )^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.12, size = 62, normalized size = 2.07 \begin {gather*} \frac {2}{25} \left (50 x^2+50 x^3+\frac {25 x^4}{2}+\frac {9}{2 x^2 \left (7-\log ^2(5)+\log (4 x)\right )^2}-\frac {15 (2+x)}{7-\log ^2(5)+\log (4 x)}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-144 + 420*x^2 - 1260*x^3 + 68600*x^4 + 102900*x^5 + 34300*x^6 + (18 - 60*x^2 + 390*x^3 - 29400*x^4
- 44100*x^5 - 14700*x^6)*Log[5]^2 + (-30*x^3 + 4200*x^4 + 6300*x^5 + 2100*x^6)*Log[5]^4 + (-200*x^4 - 300*x^5
- 100*x^6)*Log[5]^6 + (-18 + 60*x^2 - 390*x^3 + 29400*x^4 + 44100*x^5 + 14700*x^6 + (60*x^3 - 8400*x^4 - 1260
0*x^5 - 4200*x^6)*Log[5]^2 + (600*x^4 + 900*x^5 + 300*x^6)*Log[5]^4)*Log[4*x] + (-30*x^3 + 4200*x^4 + 6300*x^5
+ 2100*x^6 + (-600*x^4 - 900*x^5 - 300*x^6)*Log[5]^2)*Log[4*x]^2 + (200*x^4 + 300*x^5 + 100*x^6)*Log[4*x]^3)/
(8575*x^3 - 3675*x^3*Log[5]^2 + 525*x^3*Log[5]^4 - 25*x^3*Log[5]^6 + (3675*x^3 - 1050*x^3*Log[5]^2 + 75*x^3*Lo
g[5]^4)*Log[4*x] + (525*x^3 - 75*x^3*Log[5]^2)*Log[4*x]^2 + 25*x^3*Log[4*x]^3),x]

[Out]

(2*(50*x^2 + 50*x^3 + (25*x^4)/2 + 9/(2*x^2*(7 - Log[5]^2 + Log[4*x])^2) - (15*(2 + x))/(7 - Log[5]^2 + Log[4*
x])))/25

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fricas [B]  time = 0.61, size = 210, normalized size = 7.00 \begin {gather*} \frac {1225 \, x^{6} + 4900 \, x^{5} + 25 \, {\left (x^{6} + 4 \, x^{5} + 4 \, x^{4}\right )} \log \relax (5)^{4} + 4900 \, x^{4} - 210 \, x^{3} - 10 \, {\left (35 \, x^{6} + 140 \, x^{5} + 140 \, x^{4} - 3 \, x^{3} - 6 \, x^{2}\right )} \log \relax (5)^{2} + 25 \, {\left (x^{6} + 4 \, x^{5} + 4 \, x^{4}\right )} \log \left (4 \, x\right )^{2} - 420 \, x^{2} + 10 \, {\left (35 \, x^{6} + 140 \, x^{5} + 140 \, x^{4} - 3 \, x^{3} - 5 \, {\left (x^{6} + 4 \, x^{5} + 4 \, x^{4}\right )} \log \relax (5)^{2} - 6 \, x^{2}\right )} \log \left (4 \, x\right ) + 9}{25 \, {\left (x^{2} \log \relax (5)^{4} - 14 \, x^{2} \log \relax (5)^{2} + x^{2} \log \left (4 \, x\right )^{2} + 49 \, x^{2} - 2 \, {\left (x^{2} \log \relax (5)^{2} - 7 \, x^{2}\right )} \log \left (4 \, x\right )\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((100*x^6+300*x^5+200*x^4)*log(4*x)^3+((-300*x^6-900*x^5-600*x^4)*log(5)^2+2100*x^6+6300*x^5+4200*x^
4-30*x^3)*log(4*x)^2+((300*x^6+900*x^5+600*x^4)*log(5)^4+(-4200*x^6-12600*x^5-8400*x^4+60*x^3)*log(5)^2+14700*
x^6+44100*x^5+29400*x^4-390*x^3+60*x^2-18)*log(4*x)+(-100*x^6-300*x^5-200*x^4)*log(5)^6+(2100*x^6+6300*x^5+420
0*x^4-30*x^3)*log(5)^4+(-14700*x^6-44100*x^5-29400*x^4+390*x^3-60*x^2+18)*log(5)^2+34300*x^6+102900*x^5+68600*
x^4-1260*x^3+420*x^2-144)/(25*x^3*log(4*x)^3+(-75*x^3*log(5)^2+525*x^3)*log(4*x)^2+(75*x^3*log(5)^4-1050*x^3*l
og(5)^2+3675*x^3)*log(4*x)-25*x^3*log(5)^6+525*x^3*log(5)^4-3675*x^3*log(5)^2+8575*x^3),x, algorithm="fricas")

