3.355 \(\int (e x)^m (2-2 a x)^3 (1+a x)^4 \, dx\)
Optimal. Leaf size=156 \[ -\frac{8 a^7 (e x)^{m+8}}{e^8 (m+8)}-\frac{8 a^6 (e x)^{m+7}}{e^7 (m+7)}+\frac{24 a^5 (e x)^{m+6}}{e^6 (m+6)}+\frac{24 a^4 (e x)^{m+5}}{e^5 (m+5)}-\frac{24 a^3 (e x)^{m+4}}{e^4 (m+4)}-\frac{24 a^2 (e x)^{m+3}}{e^3 (m+3)}+\frac{8 a (e x)^{m+2}}{e^2 (m+2)}+\frac{8 (e x)^{m+1}}{e (m+1)} \]
[Out]
(8*(e*x)^(1 + m))/(e*(1 + m)) + (8*a*(e*x)^(2 + m))/(e^2*(2 + m)) - (24*a^2*(e*x
)^(3 + m))/(e^3*(3 + m)) - (24*a^3*(e*x)^(4 + m))/(e^4*(4 + m)) + (24*a^4*(e*x)^
(5 + m))/(e^5*(5 + m)) + (24*a^5*(e*x)^(6 + m))/(e^6*(6 + m)) - (8*a^6*(e*x)^(7
+ m))/(e^7*(7 + m)) - (8*a^7*(e*x)^(8 + m))/(e^8*(8 + m))
_______________________________________________________________________________________
Rubi [A] time = 0.204006, antiderivative size = 156, normalized size of antiderivative = 1.,
number of steps used = 2, number of rules used = 1, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.048
\[ -\frac{8 a^7 (e x)^{m+8}}{e^8 (m+8)}-\frac{8 a^6 (e x)^{m+7}}{e^7 (m+7)}+\frac{24 a^5 (e x)^{m+6}}{e^6 (m+6)}+\frac{24 a^4 (e x)^{m+5}}{e^5 (m+5)}-\frac{24 a^3 (e x)^{m+4}}{e^4 (m+4)}-\frac{24 a^2 (e x)^{m+3}}{e^3 (m+3)}+\frac{8 a (e x)^{m+2}}{e^2 (m+2)}+\frac{8 (e x)^{m+1}}{e (m+1)} \]
Antiderivative was successfully verified.
[In] Int[(e*x)^m*(2 - 2*a*x)^3*(1 + a*x)^4,x]
[Out]
(8*(e*x)^(1 + m))/(e*(1 + m)) + (8*a*(e*x)^(2 + m))/(e^2*(2 + m)) - (24*a^2*(e*x
)^(3 + m))/(e^3*(3 + m)) - (24*a^3*(e*x)^(4 + m))/(e^4*(4 + m)) + (24*a^4*(e*x)^
(5 + m))/(e^5*(5 + m)) + (24*a^5*(e*x)^(6 + m))/(e^6*(6 + m)) - (8*a^6*(e*x)^(7
+ m))/(e^7*(7 + m)) - (8*a^7*(e*x)^(8 + m))/(e^8*(8 + m))
_______________________________________________________________________________________
Rubi in Sympy [A] time = 36.8618, size = 141, normalized size = 0.9 \[ - \frac{8 a^{7} \left (e x\right )^{m + 8}}{e^{8} \left (m + 8\right )} - \frac{8 a^{6} \left (e x\right )^{m + 7}}{e^{7} \left (m + 7\right )} + \frac{24 a^{5} \left (e x\right )^{m + 6}}{e^{6} \left (m + 6\right )} + \frac{24 a^{4} \left (e x\right )^{m + 5}}{e^{5} \left (m + 5\right )} - \frac{24 a^{3} \left (e x\right )^{m + 4}}{e^{4} \left (m + 4\right )} - \frac{24 a^{2} \left (e x\right )^{m + 3}}{e^{3} \left (m + 3\right )} + \frac{8 a \left (e x\right )^{m + 2}}{e^{2} \left (m + 2\right )} + \frac{8 \left (e x\right )^{m + 1}}{e \left (m + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((e*x)**m*(-2*a*x+2)**3*(a*x+1)**4,x)
[Out]
-8*a**7*(e*x)**(m + 8)/(e**8*(m + 8)) - 8*a**6*(e*x)**(m + 7)/(e**7*(m + 7)) + 2
4*a**5*(e*x)**(m + 6)/(e**6*(m + 6)) + 24*a**4*(e*x)**(m + 5)/(e**5*(m + 5)) - 2
4*a**3*(e*x)**(m + 4)/(e**4*(m + 4)) - 24*a**2*(e*x)**(m + 3)/(e**3*(m + 3)) + 8
*a*(e*x)**(m + 2)/(e**2*(m + 2)) + 8*(e*x)**(m + 1)/(e*(m + 1))
_______________________________________________________________________________________
Mathematica [A] time = 0.0912675, size = 100, normalized size = 0.64 \[ 8 x \left (-\frac{a^7 x^7}{m+8}-\frac{a^6 x^6}{m+7}+\frac{3 a^5 x^5}{m+6}+\frac{3 a^4 x^4}{m+5}-\frac{3 a^3 x^3}{m+4}-\frac{3 a^2 x^2}{m+3}+\frac{a x}{m+2}+\frac{1}{m+1}\right ) (e x)^m \]
Antiderivative was successfully verified.
