3.1237 \(\int (1-2 x)^2 (2+3 x)^7 (3+5 x)^2 \, dx\)

Optimal. Leaf size=56 \[ \frac{25}{729} (3 x+2)^{12}-\frac{740 (3 x+2)^{11}}{2673}+\frac{503}{810} (3 x+2)^{10}-\frac{518 (3 x+2)^9}{2187}+\frac{49 (3 x+2)^8}{1944} \]

[Out]

(49*(2 + 3*x)^8)/1944 - (518*(2 + 3*x)^9)/2187 + (503*(2 + 3*x)^10)/810 - (740*(
2 + 3*x)^11)/2673 + (25*(2 + 3*x)^12)/729

_______________________________________________________________________________________

Rubi [A]  time = 0.106137, antiderivative size = 56, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ \frac{25}{729} (3 x+2)^{12}-\frac{740 (3 x+2)^{11}}{2673}+\frac{503}{810} (3 x+2)^{10}-\frac{518 (3 x+2)^9}{2187}+\frac{49 (3 x+2)^8}{1944} \]

Antiderivative was successfully verified.

[In]  Int[(1 - 2*x)^2*(2 + 3*x)^7*(3 + 5*x)^2,x]

[Out]

(49*(2 + 3*x)^8)/1944 - (518*(2 + 3*x)^9)/2187 + (503*(2 + 3*x)^10)/810 - (740*(
2 + 3*x)^11)/2673 + (25*(2 + 3*x)^12)/729

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 13.6179, size = 49, normalized size = 0.88 \[ \frac{25 \left (3 x + 2\right )^{12}}{729} - \frac{740 \left (3 x + 2\right )^{11}}{2673} + \frac{503 \left (3 x + 2\right )^{10}}{810} - \frac{518 \left (3 x + 2\right )^{9}}{2187} + \frac{49 \left (3 x + 2\right )^{8}}{1944} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)**2*(2+3*x)**7*(3+5*x)**2,x)

[Out]

25*(3*x + 2)**12/729 - 740*(3*x + 2)**11/2673 + 503*(3*x + 2)**10/810 - 518*(3*x
+ 2)**9/2187 + 49*(3*x + 2)**8/1944

_______________________________________________________________________________________

Mathematica [A]  time = 0.00350701, size = 69, normalized size = 1.23 \[ 18225 x^{12}+\frac{1064340 x^{11}}{11}+\frac{2116287 x^{10}}{10}+228996 x^9+\frac{719739 x^8}{8}-65934 x^7-98182 x^6-\frac{203752 x^5}{5}+5764 x^4+\frac{38816 x^3}{3}+5664 x^2+1152 x \]

Antiderivative was successfully verified.

[In]  Integrate[(1 - 2*x)^2*(2 + 3*x)^7*(3 + 5*x)^2,x]

[Out]

1152*x + 5664*x^2 + (38816*x^3)/3 + 5764*x^4 - (203752*x^5)/5 - 98182*x^6 - 6593
4*x^7 + (719739*x^8)/8 + 228996*x^9 + (2116287*x^10)/10 + (1064340*x^11)/11 + 18
225*x^12

_______________________________________________________________________________________

Maple [A]  time = 0.001, size = 60, normalized size = 1.1 \[ 18225\,{x}^{12}+{\frac{1064340\,{x}^{11}}{11}}+{\frac{2116287\,{x}^{10}}{10}}+228996\,{x}^{9}+{\frac{719739\,{x}^{8}}{8}}-65934\,{x}^{7}-98182\,{x}^{6}-{\frac{203752\,{x}^{5}}{5}}+5764\,{x}^{4}+{\frac{38816\,{x}^{3}}{3}}+5664\,{x}^{2}+1152\,x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)^2*(2+3*x)^7*(3+5*x)^2,x)

[Out]

18225*x^12+1064340/11*x^11+2116287/10*x^10+228996*x^9+719739/8*x^8-65934*x^7-981
82*x^6-203752/5*x^5+5764*x^4+38816/3*x^3+5664*x^2+1152*x

_______________________________________________________________________________________

Maxima [A]  time = 1.34683, size = 80, normalized size = 1.43 \[ 18225 \, x^{12} + \frac{1064340}{11} \, x^{11} + \frac{2116287}{10} \, x^{10} + 228996 \, x^{9} + \frac{719739}{8} \, x^{8} - 65934 \, x^{7} - 98182 \, x^{6} - \frac{203752}{5} \, x^{5} + 5764 \, x^{4} + \frac{38816}{3} \, x^{3} + 5664 \, x^{2} + 1152 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^2*(3*x + 2)^7*(2*x - 1)^2,x, algorithm="maxima")

[Out]

18225*x^12 + 1064340/11*x^11 + 2116287/10*x^10 + 228996*x^9 + 719739/8*x^8 - 659
34*x^7 - 98182*x^6 - 203752/5*x^5 + 5764*x^4 + 38816/3*x^3 + 5664*x^2 + 1152*x

_______________________________________________________________________________________

Fricas [A]  time = 0.182902, size = 1, normalized size = 0.02 \[ 18225 x^{12} + \frac{1064340}{11} x^{11} + \frac{2116287}{10} x^{10} + 228996 x^{9} + \frac{719739}{8} x^{8} - 65934 x^{7} - 98182 x^{6} - \frac{203752}{5} x^{5} + 5764 x^{4} + \frac{38816}{3} x^{3} + 5664 x^{2} + 1152 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^2*(3*x + 2)^7*(2*x - 1)^2,x, algorithm="fricas")

[Out]

18225*x^12 + 1064340/11*x^11 + 2116287/10*x^10 + 228996*x^9 + 719739/8*x^8 - 659
34*x^7 - 98182*x^6 - 203752/5*x^5 + 5764*x^4 + 38816/3*x^3 + 5664*x^2 + 1152*x

_______________________________________________________________________________________

Sympy [A]  time = 0.120827, size = 66, normalized size = 1.18 \[ 18225 x^{12} + \frac{1064340 x^{11}}{11} + \frac{2116287 x^{10}}{10} + 228996 x^{9} + \frac{719739 x^{8}}{8} - 65934 x^{7} - 98182 x^{6} - \frac{203752 x^{5}}{5} + 5764 x^{4} + \frac{38816 x^{3}}{3} + 5664 x^{2} + 1152 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)**2*(2+3*x)**7*(3+5*x)**2,x)

[Out]

18225*x**12 + 1064340*x**11/11 + 2116287*x**10/10 + 228996*x**9 + 719739*x**8/8
- 65934*x**7 - 98182*x**6 - 203752*x**5/5 + 5764*x**4 + 38816*x**3/3 + 5664*x**2
+ 1152*x

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.209483, size = 80, normalized size = 1.43 \[ 18225 \, x^{12} + \frac{1064340}{11} \, x^{11} + \frac{2116287}{10} \, x^{10} + 228996 \, x^{9} + \frac{719739}{8} \, x^{8} - 65934 \, x^{7} - 98182 \, x^{6} - \frac{203752}{5} \, x^{5} + 5764 \, x^{4} + \frac{38816}{3} \, x^{3} + 5664 \, x^{2} + 1152 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^2*(3*x + 2)^7*(2*x - 1)^2,x, algorithm="giac")

[Out]

18225*x^12 + 1064340/11*x^11 + 2116287/10*x^10 + 228996*x^9 + 719739/8*x^8 - 659
34*x^7 - 98182*x^6 - 203752/5*x^5 + 5764*x^4 + 38816/3*x^3 + 5664*x^2 + 1152*x