Integrand size = 252, antiderivative size = 30 \[ \int \frac {\left (-1024 x^4-1536 x^5\right ) \log (x)+e^4 \left (-1024 x^3-1536 x^4\right ) \log ^2(x)+e^8 \left (-384 x^2-576 x^3\right ) \log ^3(x)+e^{12} \left (-64 x-96 x^2\right ) \log ^4(x)+e^{16} (-4-6 x) \log ^5(x)+\left (-2048 x^4-3072 x^5+\left (-768 x^5+e^4 \left (-1536 x^3-2304 x^4\right )\right ) \log (x)+\left (e^8 \left (-384 x^2-576 x^3\right )+e^4 \left (-512 x^3-1536 x^4\right )\right ) \log ^2(x)+\left (e^{12} \left (-32 x-48 x^2\right )+e^8 \left (-384 x^2-864 x^3\right )\right ) \log ^3(x)+e^{12} \left (-96 x-192 x^2\right ) \log ^4(x)+e^{16} (-8-15 x) \log ^5(x)\right ) \log \left (x^2\right )}{\left (8 x^5+24 x^6+18 x^7\right ) \log ^5(x) \log ^2\left (x^2\right )} \, dx=\frac {\left (\frac {e^4}{x}+\frac {4}{\log (x)}\right )^4}{(4+6 x) \log \left (x^2\right )} \] Output:
(4/ln(x)+exp(4)/x)^4/ln(x^2)/(4+6*x)
Time = 0.14 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.20 \[ \int \frac {\left (-1024 x^4-1536 x^5\right ) \log (x)+e^4 \left (-1024 x^3-1536 x^4\right ) \log ^2(x)+e^8 \left (-384 x^2-576 x^3\right ) \log ^3(x)+e^{12} \left (-64 x-96 x^2\right ) \log ^4(x)+e^{16} (-4-6 x) \log ^5(x)+\left (-2048 x^4-3072 x^5+\left (-768 x^5+e^4 \left (-1536 x^3-2304 x^4\right )\right ) \log (x)+\left (e^8 \left (-384 x^2-576 x^3\right )+e^4 \left (-512 x^3-1536 x^4\right )\right ) \log ^2(x)+\left (e^{12} \left (-32 x-48 x^2\right )+e^8 \left (-384 x^2-864 x^3\right )\right ) \log ^3(x)+e^{12} \left (-96 x-192 x^2\right ) \log ^4(x)+e^{16} (-8-15 x) \log ^5(x)\right ) \log \left (x^2\right )}{\left (8 x^5+24 x^6+18 x^7\right ) \log ^5(x) \log ^2\left (x^2\right )} \, dx=\frac {\left (4 x+e^4 \log (x)\right )^4}{2 x^4 (2+3 x) \log ^4(x) \log \left (x^2\right )} \] Input:
Integrate[((-1024*x^4 - 1536*x^5)*Log[x] + E^4*(-1024*x^3 - 1536*x^4)*Log[ x]^2 + E^8*(-384*x^2 - 576*x^3)*Log[x]^3 + E^12*(-64*x - 96*x^2)*Log[x]^4 + E^16*(-4 - 6*x)*Log[x]^5 + (-2048*x^4 - 3072*x^5 + (-768*x^5 + E^4*(-153 6*x^3 - 2304*x^4))*Log[x] + (E^8*(-384*x^2 - 576*x^3) + E^4*(-512*x^3 - 15 36*x^4))*Log[x]^2 + (E^12*(-32*x - 48*x^2) + E^8*(-384*x^2 - 864*x^3))*Log [x]^3 + E^12*(-96*x - 192*x^2)*Log[x]^4 + E^16*(-8 - 15*x)*Log[x]^5)*Log[x ^2])/((8*x^5 + 24*x^6 + 18*x^7)*Log[x]^5*Log[x^2]^2),x]
Output:
(4*x + E^4*Log[x])^4/(2*x^4*(2 + 3*x)*Log[x]^4*Log[x^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.