[In] Integrate[(e*x)^m*(2 - 2*a*x)^3*(1 + a*x)^4,x]
[Out]
8*x*(e*x)^m*((1 + m)^(-1) + (a*x)/(2 + m) - (3*a^2*x^2)/(3 + m) - (3*a^3*x^3)/(4
+ m) + (3*a^4*x^4)/(5 + m) + (3*a^5*x^5)/(6 + m) - (a^6*x^6)/(7 + m) - (a^7*x^7
)/(8 + m))
_______________________________________________________________________________________
Maple [B] time = 0.011, size = 631, normalized size = 4. \[ -8\,{\frac{ \left ( ex \right ) ^{m} \left ({a}^{7}{m}^{7}{x}^{7}+28\,{a}^{7}{m}^{6}{x}^{7}+322\,{a}^{7}{m}^{5}{x}^{7}+{a}^{6}{m}^{7}{x}^{6}+1960\,{a}^{7}{m}^{4}{x}^{7}+29\,{a}^{6}{m}^{6}{x}^{6}+6769\,{a}^{7}{m}^{3}{x}^{7}+343\,{a}^{6}{m}^{5}{x}^{6}-3\,{a}^{5}{m}^{7}{x}^{5}+13132\,{a}^{7}{m}^{2}{x}^{7}+2135\,{a}^{6}{m}^{4}{x}^{6}-90\,{a}^{5}{m}^{6}{x}^{5}+13068\,{a}^{7}m{x}^{7}+7504\,{a}^{6}{m}^{3}{x}^{6}-1098\,{a}^{5}{m}^{5}{x}^{5}-3\,{a}^{4}{m}^{7}{x}^{4}+5040\,{a}^{7}{x}^{7}+14756\,{a}^{6}{m}^{2}{x}^{6}-7020\,{a}^{5}{m}^{4}{x}^{5}-93\,{a}^{4}{m}^{6}{x}^{4}+14832\,{a}^{6}m{x}^{6}-25227\,{a}^{5}{m}^{3}{x}^{5}-1173\,{a}^{4}{m}^{5}{x}^{4}+3\,{a}^{3}{m}^{7}{x}^{3}+5760\,{a}^{6}{x}^{6}-50490\,{a}^{5}{m}^{2}{x}^{5}-7743\,{a}^{4}{m}^{4}{x}^{4}+96\,{a}^{3}{m}^{6}{x}^{3}-51432\,{a}^{5}m{x}^{5}-28632\,{a}^{4}{m}^{3}{x}^{4}+1254\,{a}^{3}{m}^{5}{x}^{3}+3\,{a}^{2}{m}^{7}{x}^{2}-20160\,{a}^{5}{x}^{5}-58692\,{a}^{4}{m}^{2}{x}^{4}+8592\,{a}^{3}{m}^{4}{x}^{3}+99\,{a}^{2}{m}^{6}{x}^{2}-60912\,{a}^{4}m{x}^{4}+32979\,{a}^{3}{m}^{3}{x}^{3}+1341\,{a}^{2}{m}^{5}{x}^{2}-a{m}^{7}x-24192\,{a}^{4}{x}^{4}+69936\,{a}^{3}{m}^{2}{x}^{3}+9585\,{a}^{2}{m}^{4}{x}^{2}-34\,a{m}^{6}x+74628\,{a}^{3}m{x}^{3}+38592\,{a}^{2}{m}^{3}{x}^{2}-478\,a{m}^{5}x-{m}^{7}+30240\,{a}^{3}{x}^{3}+86076\,{a}^{2}{m}^{2}{x}^{2}-3580\,a{m}^{4}x-35\,{m}^{6}+96144\,{a}^{2}m{x}^{2}-15289\,a{m}^{3}x-511\,{m}^{5}+40320\,{a}^{2}{x}^{2}-36706\,a{m}^{2}x-4025\,{m}^{4}-44712\,amx-18424\,{m}^{3}-20160\,ax-48860\,{m}^{2}-69264\,m-40320 \right ) x}{ \left ( 8+m \right ) \left ( 7+m \right ) \left ( 6+m \right ) \left ( 5+m \right ) \left ( 4+m \right ) \left ( 3+m \right ) \left ( 2+m \right ) \left ( 1+m \right ) }} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((e*x)^m*(-2*a*x+2)^3*(a*x+1)^4,x)
[Out]
-8*(e*x)^m*(a^7*m^7*x^7+28*a^7*m^6*x^7+322*a^7*m^5*x^7+a^6*m^7*x^6+1960*a^7*m^4*
x^7+29*a^6*m^6*x^6+6769*a^7*m^3*x^7+343*a^6*m^5*x^6-3*a^5*m^7*x^5+13132*a^7*m^2*
x^7+2135*a^6*m^4*x^6-90*a^5*m^6*x^5+13068*a^7*m*x^7+7504*a^6*m^3*x^6-1098*a^5*m^
5*x^5-3*a^4*m^7*x^4+5040*a^7*x^7+14756*a^6*m^2*x^6-7020*a^5*m^4*x^5-93*a^4*m^6*x
^4+14832*a^6*m*x^6-25227*a^5*m^3*x^5-1173*a^4*m^5*x^4+3*a^3*m^7*x^3+5760*a^6*x^6
-50490*a^5*m^2*x^5-7743*a^4*m^4*x^4+96*a^3*m^6*x^3-51432*a^5*m*x^5-28632*a^4*m^3
*x^4+1254*a^3*m^5*x^3+3*a^2*m^7*x^2-20160*a^5*x^5-58692*a^4*m^2*x^4+8592*a^3*m^4
*x^3+99*a^2*m^6*x^2-60912*a^4*m*x^4+32979*a^3*m^3*x^3+1341*a^2*m^5*x^2-a*m^7*x-2
4192*a^4*x^4+69936*a^3*m^2*x^3+9585*a^2*m^4*x^2-34*a*m^6*x+74628*a^3*m*x^3+38592
*a^2*m^3*x^2-478*a*m^5*x-m^7+30240*a^3*x^3+86076*a^2*m^2*x^2-3580*a*m^4*x-35*m^6
+96144*a^2*m*x^2-15289*a*m^3*x-511*m^5+40320*a^2*x^2-36706*a*m^2*x-4025*m^4-4471
