Integrand size = 277, antiderivative size = 27 \[ \int \frac {e^{2/3} \left (-48 x^4-2 x^6\right )+\sqrt [3]{e} \left (-16800 x^4-480 x^5-700 x^6-20 x^7\right )+\left (e^{2/3} \left (-8 x^3+24 x^4\right )+\sqrt [3]{e} \left (-8560 x^3+8320 x^4\right )\right ) \log \left (x^2\right )+\left (4 e^{2/3} x^3+\sqrt [3]{e} \left (-1440 x^2+4280 x^3+20 x^4\right )\right ) \log ^2\left (x^2\right )+\sqrt [3]{e} \left (-80 x+720 x^2\right ) \log ^3\left (x^2\right )+40 \sqrt [3]{e} x \log ^4\left (x^2\right )}{42875 x^6+3675 x^7+105 x^8+x^9+\left (44100 x^5+2520 x^6+36 x^7\right ) \log \left (x^2\right )+\left (18795 x^4+642 x^5+3 x^6\right ) \log ^2\left (x^2\right )+\left (4248 x^3+72 x^4\right ) \log ^3\left (x^2\right )+\left (537 x^2+3 x^3\right ) \log ^4\left (x^2\right )+36 x \log ^5\left (x^2\right )+\log ^6\left (x^2\right )} \, dx=\left (10+\frac {\sqrt [3]{e}}{-1+x+\left (6+\frac {\log \left (x^2\right )}{x}\right )^2}\right )^2 \] Output:
(10+exp(1/3)/((6+ln(x^2)/x)^2+x-1))^2
Leaf count is larger than twice the leaf count of optimal. \(63\) vs. \(2(27)=54\).
Time = 0.06 (sec) , antiderivative size = 63, normalized size of antiderivative = 2.33 \[ \int \frac {e^{2/3} \left (-48 x^4-2 x^6\right )+\sqrt [3]{e} \left (-16800 x^4-480 x^5-700 x^6-20 x^7\right )+\left (e^{2/3} \left (-8 x^3+24 x^4\right )+\sqrt [3]{e} \left (-8560 x^3+8320 x^4\right )\right ) \log \left (x^2\right )+\left (4 e^{2/3} x^3+\sqrt [3]{e} \left (-1440 x^2+4280 x^3+20 x^4\right )\right ) \log ^2\left (x^2\right )+\sqrt [3]{e} \left (-80 x+720 x^2\right ) \log ^3\left (x^2\right )+40 \sqrt [3]{e} x \log ^4\left (x^2\right )}{42875 x^6+3675 x^7+105 x^8+x^9+\left (44100 x^5+2520 x^6+36 x^7\right ) \log \left (x^2\right )+\left (18795 x^4+642 x^5+3 x^6\right ) \log ^2\left (x^2\right )+\left (4248 x^3+72 x^4\right ) \log ^3\left (x^2\right )+\left (537 x^2+3 x^3\right ) \log ^4\left (x^2\right )+36 x \log ^5\left (x^2\right )+\log ^6\left (x^2\right )} \, dx=\frac {\sqrt [3]{e} x^2 \left (x^2 \left (\sqrt [3]{e}+20 (35+x)\right )+240 x \log \left (x^2\right )+20 \log ^2\left (x^2\right )\right )}{\left (x^2 (35+x)+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^2} \] Input:
Integrate[(E^(2/3)*(-48*x^4 - 2*x^6) + E^(1/3)*(-16800*x^4 - 480*x^5 - 700 *x^6 - 20*x^7) + (E^(2/3)*(-8*x^3 + 24*x^4) + E^(1/3)*(-8560*x^3 + 8320*x^ 4))*Log[x^2] + (4*E^(2/3)*x^3 + E^(1/3)*(-1440*x^2 + 4280*x^3 + 20*x^4))*L og[x^2]^2 + E^(1/3)*(-80*x + 720*x^2)*Log[x^2]^3 + 40*E^(1/3)*x*Log[x^2]^4 )/(42875*x^6 + 3675*x^7 + 105*x^8 + x^9 + (44100*x^5 + 2520*x^6 + 36*x^7)* Log[x^2] + (18795*x^4 + 642*x^5 + 3*x^6)*Log[x^2]^2 + (4248*x^3 + 72*x^4)* Log[x^2]^3 + (537*x^2 + 3*x^3)*Log[x^2]^4 + 36*x*Log[x^2]^5 + Log[x^2]^6), x]
Output:
(E^(1/3)*x^2*(x^2*(E^(1/3) + 20*(35 + x)) + 240*x*Log[x^2] + 20*Log[x^2]^2 ))/(x^2*(35 + x) + 12*x*Log[x^2] + Log[x^2]^2)^2
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.