[Out]

1/25*(1225*x^6 + 4900*x^5 + 25*(x^6 + 4*x^5 + 4*x^4)*log(5)^4 + 4900*x^4 - 210*x^3 - 10*(35*x^6 + 140*x^5 + 14
0*x^4 - 3*x^3 - 6*x^2)*log(5)^2 + 25*(x^6 + 4*x^5 + 4*x^4)*log(4*x)^2 - 420*x^2 + 10*(35*x^6 + 140*x^5 + 140*x
^4 - 3*x^3 - 5*(x^6 + 4*x^5 + 4*x^4)*log(5)^2 - 6*x^2)*log(4*x) + 9)/(x^2*log(5)^4 - 14*x^2*log(5)^2 + x^2*log
(4*x)^2 + 49*x^2 - 2*(x^2*log(5)^2 - 7*x^2)*log(4*x))

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giac [B]  time = 0.69, size = 121, normalized size = 4.03 \begin {gather*} x^{4} + 4 \, x^{3} + 4 \, x^{2} + \frac {3 \, {\left (10 \, x^{3} \log \relax (5)^{2} + 20 \, x^{2} \log \relax (5)^{2} - 10 \, x^{3} \log \left (4 \, x\right ) - 70 \, x^{3} - 20 \, x^{2} \log \left (4 \, x\right ) - 140 \, x^{2} + 3\right )}}{25 \, {\left (x^{2} \log \relax (5)^{4} - 2 \, x^{2} \log \relax (5)^{2} \log \left (4 \, x\right ) - 14 \, x^{2} \log \relax (5)^{2} + x^{2} \log \left (4 \, x\right )^{2} + 14 \, x^{2} \log \left (4 \, x\right ) + 49 \, x^{2}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((100*x^6+300*x^5+200*x^4)*log(4*x)^3+((-300*x^6-900*x^5-600*x^4)*log(5)^2+2100*x^6+6300*x^5+4200*x^
4-30*x^3)*log(4*x)^2+((300*x^6+900*x^5+600*x^4)*log(5)^4+(-4200*x^6-12600*x^5-8400*x^4+60*x^3)*log(5)^2+14700*
x^6+44100*x^5+29400*x^4-390*x^3+60*x^2-18)*log(4*x)+(-100*x^6-300*x^5-200*x^4)*log(5)^6+(2100*x^6+6300*x^5+420
0*x^4-30*x^3)*log(5)^4+(-14700*x^6-44100*x^5-29400*x^4+390*x^3-60*x^2+18)*log(5)^2+34300*x^6+102900*x^5+68600*
x^4-1260*x^3+420*x^2-144)/(25*x^3*log(4*x)^3+(-75*x^3*log(5)^2+525*x^3)*log(4*x)^2+(75*x^3*log(5)^4-1050*x^3*l
og(5)^2+3675*x^3)*log(4*x)-25*x^3*log(5)^6+525*x^3*log(5)^4-3675*x^3*log(5)^2+8575*x^3),x, algorithm="giac")

[Out]

x^4 + 4*x^3 + 4*x^2 + 3/25*(10*x^3*log(5)^2 + 20*x^2*log(5)^2 - 10*x^3*log(4*x) - 70*x^3 - 20*x^2*log(4*x) - 1
40*x^2 + 3)/(x^2*log(5)^4 - 2*x^2*log(5)^2*log(4*x) - 14*x^2*log(5)^2 + x^2*log(4*x)^2 + 14*x^2*log(4*x) + 49*
x^2)

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maple [B]  time = 0.07, size = 82, normalized size = 2.73