| \(\displaystyle \int \frac {e^{12} \left (-96 x^2-64 x\right ) \log ^4(x)+\left (-1536 x^5-1024 x^4\right ) \log (x)+e^4 \left (-1536 x^4-1024 x^3\right ) \log ^2(x)+e^8 \left (-576 x^3-384 x^2\right ) \log ^3(x)+\left (-3072 x^5-2048 x^4+e^{12} \left (-192 x^2-96 x\right ) \log ^4(x)+\left (e^{12} \left (-48 x^2-32 x\right )+e^8 \left (-864 x^3-384 x^2\right )\right ) \log ^3(x)+\left (e^4 \left (-2304 x^4-1536 x^3\right )-768 x^5\right ) \log (x)+\left (e^4 \left (-1536 x^4-512 x^3\right )+e^8 \left (-576 x^3-384 x^2\right )\right ) \log ^2(x)+e^{16} (-15 x-8) \log ^5(x)\right ) \log \left (x^2\right )+e^{16} (-6 x-4) \log ^5(x)}{\left (18 x^7+24 x^6+8 x^5\right ) \log ^5(x) \log ^2\left (x^2\right )} \, dx\) |
| \(\Big \downarrow \) 2026 |
| \(\displaystyle \int \frac {e^{12} \left (-96 x^2-64 x\right ) \log ^4(x)+\left (-1536 x^5-1024 x^4\right ) \log (x)+e^4 \left (-1536 x^4-1024 x^3\right ) \log ^2(x)+e^8 \left (-576 x^3-384 x^2\right ) \log ^3(x)+\left (-3072 x^5-2048 x^4+e^{12} \left (-192 x^2-96 x\right ) \log ^4(x)+\left (e^{12} \left (-48 x^2-32 x\right )+e^8 \left (-864 x^3-384 x^2\right )\right ) \log ^3(x)+\left (e^4 \left (-2304 x^4-1536 x^3\right )-768 x^5\right ) \log (x)+\left (e^4 \left (-1536 x^4-512 x^3\right )+e^8 \left (-576 x^3-384 x^2\right )\right ) \log ^2(x)+e^{16} (-15 x-8) \log ^5(x)\right ) \log \left (x^2\right )+e^{16} (-6 x-4) \log ^5(x)}{x^5 \left (18 x^2+24 x+8\right ) \log ^5(x) \log ^2\left (x^2\right )}dx\) |
| \(\Big \downarrow \) 2007 |
| \(\displaystyle \int \frac {e^{12} \left (-96 x^2-64 x\right ) \log ^4(x)+\left (-1536 x^5-1024 x^4\right ) \log (x)+e^4 \left (-1536 x^4-1024 x^3\right ) \log ^2(x)+e^8 \left (-576 x^3-384 x^2\right ) \log ^3(x)+\left (-3072 x^5-2048 x^4+e^{12} \left (-192 x^2-96 x\right ) \log ^4(x)+\left (e^{12} \left (-48 x^2-32 x\right )+e^8 \left (-864 x^3-384 x^2\right )\right ) \log ^3(x)+\left (e^4 \left (-2304 x^4-1536 x^3\right )-768 x^5\right ) \log (x)+\left (e^4 \left (-1536 x^4-512 x^3\right )+e^8 \left (-576 x^3-384 x^2\right )\right ) \log ^2(x)+e^{16} (-15 x-8) \log ^5(x)\right ) \log \left (x^2\right )+e^{16} (-6 x-4) \log ^5(x)}{x^5 \left (3 \sqrt {2} x+2 \sqrt {2}\right )^2 \log ^5(x) \log ^2\left (x^2\right )}dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (4 x+e^4 \log (x)\right )^3 \left (-e^4 \left ((15 x+8) \log \left (x^2\right )+6 x+4\right ) \log ^2(x)-4 x \left (3 x \log \left (x^2\right )+6 x+4\right ) \log (x)-16 x (3 x+2) \log \left (x^2\right )\right )}{2 x^5 (3 x+2)^2 \log ^5(x) \log ^2\left (x^2\right )}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{2} \int -\frac {\left (4 x+e^4 \log (x)\right )^3 \left (e^4 \left (6 x+(15 x+8) \log \left (x^2\right )+4\right ) \log ^2(x)+4 x \left (3 \log \left (x^2\right ) x+6 x+4\right ) \log (x)+16 x (3 x+2) \log \left (x^2\right )\right )}{x^5 (3 x+2)^2 \log ^5(x) \log ^2\left (x^2\right )}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -\frac {1}{2} \int \frac {\left (4 x+e^4 \log (x)\right )^3 \left (e^4 \left (6 x+(15 x+8) \log \left (x^2\right )+4\right ) \log ^2(x)+4 x \left (3 \log \left (x^2\right ) x+6 x+4\right ) \log (x)+16 x (3 x+2) \log \left (x^2\right )\right )}{x^5 (3 x+2)^2 \log ^5(x) \log ^2\left (x^2\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {1}{2} \int \left (\frac {2 \left (4 x+e^4 \log (x)\right )^4}{x^5 (3 x+2) \log ^4(x) \log ^2\left (x^2\right )}+\frac {\left (12 \log (x) x^2+48 x^2+15 e^4 \log ^2(x) x+32 x+8 e^4 \log ^2(x)\right ) \left (4 x+e^4 \log (x)\right )^3}{x^5 (3 x+2)^2 \log ^5(x) \log \left (x^2\right )}\right )dx\) |
| \(\Big \downarrow \) 7299 |
| \(\displaystyle -\frac {1}{2} \int \left (\frac {2 \left (4 x+e^4 \log (x)\right )^4}{x^5 (3 x+2) \log ^4(x) \log ^2\left (x^2\right )}+\frac {\left (12 \log (x) x^2+48 x^2+15 e^4 \log ^2(x) x+32 x+8 e^4 \log ^2(x)\right ) \left (4 x+e^4 \log (x)\right )^3}{x^5 (3 x+2)^2 \log ^5(x) \log \left (x^2\right )}\right )dx\) |
Input:
Int[((-1024*x^4 - 1536*x^5)*Log[x] + E^4*(-1024*x^3 - 1536*x^4)*Log[x]^2 + E^8*(-384*x^2 - 576*x^3)*Log[x]^3 + E^12*(-64*x - 96*x^2)*Log[x]^4 + E^16 *(-4 - 6*x)*Log[x]^5 + (-2048*x^4 - 3072*x^5 + (-768*x^5 + E^4*(-1536*x^3 - 2304*x^4))*Log[x] + (E^8*(-384*x^2 - 576*x^3) + E^4*(-512*x^3 - 1536*x^4 ))*Log[x]^2 + (E^12*(-32*x - 48*x^2) + E^8*(-384*x^2 - 864*x^3))*Log[x]^3 + E^12*(-96*x - 192*x^2)*Log[x]^4 + E^16*(-8 - 15*x)*Log[x]^5)*Log[x^2])/( (8*x^5 + 24*x^6 + 18*x^7)*Log[x]^5*Log[x^2]^2),x]
Output:
$Aborted
Result contains higher order function than in optimal. Order 9 vs. order 3.
Time = 7.94 (sec) , antiderivative size = 120, normalized size of antiderivative = 4.00
\[\frac {{\mathrm e}^{16} \ln \left (x \right )^{4}+16 x \,{\mathrm e}^{12} \ln \left (x \right )^{3}+96 \ln \left (x \right )^{2} {\mathrm e}^{8} x^{2}+256 \,{\mathrm e}^{4} x^{3} \ln \left (x \right )+256 x^{4}}{\ln \left (x \right )^{4} \left (4 \ln \left (x \right )-i \pi \operatorname {csgn}\left (i x \right )^{2} \operatorname {csgn}\left (i x^{2}\right )+2 i \pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )^{2}-i \pi \operatorname {csgn}\left (i x^{2}\right )^{3}\right ) x^{4} \left (2+3 x \right )}\]
Input:
int((((-15*x-8)*exp(4)^4*ln(x)^5+(-192*x^2-96*x)*exp(4)^3*ln(x)^4+((-48*x^ 2-32*x)*exp(4)^3+(-864*x^3-384*x^2)*exp(4)^2)*ln(x)^3+((-576*x^3-384*x^2)* exp(4)^2+(-1536*x^4-512*x^3)*exp(4))*ln(x)^2+((-2304*x^4-1536*x^3)*exp(4)- 768*x^5)*ln(x)-3072*x^5-2048*x^4)*ln(x^2)+(-4-6*x)*exp(4)^4*ln(x)^5+(-96*x ^2-64*x)*exp(4)^3*ln(x)^4+(-576*x^3-384*x^2)*exp(4)^2*ln(x)^3+(-1536*x^4-1 024*x^3)*exp(4)*ln(x)^2+(-1536*x^5-1024*x^4)*ln(x))/(18*x^7+24*x^6+8*x^5)/ ln(x)^5/ln(x^2)^2,x)
Output:
(exp(4)^4*ln(x)^4+16*exp(4)^3*x*ln(x)^3+96*exp(4)^2*x^2*ln(x)^2+256*exp(4) *x^3*ln(x)+256*x^4)/ln(x)^4/(4*ln(x)-I*Pi*csgn(I*x)^2*csgn(I*x^2)+2*I*Pi*c sgn(I*x)*csgn(I*x^2)^2-I*Pi*csgn(I*x^2)^3)/x^4/(2+3*x)
Leaf count of result is larger than twice the leaf count of optimal. 61 vs. \(2 (30) = 60\).