| \(\displaystyle \int \frac {40 \sqrt [3]{e} x \log ^4\left (x^2\right )+\sqrt [3]{e} \left (720 x^2-80 x\right ) \log ^3\left (x^2\right )+e^{2/3} \left (-2 x^6-48 x^4\right )+\left (4 e^{2/3} x^3+\sqrt [3]{e} \left (20 x^4+4280 x^3-1440 x^2\right )\right ) \log ^2\left (x^2\right )+\left (e^{2/3} \left (24 x^4-8 x^3\right )+\sqrt [3]{e} \left (8320 x^4-8560 x^3\right )\right ) \log \left (x^2\right )+\sqrt [3]{e} \left (-20 x^7-700 x^6-480 x^5-16800 x^4\right )}{x^9+105 x^8+3675 x^7+42875 x^6+\log ^6\left (x^2\right )+36 x \log ^5\left (x^2\right )+\left (3 x^3+537 x^2\right ) \log ^4\left (x^2\right )+\left (72 x^4+4248 x^3\right ) \log ^3\left (x^2\right )+\left (36 x^7+2520 x^6+44100 x^5\right ) \log \left (x^2\right )+\left (3 x^6+642 x^5+18795 x^4\right ) \log ^2\left (x^2\right )} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 \sqrt [3]{e} x \left (-\left (\left (10 (x+35)+\sqrt [3]{e}\right ) x^2\right )-10 \log ^2\left (x^2\right )-120 x \log \left (x^2\right )\right ) \left (x \left (x^2+24\right )-2 \log ^2\left (x^2\right )+(4-12 x) \log \left (x^2\right )\right )}{\left ((x+35) x^2+\log ^2\left (x^2\right )+12 x \log \left (x^2\right )\right )^3}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 2 \sqrt [3]{e} \int -\frac {x \left (-2 \log ^2\left (x^2\right )+4 (1-3 x) \log \left (x^2\right )+x \left (x^2+24\right )\right ) \left (\left (10 (x+35)+\sqrt [3]{e}\right ) x^2+120 \log \left (x^2\right ) x+10 \log ^2\left (x^2\right )\right )}{\left ((x+35) x^2+12 \log \left (x^2\right ) x+\log ^2\left (x^2\right )\right )^3}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -2 \sqrt [3]{e} \int \frac {x \left (-2 \log ^2\left (x^2\right )+4 (1-3 x) \log \left (x^2\right )+x \left (x^2+24\right )\right ) \left (\left (10 (x+35)+\sqrt [3]{e}\right ) x^2+120 \log \left (x^2\right ) x+10 \log ^2\left (x^2\right )\right )}{\left ((x+35) x^2+12 \log \left (x^2\right ) x+\log ^2\left (x^2\right )\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \sqrt [3]{e} \int \left (\frac {\sqrt [3]{e} \left (3 x^3+70 x^2+12 \log \left (x^2\right ) x+24 x+4 \log \left (x^2\right )\right ) x^3}{\left (x^3+35 x^2+12 \log \left (x^2\right ) x+\log ^2\left (x^2\right )\right )^3}-\frac {20 x}{x^3+35 x^2+12 \log \left (x^2\right ) x+\log ^2\left (x^2\right )}+\frac {2 \left (15 x^3+350 \left (1-\frac {\sqrt [3]{e}}{350}\right ) x^2+60 \log \left (x^2\right ) x+120 x+20 \log \left (x^2\right )\right ) x}{\left (x^3+35 x^2+12 \log \left (x^2\right ) x+\log ^2\left (x^2\right )\right )^2}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -2 \sqrt [3]{e} \left (4 \sqrt [3]{e} \int \frac {x^3 \log \left (x^2\right )}{\left (x^3+35 x^2+12 \log \left (x^2\right ) x+\log ^2\left (x^2\right )\right )^3}dx+240 \int \frac {x^2}{\left (x^3+35 x^2+12 \log \left (x^2\right ) x+\log ^2\left (x^2\right )\right )^2}dx+2 \left (350-\sqrt [3]{e}\right ) \int \frac {x^3}{\left (x^3+35 x^2+12 \log \left (x^2\right ) x+\log ^2\left (x^2\right )\right )^2}dx+40 \int \frac {x \log \left (x^2\right )}{\left (x^3+35 x^2+12 \log \left (x^2\right ) x+\log ^2\left (x^2\right )\right )^2}dx+120 \int \frac {x^2 \log \left (x^2\right )}{\left (x^3+35 x^2+12 \log \left (x^2\right ) x+\log ^2\left (x^2\right )\right )^2}dx-20 \int \frac {x}{x^3+35 x^2+12 \log \left (x^2\right ) x+\log ^2\left (x^2\right )}dx+3 \sqrt [3]{e} \int \frac {x^6}{\left (x^3+35 x^2+12 \log \left (x^2\right ) x+\log ^2\left (x^2\right )\right )^3}dx+70 \sqrt [3]{e} \int \frac {x^5}{\left (x^3+35 x^2+12 \log \left (x^2\right ) x+\log ^2\left (x^2\right )\right )^3}dx+24 \sqrt [3]{e} \int \frac {x^4}{\left (x^3+35 x^2+12 \log \left (x^2\right ) x+\log ^2\left (x^2\right )\right )^3}dx+12 \sqrt [3]{e} \int \frac {x^4 \log \left (x^2\right )}{\left (x^3+35 x^2+12 \log \left (x^2\right ) x+\log ^2\left (x^2\right )\right )^3}dx+30 \int \frac {x^4}{\left (x^3+35 x^2+12 \log \left (x^2\right ) x+\log ^2\left (x^2\right )\right )^2}dx\right )\) |
Input:
Int[(E^(2/3)*(-48*x^4 - 2*x^6) + E^(1/3)*(-16800*x^4 - 480*x^5 - 700*x^6 - 20*x^7) + (E^(2/3)*(-8*x^3 + 24*x^4) + E^(1/3)*(-8560*x^3 + 8320*x^4))*Lo g[x^2] + (4*E^(2/3)*x^3 + E^(1/3)*(-1440*x^2 + 4280*x^3 + 20*x^4))*Log[x^2 ]^2 + E^(1/3)*(-80*x + 720*x^2)*Log[x^2]^3 + 40*E^(1/3)*x*Log[x^2]^4)/(428 75*x^6 + 3675*x^7 + 105*x^8 + x^9 + (44100*x^5 + 2520*x^6 + 36*x^7)*Log[x^ 2] + (18795*x^4 + 642*x^5 + 3*x^6)*Log[x^2]^2 + (4248*x^3 + 72*x^4)*Log[x^ 2]^3 + (537*x^2 + 3*x^3)*Log[x^2]^4 + 36*x*Log[x^2]^5 + Log[x^2]^6),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(62\) vs. \(2(24)=48\).
Time = 136.82 (sec) , antiderivative size = 63, normalized size of antiderivative = 2.33
| method | result | size |
| risch | \(\frac {\left (x^{2} {\mathrm e}^{\frac {1}{3}}+20 x^{3}+700 x^{2}+240 x \ln \left (x^{2}\right )+20 \ln \left (x^{2}\right )^{2}\right ) x^{2} {\mathrm e}^{\frac {1}{3}}}{\left (x^{3}+\ln \left (x^{2}\right )^{2}+12 x \ln \left (x^{2}\right )+35 x^{2}\right )^{2}}\) | \(63\) |
| parallelrisch | \(\frac {1400 x^{4} {\mathrm e}^{\frac {1}{3}}+40 \,{\mathrm e}^{\frac {1}{3}} x^{5}+40 \,{\mathrm e}^{\frac {1}{3}} \ln \left (x^{2}\right )^{2} x^{2}+480 \,{\mathrm e}^{\frac {1}{3}} \ln \left (x^{2}\right ) x^{3}+2 \,{\mathrm e}^{\frac {2}{3}} x^{4}}{2 x^{6}+140 x^{5}+48 x^{4} \ln \left (x^{2}\right )+4 x^{3} \ln \left (x^{2}\right )^{2}+2450 x^{4}+1680 x^{3} \ln \left (x^{2}\right )+428 x^{2} \ln \left (x^{2}\right )^{2}+48 \ln \left (x^{2}\right )^{3} x +2 \ln \left (x^{2}\right )^{4}}\) | \(122\) |
Input:
int((40*x*exp(1/3)*ln(x^2)^4+(720*x^2-80*x)*exp(1/3)*ln(x^2)^3+(4*x^3*exp( 1/3)^2+(20*x^4+4280*x^3-1440*x^2)*exp(1/3))*ln(x^2)^2+((24*x^4-8*x^3)*exp( 1/3)^2+(8320*x^4-8560*x^3)*exp(1/3))*ln(x^2)+(-2*x^6-48*x^4)*exp(1/3)^2+(- 20*x^7-700*x^6-480*x^5-16800*x^4)*exp(1/3))/(ln(x^2)^6+36*x*ln(x^2)^5+(3*x ^3+537*x^2)*ln(x^2)^4+(72*x^4+4248*x^3)*ln(x^2)^3+(3*x^6+642*x^5+18795*x^4 )*ln(x^2)^2+(36*x^7+2520*x^6+44100*x^5)*ln(x^2)+x^9+105*x^8+3675*x^7+42875 *x^6),x,method=_RETURNVERBOSE)
Output:
(x^2*exp(1/3)+20*x^3+700*x^2+240*x*ln(x^2)+20*ln(x^2)^2)*x^2*exp(1/3)/(x^3 +ln(x^2)^2+12*x*ln(x^2)+35*x^2)^2
Leaf count of result is larger than twice the leaf count of optimal. 108 vs. \(2 (24) = 48\).