method	result	size
risch	\(x^{4}+4 x^{3}+4 x^{2}+\frac {\frac {6 x^{3} \ln \relax (5)^{2}}{5}+\frac {12 x^{2} \ln \relax (5)^{2}}{5}-\frac {6 x^{3} \ln \left (4 x \right )}{5}-\frac {42 x^{3}}{5}-\frac {12 x^{2} \ln \left (4 x \right )}{5}-\frac {84 x^{2}}{5}+\frac {9}{25}}{x^{2} \left (\ln \relax (5)^{2}-7-\ln \left (4 x \right )\right )^{2}}\)	\(82\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((100*x^6+300*x^5+200*x^4)*ln(4*x)^3+((-300*x^6-900*x^5-600*x^4)*ln(5)^2+2100*x^6+6300*x^5+4200*x^4-30*x^3
)*ln(4*x)^2+((300*x^6+900*x^5+600*x^4)*ln(5)^4+(-4200*x^6-12600*x^5-8400*x^4+60*x^3)*ln(5)^2+14700*x^6+44100*x
^5+29400*x^4-390*x^3+60*x^2-18)*ln(4*x)+(-100*x^6-300*x^5-200*x^4)*ln(5)^6+(2100*x^6+6300*x^5+4200*x^4-30*x^3)
*ln(5)^4+(-14700*x^6-44100*x^5-29400*x^4+390*x^3-60*x^2+18)*ln(5)^2+34300*x^6+102900*x^5+68600*x^4-1260*x^3+42
0*x^2-144)/(25*x^3*ln(4*x)^3+(-75*x^3*ln(5)^2+525*x^3)*ln(4*x)^2+(75*x^3*ln(5)^4-1050*x^3*ln(5)^2+3675*x^3)*ln
(4*x)-25*x^3*ln(5)^6+525*x^3*ln(5)^4-3675*x^3*ln(5)^2+8575*x^3),x,method=_RETURNVERBOSE)

[Out]

x^4+4*x^3+4*x^2+3/25*(10*x^3*ln(5)^2+20*x^2*ln(5)^2-10*x^3*ln(4*x)-70*x^3-20*x^2*ln(4*x)-140*x^2+3)/x^2/(ln(5)
^2-7-ln(4*x))^2

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maxima [B]  time = 0.49, size = 275, normalized size = 9.17 \begin {gather*} -\frac {25 \, {\left (\log \relax (5)^{4} - 14 \, \log \relax (5)^{2} - 4 \, {\left (\log \relax (5)^{2} - 7\right )} \log \relax (2) + 4 \, \log \relax (2)^{2} + 49\right )} x^{6} + 100 \, {\left (\log \relax (5)^{4} - 14 \, \log \relax (5)^{2} - 4 \, {\left (\log \relax (5)^{2} - 7\right )} \log \relax (2) + 4 \, \log \relax (2)^{2} + 49\right )} x^{5} + 100 \, {\left (\log \relax (5)^{4} - 14 \, \log \relax (5)^{2} - 4 \, {\left (\log \relax (5)^{2} - 7\right )} \log \relax (2) + 4 \, \log \relax (2)^{2} + 49\right )} x^{4} + 30 \, {\left (\log \relax (5)^{2} - 2 \, \log \relax (2) - 7\right )} x^{3} + 60 \, {\left (\log \relax (5)^{2} - 2 \, \log \relax (2) - 7\right )} x^{2} + 25 \, {\left (x^{6} + 4 \, x^{5} + 4 \, x^{4}\right )} \log \relax (x)^{2} - 10 \, {\left (5 \, {\left (\log \relax (5)^{2} - 2 \, \log \relax (2) - 7\right )} x^{6} + 20 \, {\left (\log \relax (5)^{2} - 2 \, \log \relax (2) - 7\right )} x^{5} + 20 \, {\left (\log \relax (5)^{2} - 2 \, \log \relax (2) - 7\right )} x^{4} + 3 \, x^{3} + 6 \, x^{2}\right )} \log \relax (x) + 9}{25 \, {\left (2 \, {\left (\log \relax (5)^{2} - 2 \, \log \relax (2) - 7\right )} x^{2} \log \relax (x) - x^{2} \log \relax (x)^{2} - {\left (\log \relax (5)^{4} - 14 \, \log \relax (5)^{2} - 4 \, {\left (\log \relax (5)^{2} - 7\right )} \log \relax (2) + 4 \, \log \relax (2)^{2} + 49\right )} x^{2}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((100*x^6+300*x^5+200*x^4)*log(4*x)^3+((-300*x^6-900*x^5-600*x^4)*log(5)^2+2100*x^6+6300*x^5+4200*x^
4-30*x^3)*log(4*x)^2+((300*x^6+900*x^5+600*x^4)*log(5)^4+(-4200*x^6-12600*x^5-8400*x^4+60*x^3)*log(5)^2+14700*
x^6+44100*x^5+29400*x^4-390*x^3+60*x^2-18)*log(4*x)+(-100*x^6-300*x^5-200*x^4)*log(5)^6+(2100*x^6+6300*x^5+420
0*x^4-30*x^3)*log(5)^4+(-14700*x^6-44100*x^5-29400*x^4+390*x^3-60*x^2+18)*log(5)^2+34300*x^6+102900*x^5+68600*
x^4-1260*x^3+420*x^2-144)/(25*x^3*log(4*x)^3+(-75*x^3*log(5)^2+525*x^3)*log(4*x)^2+(75*x^3*log(5)^4-1050*x^3*l
og(5)^2+3675*x^3)*log(4*x)-25*x^3*log(5)^6+525*x^3*log(5)^4-3675*x^3*log(5)^2+8575*x^3),x, algorithm="maxima")