Time = 0.13 (sec) , antiderivative size = 61, normalized size of antiderivative = 2.03 \[ \int \frac {\left (-1024 x^4-1536 x^5\right ) \log (x)+e^4 \left (-1024 x^3-1536 x^4\right ) \log ^2(x)+e^8 \left (-384 x^2-576 x^3\right ) \log ^3(x)+e^{12} \left (-64 x-96 x^2\right ) \log ^4(x)+e^{16} (-4-6 x) \log ^5(x)+\left (-2048 x^4-3072 x^5+\left (-768 x^5+e^4 \left (-1536 x^3-2304 x^4\right )\right ) \log (x)+\left (e^8 \left (-384 x^2-576 x^3\right )+e^4 \left (-512 x^3-1536 x^4\right )\right ) \log ^2(x)+\left (e^{12} \left (-32 x-48 x^2\right )+e^8 \left (-384 x^2-864 x^3\right )\right ) \log ^3(x)+e^{12} \left (-96 x-192 x^2\right ) \log ^4(x)+e^{16} (-8-15 x) \log ^5(x)\right ) \log \left (x^2\right )}{\left (8 x^5+24 x^6+18 x^7\right ) \log ^5(x) \log ^2\left (x^2\right )} \, dx=\frac {256 \, x^{3} e^{4} \log \left (x\right ) + 96 \, x^{2} e^{8} \log \left (x\right )^{2} + 16 \, x e^{12} \log \left (x\right )^{3} + e^{16} \log \left (x\right )^{4} + 256 \, x^{4}}{4 \, {\left (3 \, x^{5} + 2 \, x^{4}\right )} \log \left (x\right )^{5}} \] Input:
integrate((((-15*x-8)*exp(4)^4*log(x)^5+(-192*x^2-96*x)*exp(4)^3*log(x)^4+ ((-48*x^2-32*x)*exp(4)^3+(-864*x^3-384*x^2)*exp(4)^2)*log(x)^3+((-576*x^3- 384*x^2)*exp(4)^2+(-1536*x^4-512*x^3)*exp(4))*log(x)^2+((-2304*x^4-1536*x^ 3)*exp(4)-768*x^5)*log(x)-3072*x^5-2048*x^4)*log(x^2)+(-4-6*x)*exp(4)^4*lo g(x)^5+(-96*x^2-64*x)*exp(4)^3*log(x)^4+(-576*x^3-384*x^2)*exp(4)^2*log(x) ^3+(-1536*x^4-1024*x^3)*exp(4)*log(x)^2+(-1536*x^5-1024*x^4)*log(x))/(18*x ^7+24*x^6+8*x^5)/log(x)^5/log(x^2)^2,x, algorithm="fricas")
Output:
1/4*(256*x^3*e^4*log(x) + 96*x^2*e^8*log(x)^2 + 16*x*e^12*log(x)^3 + e^16* log(x)^4 + 256*x^4)/((3*x^5 + 2*x^4)*log(x)^5)
Leaf count of result is larger than twice the leaf count of optimal. 65 vs. \(2 (20) = 40\).