Time = 0.09 (sec) , antiderivative size = 108, normalized size of antiderivative = 4.00 \[ \int \frac {e^{2/3} \left (-48 x^4-2 x^6\right )+\sqrt [3]{e} \left (-16800 x^4-480 x^5-700 x^6-20 x^7\right )+\left (e^{2/3} \left (-8 x^3+24 x^4\right )+\sqrt [3]{e} \left (-8560 x^3+8320 x^4\right )\right ) \log \left (x^2\right )+\left (4 e^{2/3} x^3+\sqrt [3]{e} \left (-1440 x^2+4280 x^3+20 x^4\right )\right ) \log ^2\left (x^2\right )+\sqrt [3]{e} \left (-80 x+720 x^2\right ) \log ^3\left (x^2\right )+40 \sqrt [3]{e} x \log ^4\left (x^2\right )}{42875 x^6+3675 x^7+105 x^8+x^9+\left (44100 x^5+2520 x^6+36 x^7\right ) \log \left (x^2\right )+\left (18795 x^4+642 x^5+3 x^6\right ) \log ^2\left (x^2\right )+\left (4248 x^3+72 x^4\right ) \log ^3\left (x^2\right )+\left (537 x^2+3 x^3\right ) \log ^4\left (x^2\right )+36 x \log ^5\left (x^2\right )+\log ^6\left (x^2\right )} \, dx=\frac {x^{4} e^{\frac {2}{3}} + 240 \, x^{3} e^{\frac {1}{3}} \log \left (x^{2}\right ) + 20 \, x^{2} e^{\frac {1}{3}} \log \left (x^{2}\right )^{2} + 20 \, {\left (x^{5} + 35 \, x^{4}\right )} e^{\frac {1}{3}}}{x^{6} + 70 \, x^{5} + 1225 \, x^{4} + 24 \, x \log \left (x^{2}\right )^{3} + \log \left (x^{2}\right )^{4} + 2 \, {\left (x^{3} + 107 \, x^{2}\right )} \log \left (x^{2}\right )^{2} + 24 \, {\left (x^{4} + 35 \, x^{3}\right )} \log \left (x^{2}\right )} \] Input:
integrate((40*x*exp(1/3)*log(x^2)^4+(720*x^2-80*x)*exp(1/3)*log(x^2)^3+(4* x^3*exp(1/3)^2+(20*x^4+4280*x^3-1440*x^2)*exp(1/3))*log(x^2)^2+((24*x^4-8* x^3)*exp(1/3)^2+(8320*x^4-8560*x^3)*exp(1/3))*log(x^2)+(-2*x^6-48*x^4)*exp (1/3)^2+(-20*x^7-700*x^6-480*x^5-16800*x^4)*exp(1/3))/(log(x^2)^6+36*x*log (x^2)^5+(3*x^3+537*x^2)*log(x^2)^4+(72*x^4+4248*x^3)*log(x^2)^3+(3*x^6+642 *x^5+18795*x^4)*log(x^2)^2+(36*x^7+2520*x^6+44100*x^5)*log(x^2)+x^9+105*x^ 8+3675*x^7+42875*x^6),x, algorithm="fricas")
Output:
(x^4*e^(2/3) + 240*x^3*e^(1/3)*log(x^2) + 20*x^2*e^(1/3)*log(x^2)^2 + 20*( x^5 + 35*x^4)*e^(1/3))/(x^6 + 70*x^5 + 1225*x^4 + 24*x*log(x^2)^3 + log(x^ 2)^4 + 2*(x^3 + 107*x^2)*log(x^2)^2 + 24*(x^4 + 35*x^3)*log(x^2))
Leaf count of result is larger than twice the leaf count of optimal. 122 vs. \(2 (20) = 40\).