[Out]

-1/25*(25*(log(5)^4 - 14*log(5)^2 - 4*(log(5)^2 - 7)*log(2) + 4*log(2)^2 + 49)*x^6 + 100*(log(5)^4 - 14*log(5)
^2 - 4*(log(5)^2 - 7)*log(2) + 4*log(2)^2 + 49)*x^5 + 100*(log(5)^4 - 14*log(5)^2 - 4*(log(5)^2 - 7)*log(2) +
4*log(2)^2 + 49)*x^4 + 30*(log(5)^2 - 2*log(2) - 7)*x^3 + 60*(log(5)^2 - 2*log(2) - 7)*x^2 + 25*(x^6 + 4*x^5 +
4*x^4)*log(x)^2 - 10*(5*(log(5)^2 - 2*log(2) - 7)*x^6 + 20*(log(5)^2 - 2*log(2) - 7)*x^5 + 20*(log(5)^2 - 2*l
og(2) - 7)*x^4 + 3*x^3 + 6*x^2)*log(x) + 9)/(2*(log(5)^2 - 2*log(2) - 7)*x^2*log(x) - x^2*log(x)^2 - (log(5)^4
- 14*log(5)^2 - 4*(log(5)^2 - 7)*log(2) + 4*log(2)^2 + 49)*x^2)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {{\ln \left (4\,x\right )}^3\,\left (100\,x^6+300\,x^5+200\,x^4\right )-{\ln \relax (5)}^6\,\left (100\,x^6+300\,x^5+200\,x^4\right )+{\ln \relax (5)}^4\,\left (2100\,x^6+6300\,x^5+4200\,x^4-30\,x^3\right )+{\ln \left (4\,x\right )}^2\,\left (4200\,x^4-30\,x^3-{\ln \relax (5)}^2\,\left (300\,x^6+900\,x^5+600\,x^4\right )+6300\,x^5+2100\,x^6\right )-{\ln \relax (5)}^2\,\left (14700\,x^6+44100\,x^5+29400\,x^4-390\,x^3+60\,x^2-18\right )+\ln \left (4\,x\right )\,\left ({\ln \relax (5)}^4\,\left (300\,x^6+900\,x^5+600\,x^4\right )-{\ln \relax (5)}^2\,\left (4200\,x^6+12600\,x^5+8400\,x^4-60\,x^3\right )+60\,x^2-390\,x^3+29400\,x^4+44100\,x^5+14700\,x^6-18\right )+420\,x^2-1260\,x^3+68600\,x^4+102900\,x^5+34300\,x^6-144}{525\,x^3\,{\ln \relax (5)}^4-3675\,x^3\,{\ln \relax (5)}^2-25\,x^3\,{\ln \relax (5)}^6+\ln \left (4\,x\right )\,\left (75\,x^3\,{\ln \relax (5)}^4-1050\,x^3\,{\ln \relax (5)}^2+3675\,x^3\right )-{\ln \left (4\,x\right )}^2\,\left (75\,x^3\,{\ln \relax (5)}^2-525\,x^3\right )+8575\,x^3+25\,x^3\,{\ln \left (4\,x\right )}^3} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(4*x)^3*(200*x^4 + 300*x^5 + 100*x^6) - log(5)^6*(200*x^4 + 300*x^5 + 100*x^6) + log(5)^4*(4200*x^4 -
30*x^3 + 6300*x^5 + 2100*x^6) + log(4*x)^2*(4200*x^4 - 30*x^3 - log(5)^2*(600*x^4 + 900*x^5 + 300*x^6) + 6300*
x^5 + 2100*x^6) - log(5)^2*(60*x^2 - 390*x^3 + 29400*x^4 + 44100*x^5 + 14700*x^6 - 18) + log(4*x)*(log(5)^4*(6
00*x^4 + 900*x^5 + 300*x^6) - log(5)^2*(8400*x^4 - 60*x^3 + 12600*x^5 + 4200*x^6) + 60*x^2 - 390*x^3 + 29400*x
^4 + 44100*x^5 + 14700*x^6 - 18) + 420*x^2 - 1260*x^3 + 68600*x^4 + 102900*x^5 + 34300*x^6 - 144)/(525*x^3*log
(5)^4 - 3675*x^3*log(5)^2 - 25*x^3*log(5)^6 + log(4*x)*(75*x^3*log(5)^4 - 1050*x^3*log(5)^2 + 3675*x^3) - log(
4*x)^2*(75*x^3*log(5)^2 - 525*x^3) + 8575*x^3 + 25*x^3*log(4*x)^3),x)