Time = 0.17 (sec) , antiderivative size = 65, normalized size of antiderivative = 2.17 \[ \int \frac {\left (-1024 x^4-1536 x^5\right ) \log (x)+e^4 \left (-1024 x^3-1536 x^4\right ) \log ^2(x)+e^8 \left (-384 x^2-576 x^3\right ) \log ^3(x)+e^{12} \left (-64 x-96 x^2\right ) \log ^4(x)+e^{16} (-4-6 x) \log ^5(x)+\left (-2048 x^4-3072 x^5+\left (-768 x^5+e^4 \left (-1536 x^3-2304 x^4\right )\right ) \log (x)+\left (e^8 \left (-384 x^2-576 x^3\right )+e^4 \left (-512 x^3-1536 x^4\right )\right ) \log ^2(x)+\left (e^{12} \left (-32 x-48 x^2\right )+e^8 \left (-384 x^2-864 x^3\right )\right ) \log ^3(x)+e^{12} \left (-96 x-192 x^2\right ) \log ^4(x)+e^{16} (-8-15 x) \log ^5(x)\right ) \log \left (x^2\right )}{\left (8 x^5+24 x^6+18 x^7\right ) \log ^5(x) \log ^2\left (x^2\right )} \, dx=\frac {256 x^{4} + 256 x^{3} e^{4} \log {\left (x \right )} + 96 x^{2} e^{8} \log {\left (x \right )}^{2} + 16 x e^{12} \log {\left (x \right )}^{3} + e^{16} \log {\left (x \right )}^{4}}{\left (12 x^{5} + 8 x^{4}\right ) \log {\left (x \right )}^{5}} \] Input:
integrate((((-15*x-8)*exp(4)**4*ln(x)**5+(-192*x**2-96*x)*exp(4)**3*ln(x)* *4+((-48*x**2-32*x)*exp(4)**3+(-864*x**3-384*x**2)*exp(4)**2)*ln(x)**3+((- 576*x**3-384*x**2)*exp(4)**2+(-1536*x**4-512*x**3)*exp(4))*ln(x)**2+((-230 4*x**4-1536*x**3)*exp(4)-768*x**5)*ln(x)-3072*x**5-2048*x**4)*ln(x**2)+(-4 -6*x)*exp(4)**4*ln(x)**5+(-96*x**2-64*x)*exp(4)**3*ln(x)**4+(-576*x**3-384 *x**2)*exp(4)**2*ln(x)**3+(-1536*x**4-1024*x**3)*exp(4)*ln(x)**2+(-1536*x* *5-1024*x**4)*ln(x))/(18*x**7+24*x**6+8*x**5)/ln(x)**5/ln(x**2)**2,x)
Output:
(256*x**4 + 256*x**3*exp(4)*log(x) + 96*x**2*exp(8)*log(x)**2 + 16*x*exp(1 2)*log(x)**3 + exp(16)*log(x)**4)/((12*x**5 + 8*x**4)*log(x)**5)
Leaf count of result is larger than twice the leaf count of optimal. 61 vs. \(2 (30) = 60\).
Time = 0.13 (sec) , antiderivative size = 61, normalized size of antiderivative = 2.03 \[ \int \frac {\left (-1024 x^4-1536 x^5\right ) \log (x)+e^4 \left (-1024 x^3-1536 x^4\right ) \log ^2(x)+e^8 \left (-384 x^2-576 x^3\right ) \log ^3(x)+e^{12} \left (-64 x-96 x^2\right ) \log ^4(x)+e^{16} (-4-6 x) \log ^5(x)+\left (-2048 x^4-3072 x^5+\left (-768 x^5+e^4 \left (-1536 x^3-2304 x^4\right )\right ) \log (x)+\left (e^8 \left (-384 x^2-576 x^3\right )+e^4 \left (-512 x^3-1536 x^4\right )\right ) \log ^2(x)+\left (e^{12} \left (-32 x-48 x^2\right )+e^8 \left (-384 x^2-864 x^3\right )\right ) \log ^3(x)+e^{12} \left (-96 x-192 x^2\right ) \log ^4(x)+e^{16} (-8-15 x) \log ^5(x)\right ) \log \left (x^2\right )}{\left (8 x^5+24 x^6+18 x^7\right ) \log ^5(x) \log ^2\left (x^2\right )} \, dx=\frac {256 \, x^{3} e^{4} \log \left (x\right ) + 96 \, x^{2} e^{8} \log \left (x\right )^{2} + 16 \, x e^{12} \log \left (x\right )^{3} + e^{16} \log \left (x\right )^{4} + 256 \, x^{4}}{4 \, {\left (3 \, x^{5} + 2 \, x^{4}\right )} \log \left (x\right )^{5}} \] Input:
integrate((((-15*x-8)*exp(4)^4*log(x)^5+(-192*x^2-96*x)*exp(4)^3*log(x)^4+ ((-48*x^2-32*x)*exp(4)^3+(-864*x^3-384*x^2)*exp(4)^2)*log(x)^3+((-576*x^3- 384*x^2)*exp(4)^2+(-1536*x^4-512*x^3)*exp(4))*log(x)^2+((-2304*x^4-1536*x^ 3)*exp(4)-768*x^5)*log(x)-3072*x^5-2048*x^4)*log(x^2)+(-4-6*x)*exp(4)^4*lo g(x)^5+(-96*x^2-64*x)*exp(4)^3*log(x)^4+(-576*x^3-384*x^2)*exp(4)^2*log(x) ^3+(-1536*x^4-1024*x^3)*exp(4)*log(x)^2+(-1536*x^5-1024*x^4)*log(x))/(18*x ^7+24*x^6+8*x^5)/log(x)^5/log(x^2)^2,x, algorithm="maxima")
Output:
1/4*(256*x^3*e^4*log(x) + 96*x^2*e^8*log(x)^2 + 16*x*e^12*log(x)^3 + e^16* log(x)^4 + 256*x^4)/((3*x^5 + 2*x^4)*log(x)^5)
Leaf count of result is larger than twice the leaf count of optimal. 65 vs. \(2 (30) = 60\).
Time = 0.19 (sec) , antiderivative size = 65, normalized size of antiderivative = 2.17 \[ \int \frac {\left (-1024 x^4-1536 x^5\right ) \log (x)+e^4 \left (-1024 x^3-1536 x^4\right ) \log ^2(x)+e^8 \left (-384 x^2-576 x^3\right ) \log ^3(x)+e^{12} \left (-64 x-96 x^2\right ) \log ^4(x)+e^{16} (-4-6 x) \log ^5(x)+\left (-2048 x^4-3072 x^5+\left (-768 x^5+e^4 \left (-1536 x^3-2304 x^4\right )\right ) \log (x)+\left (e^8 \left (-384 x^2-576 x^3\right )+e^4 \left (-512 x^3-1536 x^4\right )\right ) \log ^2(x)+\left (e^{12} \left (-32 x-48 x^2\right )+e^8 \left (-384 x^2-864 x^3\right )\right ) \log ^3(x)+e^{12} \left (-96 x-192 x^2\right ) \log ^4(x)+e^{16} (-8-15 x) \log ^5(x)\right ) \log \left (x^2\right )}{\left (8 x^5+24 x^6+18 x^7\right ) \log ^5(x) \log ^2\left (x^2\right )} \, dx=\frac {256 \, x^{3} e^{4} \log \left (x\right ) + 96 \, x^{2} e^{8} \log \left (x\right )^{2} + 16 \, x e^{12} \log \left (x\right )^{3} + e^{16} \log \left (x\right )^{4} + 256 \, x^{4}}{4 \, {\left (3 \, x^{5} \log \left (x\right )^{5} + 2 \, x^{4} \log \left (x\right )^{5}\right )}} \] Input:
integrate((((-15*x-8)*exp(4)^4*log(x)^5+(-192*x^2-96*x)*exp(4)^3*log(x)^4+ ((-48*x^2-32*x)*exp(4)^3+(-864*x^3-384*x^2)*exp(4)^2)*log(x)^3+((-576*x^3- 384*x^2)*exp(4)^2+(-1536*x^4-512*x^3)*exp(4))*log(x)^2+((-2304*x^4-1536*x^ 3)*exp(4)-768*x^5)*log(x)-3072*x^5-2048*x^4)*log(x^2)+(-4-6*x)*exp(4)^4*lo g(x)^5+(-96*x^2-64*x)*exp(4)^3*log(x)^4+(-576*x^3-384*x^2)*exp(4)^2*log(x) ^3+(-1536*x^4-1024*x^3)*exp(4)*log(x)^2+(-1536*x^5-1024*x^4)*log(x))/(18*x ^7+24*x^6+8*x^5)/log(x)^5/log(x^2)^2,x, algorithm="giac")
Output:
1/4*(256*x^3*e^4*log(x) + 96*x^2*e^8*log(x)^2 + 16*x*e^12*log(x)^3 + e^16* log(x)^4 + 256*x^4)/(3*x^5*log(x)^5 + 2*x^4*log(x)^5)