Time = 0.16 (sec) , antiderivative size = 122, normalized size of antiderivative = 4.52 \[ \int \frac {e^{2/3} \left (-48 x^4-2 x^6\right )+\sqrt [3]{e} \left (-16800 x^4-480 x^5-700 x^6-20 x^7\right )+\left (e^{2/3} \left (-8 x^3+24 x^4\right )+\sqrt [3]{e} \left (-8560 x^3+8320 x^4\right )\right ) \log \left (x^2\right )+\left (4 e^{2/3} x^3+\sqrt [3]{e} \left (-1440 x^2+4280 x^3+20 x^4\right )\right ) \log ^2\left (x^2\right )+\sqrt [3]{e} \left (-80 x+720 x^2\right ) \log ^3\left (x^2\right )+40 \sqrt [3]{e} x \log ^4\left (x^2\right )}{42875 x^6+3675 x^7+105 x^8+x^9+\left (44100 x^5+2520 x^6+36 x^7\right ) \log \left (x^2\right )+\left (18795 x^4+642 x^5+3 x^6\right ) \log ^2\left (x^2\right )+\left (4248 x^3+72 x^4\right ) \log ^3\left (x^2\right )+\left (537 x^2+3 x^3\right ) \log ^4\left (x^2\right )+36 x \log ^5\left (x^2\right )+\log ^6\left (x^2\right )} \, dx=\frac {20 x^{5} e^{\frac {1}{3}} + x^{4} e^{\frac {2}{3}} + 700 x^{4} e^{\frac {1}{3}} + 240 x^{3} e^{\frac {1}{3}} \log {\left (x^{2} \right )} + 20 x^{2} e^{\frac {1}{3}} \log {\left (x^{2} \right )}^{2}}{x^{6} + 70 x^{5} + 1225 x^{4} + 24 x \log {\left (x^{2} \right )}^{3} + \left (2 x^{3} + 214 x^{2}\right ) \log {\left (x^{2} \right )}^{2} + \left (24 x^{4} + 840 x^{3}\right ) \log {\left (x^{2} \right )} + \log {\left (x^{2} \right )}^{4}} \] Input:
integrate((40*x*exp(1/3)*ln(x**2)**4+(720*x**2-80*x)*exp(1/3)*ln(x**2)**3+ (4*x**3*exp(1/3)**2+(20*x**4+4280*x**3-1440*x**2)*exp(1/3))*ln(x**2)**2+(( 24*x**4-8*x**3)*exp(1/3)**2+(8320*x**4-8560*x**3)*exp(1/3))*ln(x**2)+(-2*x **6-48*x**4)*exp(1/3)**2+(-20*x**7-700*x**6-480*x**5-16800*x**4)*exp(1/3)) /(ln(x**2)**6+36*x*ln(x**2)**5+(3*x**3+537*x**2)*ln(x**2)**4+(72*x**4+4248 *x**3)*ln(x**2)**3+(3*x**6+642*x**5+18795*x**4)*ln(x**2)**2+(36*x**7+2520* x**6+44100*x**5)*ln(x**2)+x**9+105*x**8+3675*x**7+42875*x**6),x)
Output:
(20*x**5*exp(1/3) + x**4*exp(2/3) + 700*x**4*exp(1/3) + 240*x**3*exp(1/3)* log(x**2) + 20*x**2*exp(1/3)*log(x**2)**2)/(x**6 + 70*x**5 + 1225*x**4 + 2 4*x*log(x**2)**3 + (2*x**3 + 214*x**2)*log(x**2)**2 + (24*x**4 + 840*x**3) *log(x**2) + log(x**2)**4)
Leaf count of result is larger than twice the leaf count of optimal. 97 vs. \(2 (24) = 48\).
Time = 4.96 (sec) , antiderivative size = 97, normalized size of antiderivative = 3.59 \[ \int \frac {e^{2/3} \left (-48 x^4-2 x^6\right )+\sqrt [3]{e} \left (-16800 x^4-480 x^5-700 x^6-20 x^7\right )+\left (e^{2/3} \left (-8 x^3+24 x^4\right )+\sqrt [3]{e} \left (-8560 x^3+8320 x^4\right )\right ) \log \left (x^2\right )+\left (4 e^{2/3} x^3+\sqrt [3]{e} \left (-1440 x^2+4280 x^3+20 x^4\right )\right ) \log ^2\left (x^2\right )+\sqrt [3]{e} \left (-80 x+720 x^2\right ) \log ^3\left (x^2\right )+40 \sqrt [3]{e} x \log ^4\left (x^2\right )}{42875 x^6+3675 x^7+105 x^8+x^9+\left (44100 x^5+2520 x^6+36 x^7\right ) \log \left (x^2\right )+\left (18795 x^4+642 x^5+3 x^6\right ) \log ^2\left (x^2\right )+\left (4248 x^3+72 x^4\right ) \log ^3\left (x^2\right )+\left (537 x^2+3 x^3\right ) \log ^4\left (x^2\right )+36 x \log ^5\left (x^2\right )+\log ^6\left (x^2\right )} \, dx=\frac {20 \, x^{5} e^{\frac {1}{3}} + x^{4} {\left (e^{\frac {2}{3}} + 700 \, e^{\frac {1}{3}}\right )} + 480 \, x^{3} e^{\frac {1}{3}} \log \left (x\right ) + 80 \, x^{2} e^{\frac {1}{3}} \log \left (x\right )^{2}}{x^{6} + 70 \, x^{5} + 1225 \, x^{4} + 192 \, x \log \left (x\right )^{3} + 16 \, \log \left (x\right )^{4} + 8 \, {\left (x^{3} + 107 \, x^{2}\right )} \log \left (x\right )^{2} + 48 \, {\left (x^{4} + 35 \, x^{3}\right )} \log \left (x\right )} \] Input:
integrate((40*x*exp(1/3)*log(x^2)^4+(720*x^2-80*x)*exp(1/3)*log(x^2)^3+(4* x^3*exp(1/3)^2+(20*x^4+4280*x^3-1440*x^2)*exp(1/3))*log(x^2)^2+((24*x^4-8* x^3)*exp(1/3)^2+(8320*x^4-8560*x^3)*exp(1/3))*log(x^2)+(-2*x^6-48*x^4)*exp (1/3)^2+(-20*x^7-700*x^6-480*x^5-16800*x^4)*exp(1/3))/(log(x^2)^6+36*x*log (x^2)^5+(3*x^3+537*x^2)*log(x^2)^4+(72*x^4+4248*x^3)*log(x^2)^3+(3*x^6+642 *x^5+18795*x^4)*log(x^2)^2+(36*x^7+2520*x^6+44100*x^5)*log(x^2)+x^9+105*x^ 8+3675*x^7+42875*x^6),x, algorithm="maxima")
Output:
(20*x^5*e^(1/3) + x^4*(e^(2/3) + 700*e^(1/3)) + 480*x^3*e^(1/3)*log(x) + 8 0*x^2*e^(1/3)*log(x)^2)/(x^6 + 70*x^5 + 1225*x^4 + 192*x*log(x)^3 + 16*log (x)^4 + 8*(x^3 + 107*x^2)*log(x)^2 + 48*(x^4 + 35*x^3)*log(x))
Leaf count of result is larger than twice the leaf count of optimal. 117 vs. \(2 (24) = 48\).