2*a*m*x-18424*m^3-20160*a*x-48860*m^2-69264*m-40320)*x/(8+m)/(7+m)/(6+m)/(5+m)/(
4+m)/(3+m)/(2+m)/(1+m)
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-8*(a*x + 1)^4*(a*x - 1)^3*(e*x)^m,x, algorithm="maxima")
[Out]
Exception raised: ValueError
_______________________________________________________________________________________
Fricas [A] time = 0.218824, size = 694, normalized size = 4.45 \[ -\frac{8 \,{\left ({\left (a^{7} m^{7} + 28 \, a^{7} m^{6} + 322 \, a^{7} m^{5} + 1960 \, a^{7} m^{4} + 6769 \, a^{7} m^{3} + 13132 \, a^{7} m^{2} + 13068 \, a^{7} m + 5040 \, a^{7}\right )} x^{8} +{\left (a^{6} m^{7} + 29 \, a^{6} m^{6} + 343 \, a^{6} m^{5} + 2135 \, a^{6} m^{4} + 7504 \, a^{6} m^{3} + 14756 \, a^{6} m^{2} + 14832 \, a^{6} m + 5760 \, a^{6}\right )} x^{7} - 3 \,{\left (a^{5} m^{7} + 30 \, a^{5} m^{6} + 366 \, a^{5} m^{5} + 2340 \, a^{5} m^{4} + 8409 \, a^{5} m^{3} + 16830 \, a^{5} m^{2} + 17144 \, a^{5} m + 6720 \, a^{5}\right )} x^{6} - 3 \,{\left (a^{4} m^{7} + 31 \, a^{4} m^{6} + 391 \, a^{4} m^{5} + 2581 \, a^{4} m^{4} + 9544 \, a^{4} m^{3} + 19564 \, a^{4} m^{2} + 20304 \, a^{4} m + 8064 \, a^{4}\right )} x^{5} + 3 \,{\left (a^{3} m^{7} + 32 \, a^{3} m^{6} + 418 \, a^{3} m^{5} + 2864 \, a^{3} m^{4} + 10993 \, a^{3} m^{3} + 23312 \, a^{3} m^{2} + 24876 \, a^{3} m + 10080 \, a^{3}\right )} x^{4} + 3 \,{\left (a^{2} m^{7} + 33 \, a^{2} m^{6} + 447 \, a^{2} m^{5} + 3195 \, a^{2} m^{4} + 12864 \, a^{2} m^{3} + 28692 \, a^{2} m^{2} + 32048 \, a^{2} m + 13440 \, a^{2}\right )} x^{3} -{\left (a m^{7} + 34 \, a m^{6} + 478 \, a m^{5} + 3580 \, a m^{4} + 15289 \, a m^{3} + 36706 \, a m^{2} + 44712 \, a m + 20160 \, a\right )} x^{2} -{\left (m^{7} + 35 \, m^{6} + 511 \, m^{5} + 4025 \, m^{4} + 18424 \, m^{3} + 48860 \, m^{2} + 69264 \, m + 40320\right )} x\right )} \left (e x\right )^{m}}{m^{8} + 36 \, m^{7} + 546 \, m^{6} + 4536 \, m^{5} + 22449 \, m^{4} + 67284 \, m^{3} + 118124 \, m^{2} + 109584 \, m + 40320} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-8*(a*x + 1)^4*(a*x - 1)^3*(e*x)^m,x, algorithm="fricas")
[Out]
-8*((a^7*m^7 + 28*a^7*m^6 + 322*a^7*m^5 + 1960*a^7*m^4 + 6769*a^7*m^3 + 13132*a^
7*m^2 + 13068*a^7*m + 5040*a^7)*x^8 + (a^6*m^7 + 29*a^6*m^6 + 343*a^6*m^5 + 2135
*a^6*m^4 + 7504*a^6*m^3 + 14756*a^6*m^2 + 14832*a^6*m + 5760*a^6)*x^7 - 3*(a^5*m
^7 + 30*a^5*m^6 + 366*a^5*m^5 + 2340*a^5*m^4 + 8409*a^5*m^3 + 16830*a^5*m^2 + 17
144*a^5*m + 6720*a^5)*x^6 - 3*(a^4*m^7 + 31*a^4*m^6 + 391*a^4*m^5 + 2581*a^4*m^4
+ 9544*a^4*m^3 + 19564*a^4*m^2 + 20304*a^4*m + 8064*a^4)*x^5 + 3*(a^3*m^7 + 32*
a^3*m^6 + 418*a^3*m^5 + 2864*a^3*m^4 + 10993*a^3*m^3 + 23312*a^3*m^2 + 24876*a^3
*m + 10080*a^3)*x^4 + 3*(a^2*m^7 + 33*a^2*m^6 + 447*a^2*m^5 + 3195*a^2*m^4 + 128
64*a^2*m^3 + 28692*a^2*m^2 + 32048*a^2*m + 13440*a^2)*x^3 - (a*m^7 + 34*a*m^6 +
478*a*m^5 + 3580*a*m^4 + 15289*a*m^3 + 36706*a*m^2 + 44712*a*m + 20160*a)*x^2 -
(m^7 + 35*m^6 + 511*m^5 + 4025*m^4 + 18424*m^3 + 48860*m^2 + 69264*m + 40320)*x)
*(e*x)^m/(m^8 + 36*m^7 + 546*m^6 + 4536*m^5 + 22449*m^4 + 67284*m^3 + 118124*m^2