[Out]

int((log(4*x)^3*(200*x^4 + 300*x^5 + 100*x^6) - log(5)^6*(200*x^4 + 300*x^5 + 100*x^6) + log(5)^4*(4200*x^4 -
30*x^3 + 6300*x^5 + 2100*x^6) + log(4*x)^2*(4200*x^4 - 30*x^3 - log(5)^2*(600*x^4 + 900*x^5 + 300*x^6) + 6300*
x^5 + 2100*x^6) - log(5)^2*(60*x^2 - 390*x^3 + 29400*x^4 + 44100*x^5 + 14700*x^6 - 18) + log(4*x)*(log(5)^4*(6
00*x^4 + 900*x^5 + 300*x^6) - log(5)^2*(8400*x^4 - 60*x^3 + 12600*x^5 + 4200*x^6) + 60*x^2 - 390*x^3 + 29400*x
^4 + 44100*x^5 + 14700*x^6 - 18) + 420*x^2 - 1260*x^3 + 68600*x^4 + 102900*x^5 + 34300*x^6 - 144)/(525*x^3*log
(5)^4 - 3675*x^3*log(5)^2 - 25*x^3*log(5)^6 + log(4*x)*(75*x^3*log(5)^4 - 1050*x^3*log(5)^2 + 3675*x^3) - log(
4*x)^2*(75*x^3*log(5)^2 - 525*x^3) + 8575*x^3 + 25*x^3*log(4*x)^3), x)

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sympy [B]  time = 0.45, size = 119, normalized size = 3.97 \begin {gather*} x^{4} + 4 x^{3} + 4 x^{2} + \frac {- 210 x^{3} + 30 x^{3} \log {\relax (5 )}^{2} - 420 x^{2} + 60 x^{2} \log {\relax (5 )}^{2} + \left (- 30 x^{3} - 60 x^{2}\right ) \log {\left (4 x \right )} + 9}{25 x^{2} \log {\left (4 x \right )}^{2} - 350 x^{2} \log {\relax (5 )}^{2} + 25 x^{2} \log {\relax (5 )}^{4} + 1225 x^{2} + \left (- 50 x^{2} \log {\relax (5 )}^{2} + 350 x^{2}\right ) \log {\left (4 x \right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((100*x**6+300*x**5+200*x**4)*ln(4*x)**3+((-300*x**6-900*x**5-600*x**4)*ln(5)**2+2100*x**6+6300*x**5
+4200*x**4-30*x**3)*ln(4*x)**2+((300*x**6+900*x**5+600*x**4)*ln(5)**4+(-4200*x**6-12600*x**5-8400*x**4+60*x**3
)*ln(5)**2+14700*x**6+44100*x**5+29400*x**4-390*x**3+60*x**2-18)*ln(4*x)+(-100*x**6-300*x**5-200*x**4)*ln(5)**
6+(2100*x**6+6300*x**5+4200*x**4-30*x**3)*ln(5)**4+(-14700*x**6-44100*x**5-29400*x**4+390*x**3-60*x**2+18)*ln(
5)**2+34300*x**6+102900*x**5+68600*x**4-1260*x**3+420*x**2-144)/(25*x**3*ln(4*x)**3+(-75*x**3*ln(5)**2+525*x**
3)*ln(4*x)**2+(75*x**3*ln(5)**4-1050*x**3*ln(5)**2+3675*x**3)*ln(4*x)-25*x**3*ln(5)**6+525*x**3*ln(5)**4-3675*
x**3*ln(5)**2+8575*x**3),x)

[Out]

x**4 + 4*x**3 + 4*x**2 + (-210*x**3 + 30*x**3*log(5)**2 - 420*x**2 + 60*x**2*log(5)**2 + (-30*x**3 - 60*x**2)*
log(4*x) + 9)/(25*x**2*log(4*x)**2 - 350*x**2*log(5)**2 + 25*x**2*log(5)**4 + 1225*x**2 + (-50*x**2*log(5)**2
+ 350*x**2)*log(4*x))

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