Time = 0.36 (sec) , antiderivative size = 117, normalized size of antiderivative = 4.33 \[ \int \frac {e^{2/3} \left (-48 x^4-2 x^6\right )+\sqrt [3]{e} \left (-16800 x^4-480 x^5-700 x^6-20 x^7\right )+\left (e^{2/3} \left (-8 x^3+24 x^4\right )+\sqrt [3]{e} \left (-8560 x^3+8320 x^4\right )\right ) \log \left (x^2\right )+\left (4 e^{2/3} x^3+\sqrt [3]{e} \left (-1440 x^2+4280 x^3+20 x^4\right )\right ) \log ^2\left (x^2\right )+\sqrt [3]{e} \left (-80 x+720 x^2\right ) \log ^3\left (x^2\right )+40 \sqrt [3]{e} x \log ^4\left (x^2\right )}{42875 x^6+3675 x^7+105 x^8+x^9+\left (44100 x^5+2520 x^6+36 x^7\right ) \log \left (x^2\right )+\left (18795 x^4+642 x^5+3 x^6\right ) \log ^2\left (x^2\right )+\left (4248 x^3+72 x^4\right ) \log ^3\left (x^2\right )+\left (537 x^2+3 x^3\right ) \log ^4\left (x^2\right )+36 x \log ^5\left (x^2\right )+\log ^6\left (x^2\right )} \, dx=\frac {20 \, x^{5} e^{\frac {1}{3}} + x^{4} e^{\frac {2}{3}} + 700 \, x^{4} e^{\frac {1}{3}} + 240 \, x^{3} e^{\frac {1}{3}} \log \left (x^{2}\right ) + 20 \, x^{2} e^{\frac {1}{3}} \log \left (x^{2}\right )^{2}}{x^{6} + 70 \, x^{5} + 24 \, x^{4} \log \left (x^{2}\right ) + 2 \, x^{3} \log \left (x^{2}\right )^{2} + 1225 \, x^{4} + 840 \, x^{3} \log \left (x^{2}\right ) + 214 \, x^{2} \log \left (x^{2}\right )^{2} + 24 \, x \log \left (x^{2}\right )^{3} + \log \left (x^{2}\right )^{4}} \] Input:
integrate((40*x*exp(1/3)*log(x^2)^4+(720*x^2-80*x)*exp(1/3)*log(x^2)^3+(4* x^3*exp(1/3)^2+(20*x^4+4280*x^3-1440*x^2)*exp(1/3))*log(x^2)^2+((24*x^4-8* x^3)*exp(1/3)^2+(8320*x^4-8560*x^3)*exp(1/3))*log(x^2)+(-2*x^6-48*x^4)*exp (1/3)^2+(-20*x^7-700*x^6-480*x^5-16800*x^4)*exp(1/3))/(log(x^2)^6+36*x*log (x^2)^5+(3*x^3+537*x^2)*log(x^2)^4+(72*x^4+4248*x^3)*log(x^2)^3+(3*x^6+642 *x^5+18795*x^4)*log(x^2)^2+(36*x^7+2520*x^6+44100*x^5)*log(x^2)+x^9+105*x^ 8+3675*x^7+42875*x^6),x, algorithm="giac")
Output:
(20*x^5*e^(1/3) + x^4*e^(2/3) + 700*x^4*e^(1/3) + 240*x^3*e^(1/3)*log(x^2) + 20*x^2*e^(1/3)*log(x^2)^2)/(x^6 + 70*x^5 + 24*x^4*log(x^2) + 2*x^3*log( x^2)^2 + 1225*x^4 + 840*x^3*log(x^2) + 214*x^2*log(x^2)^2 + 24*x*log(x^2)^ 3 + log(x^2)^4)
Timed out. \[ \int \frac {e^{2/3} \left (-48 x^4-2 x^6\right )+\sqrt [3]{e} \left (-16800 x^4-480 x^5-700 x^6-20 x^7\right )+\left (e^{2/3} \left (-8 x^3+24 x^4\right )+\sqrt [3]{e} \left (-8560 x^3+8320 x^4\right )\right ) \log \left (x^2\right )+\left (4 e^{2/3} x^3+\sqrt [3]{e} \left (-1440 x^2+4280 x^3+20 x^4\right )\right ) \log ^2\left (x^2\right )+\sqrt [3]{e} \left (-80 x+720 x^2\right ) \log ^3\left (x^2\right )+40 \sqrt [3]{e} x \log ^4\left (x^2\right )}{42875 x^6+3675 x^7+105 x^8+x^9+\left (44100 x^5+2520 x^6+36 x^7\right ) \log \left (x^2\right )+\left (18795 x^4+642 x^5+3 x^6\right ) \log ^2\left (x^2\right )+\left (4248 x^3+72 x^4\right ) \log ^3\left (x^2\right )+\left (537 x^2+3 x^3\right ) \log ^4\left (x^2\right )+36 x \log ^5\left (x^2\right )+\log ^6\left (x^2\right )} \, dx=\int -\frac {-40\,x\,{\mathrm {e}}^{1/3}\,{\ln \left (x^2\right )}^4+{\mathrm {e}}^{1/3}\,\left (80\,x-720\,x^2\right )\,{\ln \left (x^2\right )}^3+\left (-4\,x^3\,{\mathrm {e}}^{2/3}-{\mathrm {e}}^{1/3}\,\left (20\,x^4+4280\,x^3-1440\,x^2\right )\right )\,{\ln \left (x^2\right )}^2+\left ({\mathrm {e}}^{2/3}\,\left (8\,x^3-24\,x^4\right )+{\mathrm {e}}^{1/3}\,\left (8560\,x^3-8320\,x^4\right )\right )\,\ln \left (x^2\right )+{\mathrm {e}}^{2/3}\,\left (2\,x^6+48\,x^4\right )+{\mathrm {e}}^{1/3}\,\left (20\,x^7+700\,x^6+480\,x^5+16800\,x^4\right )}{{\ln \left (x^2\right )}^2\,\left (3\,x^6+642\,x^5+18795\,x^4\right )+36\,x\,{\ln \left (x^2\right )}^5+{\ln \left (x^2\right )}^6+\ln \left (x^2\right )\,\left (36\,x^7+2520\,x^6+44100\,x^5\right )+{\ln \left (x^2\right )}^4\,\left (3\,x^3+537\,x^2\right )+{\ln \left (x^2\right )}^3\,\left (72\,x^4+4248\,x^3\right )+42875\,x^6+3675\,x^7+105\,x^8+x^9} \,d x \] Input:
int(-(log(x^2)*(exp(2/3)*(8*x^3 - 24*x^4) + exp(1/3)*(8560*x^3 - 8320*x^4) ) + exp(2/3)*(48*x^4 + 2*x^6) - log(x^2)^2*(4*x^3*exp(2/3) + exp(1/3)*(428 0*x^3 - 1440*x^2 + 20*x^4)) + exp(1/3)*(16800*x^4 + 480*x^5 + 700*x^6 + 20 *x^7) + log(x^2)^3*exp(1/3)*(80*x - 720*x^2) - 40*x*log(x^2)^4*exp(1/3))/( log(x^2)^2*(18795*x^4 + 642*x^5 + 3*x^6) + 36*x*log(x^2)^5 + log(x^2)^6 + log(x^2)*(44100*x^5 + 2520*x^6 + 36*x^7) + log(x^2)^4*(537*x^2 + 3*x^3) + log(x^2)^3*(4248*x^3 + 72*x^4) + 42875*x^6 + 3675*x^7 + 105*x^8 + x^9),x)
Output:
int(-(log(x^2)*(exp(2/3)*(8*x^3 - 24*x^4) + exp(1/3)*(8560*x^3 - 8320*x^4) ) + exp(2/3)*(48*x^4 + 2*x^6) - log(x^2)^2*(4*x^3*exp(2/3) + exp(1/3)*(428 0*x^3 - 1440*x^2 + 20*x^4)) + exp(1/3)*(16800*x^4 + 480*x^5 + 700*x^6 + 20 *x^7) + log(x^2)^3*exp(1/3)*(80*x - 720*x^2) - 40*x*log(x^2)^4*exp(1/3))/( log(x^2)^2*(18795*x^4 + 642*x^5 + 3*x^6) + 36*x*log(x^2)^5 + log(x^2)^6 + log(x^2)*(44100*x^5 + 2520*x^6 + 36*x^7) + log(x^2)^4*(537*x^2 + 3*x^3) + log(x^2)^3*(4248*x^3 + 72*x^4) + 42875*x^6 + 3675*x^7 + 105*x^8 + x^9), x)