+ 109584*m + 40320)
_______________________________________________________________________________________
Sympy [A] time = 9.29967, size = 4136, normalized size = 26.51 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x)**m*(-2*a*x+2)**3*(a*x+1)**4,x)
[Out]
Piecewise(((-8*a**7*log(x) + 8*a**6/x - 12*a**5/x**2 - 8*a**4/x**3 + 6*a**3/x**4
+ 24*a**2/(5*x**5) - 4*a/(3*x**6) - 8/(7*x**7))/e**8, Eq(m, -8)), ((-8*a**7*x -
8*a**6*log(x) - 24*a**5/x - 12*a**4/x**2 + 8*a**3/x**3 + 6*a**2/x**4 - 8*a/(5*x
**5) - 4/(3*x**6))/e**7, Eq(m, -7)), ((-4*a**7*x**2 - 8*a**6*x + 24*a**5*log(x)
- 24*a**4/x + 12*a**3/x**2 + 8*a**2/x**3 - 2*a/x**4 - 8/(5*x**5))/e**6, Eq(m, -6
)), ((-8*a**7*x**3/3 - 4*a**6*x**2 + 24*a**5*x + 24*a**4*log(x) + 24*a**3/x + 12
*a**2/x**2 - 8*a/(3*x**3) - 2/x**4)/e**5, Eq(m, -5)), ((-2*a**7*x**4 - 8*a**6*x*
*3/3 + 12*a**5*x**2 + 24*a**4*x - 24*a**3*log(x) + 24*a**2/x - 4*a/x**2 - 8/(3*x
**3))/e**4, Eq(m, -4)), ((-8*a**7*x**5/5 - 2*a**6*x**4 + 8*a**5*x**3 + 12*a**4*x
**2 - 24*a**3*x - 24*a**2*log(x) - 8*a/x - 4/x**2)/e**3, Eq(m, -3)), ((-4*a**7*x
**6/3 - 8*a**6*x**5/5 + 6*a**5*x**4 + 8*a**4*x**3 - 12*a**3*x**2 - 24*a**2*x + 8
*a*log(x) - 8/x)/e**2, Eq(m, -2)), ((-8*a**7*x**7/7 - 4*a**6*x**6/3 + 24*a**5*x*
*5/5 + 6*a**4*x**4 - 8*a**3*x**3 - 12*a**2*x**2 + 8*a*x + 8*log(x))/e, Eq(m, -1)
), (-8*a**7*e**m*m**7*x**8*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m
**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) - 224*a**7*e**m*m**6*x**8*x**
m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2
+ 109584*m + 40320) - 2576*a**7*e**m*m**5*x**8*x**m/(m**8 + 36*m**7 + 546*m**6
+ 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) - 15680*
a**7*e**m*m**4*x**8*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 6
7284*m**3 + 118124*m**2 + 109584*m + 40320) - 54152*a**7*e**m*m**3*x**8*x**m/(m*
*8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 10
9584*m + 40320) - 105056*a**7*e**m*m**2*x**8*x**m/(m**8 + 36*m**7 + 546*m**6 + 4
536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) - 104544*a*
*7*e**m*m*x**8*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*
m**3 + 118124*m**2 + 109584*m + 40320) - 40320*a**7*e**m*x**8*x**m/(m**8 + 36*m*
*7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 4
0320) - 8*a**6*e**m*m**7*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 2244
9*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) - 232*a**6*e**m*m**6*x**7*
x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m
**2 + 109584*m + 40320) - 2744*a**6*e**m*m**5*x**7*x**m/(m**8 + 36*m**7 + 546*m*
*6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) - 170
80*a**6*e**m*m**4*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4
+ 67284*m**3 + 118124*m**2 + 109584*m + 40320) - 60032*a**6*e**m*m**3*x**7*x**m/
(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 +
109584*m + 40320) - 118048*a**6*e**m*m**2*x**7*x**m/(m**8 + 36*m**7 + 546*m**6
+ 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) - 118656