Time = 5.68 (sec) , antiderivative size = 892, normalized size of antiderivative = 29.73 \[ \int \frac {\left (-1024 x^4-1536 x^5\right ) \log (x)+e^4 \left (-1024 x^3-1536 x^4\right ) \log ^2(x)+e^8 \left (-384 x^2-576 x^3\right ) \log ^3(x)+e^{12} \left (-64 x-96 x^2\right ) \log ^4(x)+e^{16} (-4-6 x) \log ^5(x)+\left (-2048 x^4-3072 x^5+\left (-768 x^5+e^4 \left (-1536 x^3-2304 x^4\right )\right ) \log (x)+\left (e^8 \left (-384 x^2-576 x^3\right )+e^4 \left (-512 x^3-1536 x^4\right )\right ) \log ^2(x)+\left (e^{12} \left (-32 x-48 x^2\right )+e^8 \left (-384 x^2-864 x^3\right )\right ) \log ^3(x)+e^{12} \left (-96 x-192 x^2\right ) \log ^4(x)+e^{16} (-8-15 x) \log ^5(x)\right ) \log \left (x^2\right )}{\left (8 x^5+24 x^6+18 x^7\right ) \log ^5(x) \log ^2\left (x^2\right )} \, dx=\text {Too large to display} \] Input:
int(-(log(x)*(1024*x^4 + 1536*x^5) + log(x^2)*(log(x)^2*(exp(8)*(384*x^2 + 576*x^3) + exp(4)*(512*x^3 + 1536*x^4)) + log(x)*(exp(4)*(1536*x^3 + 2304 *x^4) + 768*x^5) + log(x)^3*(exp(12)*(32*x + 48*x^2) + exp(8)*(384*x^2 + 8 64*x^3)) + 2048*x^4 + 3072*x^5 + exp(16)*log(x)^5*(15*x + 8) + exp(12)*log (x)^4*(96*x + 192*x^2)) + exp(16)*log(x)^5*(6*x + 4) + exp(12)*log(x)^4*(6 4*x + 96*x^2) + exp(8)*log(x)^3*(384*x^2 + 576*x^3) + exp(4)*log(x)^2*(102 4*x^3 + 1536*x^4))/(log(x^2)^2*log(x)^5*(8*x^5 + 24*x^6 + 18*x^7)),x)
Output:
((4*exp(16)*(log(x^2) - 2*log(x))^4 + 8*exp(16)*(log(x^2) - 2*log(x))^5 + 12288*x^5*(log(x^2) - 2*log(x)) + 16384*x^4 + 24576*x^5 - 8192*x^3*exp(4)* (log(x^2) - 2*log(x)) - 12288*x^4*exp(4)*(log(x^2) - 2*log(x)) - 128*x*exp (12)*(log(x^2) - 2*log(x))^3 - 192*x*exp(12)*(log(x^2) - 2*log(x))^4 + 6*x *exp(16)*(log(x^2) - 2*log(x))^4 + 15*x*exp(16)*(log(x^2) - 2*log(x))^5 - 4096*x^3*exp(4)*(log(x^2) - 2*log(x))^2 - 12288*x^4*exp(4)*(log(x^2) - 2*l og(x))^2 + 1536*x^2*exp(8)*(log(x^2) - 2*log(x))^2 + 1536*x^2*exp(8)*(log( x^2) - 2*log(x))^3 + 2304*x^3*exp(8)*(log(x^2) - 2*log(x))^2 + 3456*x^3*ex p(8)*(log(x^2) - 2*log(x))^3 - 192*x^2*exp(12)*(log(x^2) - 2*log(x))^3 - 3 84*x^2*exp(12)*(log(x^2) - 2*log(x))^4)/(4*x^4*(3*x + 2)^2*(log(x^2) - 2*l og(x))^4) + (log(x)*(8*exp(16)*(log(x^2) - 2*log(x))^4 + 12288*x^5 - 4096* x^3*exp(4)*(log(x^2) - 2*log(x)) - 12288*x^4*exp(4)*(log(x^2) - 2*log(x)) - 192*x*exp(12)*(log(x^2) - 2*log(x))^3 + 15*x*exp(16)*(log(x^2) - 2*log(x ))^4 + 1536*x^2*exp(8)*(log(x^2) - 2*log(x))^2 + 3456*x^3*exp(8)*(log(x^2) - 2*log(x))^2 - 384*x^2*exp(12)*(log(x^2) - 2*log(x))^3))/(2*x^4*(3*x + 2 )^2*(log(x^2) - 2*log(x))^4))/log(x^2) - (8*exp(16)*(log(x^2) - 2*log(x))^ 4 - x*(192*exp(12)*(log(x^2) - 2*log(x))^3 - 15*exp(16)*(log(x^2) - 2*log( x))^4) + x^3*(3456*exp(8)*(log(x^2) - 2*log(x))^2 - 4096*exp(4)*(log(x^2) - 2*log(x))) + x^2*(1536*exp(8)*(log(x^2) - 2*log(x))^2 - 384*exp(12)*(log (x^2) - 2*log(x))^3) + 12288*x^5 - 12288*x^4*exp(4)*(log(x^2) - 2*log(x...