\[ \int \frac {e^{2/3} \left (-48 x^4-2 x^6\right )+\sqrt [3]{e} \left (-16800 x^4-480 x^5-700 x^6-20 x^7\right )+\left (e^{2/3} \left (-8 x^3+24 x^4\right )+\sqrt [3]{e} \left (-8560 x^3+8320 x^4\right )\right ) \log \left (x^2\right )+\left (4 e^{2/3} x^3+\sqrt [3]{e} \left (-1440 x^2+4280 x^3+20 x^4\right )\right ) \log ^2\left (x^2\right )+\sqrt [3]{e} \left (-80 x+720 x^2\right ) \log ^3\left (x^2\right )+40 \sqrt [3]{e} x \log ^4\left (x^2\right )}{42875 x^6+3675 x^7+105 x^8+x^9+\left (44100 x^5+2520 x^6+36 x^7\right ) \log \left (x^2\right )+\left (18795 x^4+642 x^5+3 x^6\right ) \log ^2\left (x^2\right )+\left (4248 x^3+72 x^4\right ) \log ^3\left (x^2\right )+\left (537 x^2+3 x^3\right ) \log ^4\left (x^2\right )+36 x \log ^5\left (x^2\right )+\log ^6\left (x^2\right )} \, dx=\text {too large to display} \] Input:
int((40*x*exp(1/3)*log(x^2)^4+(720*x^2-80*x)*exp(1/3)*log(x^2)^3+(4*x^3*ex p(1/3)^2+(20*x^4+4280*x^3-1440*x^2)*exp(1/3))*log(x^2)^2+((24*x^4-8*x^3)*e xp(1/3)^2+(8320*x^4-8560*x^3)*exp(1/3))*log(x^2)+(-2*x^6-48*x^4)*exp(1/3)^ 2+(-20*x^7-700*x^6-480*x^5-16800*x^4)*exp(1/3))/(log(x^2)^6+36*x*log(x^2)^ 5+(3*x^3+537*x^2)*log(x^2)^4+(72*x^4+4248*x^3)*log(x^2)^3+(3*x^6+642*x^5+1 8795*x^4)*log(x^2)^2+(36*x^7+2520*x^6+44100*x^5)*log(x^2)+x^9+105*x^8+3675 *x^7+42875*x^6),x)
Output:
2*e**(1/3)*( - e**(1/3)*int(x**6/(log(x**2)**6 + 36*log(x**2)**5*x + 3*log (x**2)**4*x**3 + 537*log(x**2)**4*x**2 + 72*log(x**2)**3*x**4 + 4248*log(x **2)**3*x**3 + 3*log(x**2)**2*x**6 + 642*log(x**2)**2*x**5 + 18795*log(x** 2)**2*x**4 + 36*log(x**2)*x**7 + 2520*log(x**2)*x**6 + 44100*log(x**2)*x** 5 + x**9 + 105*x**8 + 3675*x**7 + 42875*x**6),x) - 24*e**(1/3)*int(x**4/(l og(x**2)**6 + 36*log(x**2)**5*x + 3*log(x**2)**4*x**3 + 537*log(x**2)**4*x **2 + 72*log(x**2)**3*x**4 + 4248*log(x**2)**3*x**3 + 3*log(x**2)**2*x**6 + 642*log(x**2)**2*x**5 + 18795*log(x**2)**2*x**4 + 36*log(x**2)*x**7 + 25 20*log(x**2)*x**6 + 44100*log(x**2)*x**5 + x**9 + 105*x**8 + 3675*x**7 + 4 2875*x**6),x) + 2*e**(1/3)*int((log(x**2)**2*x**3)/(log(x**2)**6 + 36*log( x**2)**5*x + 3*log(x**2)**4*x**3 + 537*log(x**2)**4*x**2 + 72*log(x**2)**3 *x**4 + 4248*log(x**2)**3*x**3 + 3*log(x**2)**2*x**6 + 642*log(x**2)**2*x* *5 + 18795*log(x**2)**2*x**4 + 36*log(x**2)*x**7 + 2520*log(x**2)*x**6 + 4 4100*log(x**2)*x**5 + x**9 + 105*x**8 + 3675*x**7 + 42875*x**6),x) + 12*e* *(1/3)*int((log(x**2)*x**4)/(log(x**2)**6 + 36*log(x**2)**5*x + 3*log(x**2 )**4*x**3 + 537*log(x**2)**4*x**2 + 72*log(x**2)**3*x**4 + 4248*log(x**2)* *3*x**3 + 3*log(x**2)**2*x**6 + 642*log(x**2)**2*x**5 + 18795*log(x**2)**2 *x**4 + 36*log(x**2)*x**7 + 2520*log(x**2)*x**6 + 44100*log(x**2)*x**5 + x **9 + 105*x**8 + 3675*x**7 + 42875*x**6),x) - 4*e**(1/3)*int((log(x**2)*x* *3)/(log(x**2)**6 + 36*log(x**2)**5*x + 3*log(x**2)**4*x**3 + 537*log(x...