*a**6*e**m*m*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 672
84*m**3 + 118124*m**2 + 109584*m + 40320) - 46080*a**6*e**m*x**7*x**m/(m**8 + 36
*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m
+ 40320) + 24*a**5*e**m*m**7*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 +
22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 720*a**5*e**m*m**6*x
**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 1181
24*m**2 + 109584*m + 40320) + 8784*a**5*e**m*m**5*x**6*x**m/(m**8 + 36*m**7 + 54
6*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) +
56160*a**5*e**m*m**4*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m
**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 201816*a**5*e**m*m**3*x**6*
x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m
**2 + 109584*m + 40320) + 403920*a**5*e**m*m**2*x**6*x**m/(m**8 + 36*m**7 + 546*
m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 4
11456*a**5*e**m*m*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4
+ 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 161280*a**5*e**m*x**6*x**m/(m**
8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109
584*m + 40320) + 24*a**4*e**m*m**7*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m
**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 744*a**4*e**m*
m**6*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3
+ 118124*m**2 + 109584*m + 40320) + 9384*a**4*e**m*m**5*x**5*x**m/(m**8 + 36*m**
7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40
320) + 61944*a**4*e**m*m**4*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 2
2449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 229056*a**4*e**m*m**3
*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 11
8124*m**2 + 109584*m + 40320) + 469536*a**4*e**m*m**2*x**5*x**m/(m**8 + 36*m**7
+ 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 4032
0) + 487296*a**4*e**m*m*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449
*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 193536*a**4*e**m*x**5*x**
m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2
+ 109584*m + 40320) - 24*a**3*e**m*m**7*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 +
4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) - 768*a**3
*e**m*m**6*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284
*m**3 + 118124*m**2 + 109584*m + 40320) - 10032*a**3*e**m*m**5*x**4*x**m/(m**8 +
36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584
*m + 40320) - 68736*a**3*e**m*m**4*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m
**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) - 263832*a**3*e*
*m*m**3*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m*
*3 + 118124*m**2 + 109584*m + 40320) - 559488*a**3*e**m*m**2*x**4*x**m/(m**8 + 3
6*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m
+ 40320) - 597024*a**3*e**m*m*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5
+ 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) - 241920*a**3*e**m*x