Time = 0.15 (sec) , antiderivative size = 68, normalized size of antiderivative = 2.27 \[ \int \frac {\left (-1024 x^4-1536 x^5\right ) \log (x)+e^4 \left (-1024 x^3-1536 x^4\right ) \log ^2(x)+e^8 \left (-384 x^2-576 x^3\right ) \log ^3(x)+e^{12} \left (-64 x-96 x^2\right ) \log ^4(x)+e^{16} (-4-6 x) \log ^5(x)+\left (-2048 x^4-3072 x^5+\left (-768 x^5+e^4 \left (-1536 x^3-2304 x^4\right )\right ) \log (x)+\left (e^8 \left (-384 x^2-576 x^3\right )+e^4 \left (-512 x^3-1536 x^4\right )\right ) \log ^2(x)+\left (e^{12} \left (-32 x-48 x^2\right )+e^8 \left (-384 x^2-864 x^3\right )\right ) \log ^3(x)+e^{12} \left (-96 x-192 x^2\right ) \log ^4(x)+e^{16} (-8-15 x) \log ^5(x)\right ) \log \left (x^2\right )}{\left (8 x^5+24 x^6+18 x^7\right ) \log ^5(x) \log ^2\left (x^2\right )} \, dx=\frac {\mathrm {log}\left (x \right )^{4} e^{16}+16 \mathrm {log}\left (x \right )^{3} e^{12} x +96 \mathrm {log}\left (x \right )^{2} e^{8} x^{2}+256 \,\mathrm {log}\left (x \right ) e^{4} x^{3}+256 x^{4}}{2 \,\mathrm {log}\left (x^{2}\right ) \mathrm {log}\left (x \right )^{4} x^{4} \left (3 x +2\right )} \] Input:
int((((-15*x-8)*exp(4)^4*log(x)^5+(-192*x^2-96*x)*exp(4)^3*log(x)^4+((-48* x^2-32*x)*exp(4)^3+(-864*x^3-384*x^2)*exp(4)^2)*log(x)^3+((-576*x^3-384*x^ 2)*exp(4)^2+(-1536*x^4-512*x^3)*exp(4))*log(x)^2+((-2304*x^4-1536*x^3)*exp (4)-768*x^5)*log(x)-3072*x^5-2048*x^4)*log(x^2)+(-4-6*x)*exp(4)^4*log(x)^5 +(-96*x^2-64*x)*exp(4)^3*log(x)^4+(-576*x^3-384*x^2)*exp(4)^2*log(x)^3+(-1 536*x^4-1024*x^3)*exp(4)*log(x)^2+(-1536*x^5-1024*x^4)*log(x))/(18*x^7+24* x^6+8*x^5)/log(x)^5/log(x^2)^2,x)
Output:
(log(x)**4*e**16 + 16*log(x)**3*e**12*x + 96*log(x)**2*e**8*x**2 + 256*log (x)*e**4*x**3 + 256*x**4)/(2*log(x**2)*log(x)**4*x**4*(3*x + 2))