**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 1181
24*m**2 + 109584*m + 40320) - 24*a**2*e**m*m**7*x**3*x**m/(m**8 + 36*m**7 + 546*
m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) - 7
92*a**2*e**m*m**6*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4
+ 67284*m**3 + 118124*m**2 + 109584*m + 40320) - 10728*a**2*e**m*m**5*x**3*x**m/
(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 +
109584*m + 40320) - 76680*a**2*e**m*m**4*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 +
4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) - 308736*
a**2*e**m*m**3*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 6
7284*m**3 + 118124*m**2 + 109584*m + 40320) - 688608*a**2*e**m*m**2*x**3*x**m/(m
**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 1
09584*m + 40320) - 769152*a**2*e**m*m*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 453
6*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) - 322560*a**2
*e**m*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3
+ 118124*m**2 + 109584*m + 40320) + 8*a*e**m*m**7*x**2*x**m/(m**8 + 36*m**7 + 5
46*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320)
+ 272*a*e**m*m**6*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4
+ 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 3824*a*e**m*m**5*x**2*x**m/(m**
8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109
584*m + 40320) + 28640*a*e**m*m**4*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m
**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 122312*a*e**m*
m**3*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3
+ 118124*m**2 + 109584*m + 40320) + 293648*a*e**m*m**2*x**2*x**m/(m**8 + 36*m**7
+ 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 403
20) + 357696*a*e**m*m*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m
**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 161280*a*e**m*x**2*x**m/(m*
*8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 10
9584*m + 40320) + 8*e**m*m**7*x*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22
449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 280*e**m*m**6*x*x**m/(
m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 +
109584*m + 40320) + 4088*e**m*m**5*x*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5
+ 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 32200*e**m*m**4*x
*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*
m**2 + 109584*m + 40320) + 147392*e**m*m**3*x*x**m/(m**8 + 36*m**7 + 546*m**6 +
4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 390880*e
**m*m**2*x*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3
+ 118124*m**2 + 109584*m + 40320) + 554112*e**m*m*x*x**m/(m**8 + 36*m**7 + 546*
m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 3
22560*e**m*x*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m*
*3 + 118124*m**2 + 109584*m + 40320), True))
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.212407, size = 1, normalized size = 0.01 \[ \mathit{Done} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-8*(a*x + 1)^4*(a*x - 1)^3*(e*x)^m,x, algorithm="giac")
[Out]
Done