3.1161 \(\int (1-2 x) (2+3 x)^5 (3+5 x)^3 \, dx\)

Optimal. Leaf size=56 \[ -\frac{25}{243} (3 x+2)^{10}+\frac{1025 (3 x+2)^9}{2187}-\frac{185}{648} (3 x+2)^8+\frac{107 (3 x+2)^7}{1701}-\frac{7 (3 x+2)^6}{1458} \]

[Out]

(-7*(2 + 3*x)^6)/1458 + (107*(2 + 3*x)^7)/1701 - (185*(2 + 3*x)^8)/648 + (1025*(
2 + 3*x)^9)/2187 - (25*(2 + 3*x)^10)/243

_______________________________________________________________________________________

Rubi [A]  time = 0.0815454, antiderivative size = 56, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ -\frac{25}{243} (3 x+2)^{10}+\frac{1025 (3 x+2)^9}{2187}-\frac{185}{648} (3 x+2)^8+\frac{107 (3 x+2)^7}{1701}-\frac{7 (3 x+2)^6}{1458} \]

Antiderivative was successfully verified.

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

[Out]

(-7*(2 + 3*x)^6)/1458 + (107*(2 + 3*x)^7)/1701 - (185*(2 + 3*x)^8)/648 + (1025*(
2 + 3*x)^9)/2187 - (25*(2 + 3*x)^10)/243

_______________________________________________________________________________________

Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - 6075 x^{10} - 31275 x^{9} - \frac{544185 x^{8}}{8} - \frac{547767 x^{7}}{7} - \frac{90143 x^{6}}{2} - 1810 x^{5} + 16570 x^{4} + 12480 x^{3} + 864 x + 9072 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-6075*x**10 - 31275*x**9 - 544185*x**8/8 - 547767*x**7/7 - 90143*x**6/2 - 1810*x
**5 + 16570*x**4 + 12480*x**3 + 864*x + 9072*Integral(x, x)

_______________________________________________________________________________________

Mathematica [A]  time = 0.00302704, size = 55, normalized size = 0.98 \[ -6075 x^{10}-31275 x^9-\frac{544185 x^8}{8}-\frac{547767 x^7}{7}-\frac{90143 x^6}{2}-1810 x^5+16570 x^4+12480 x^3+4536 x^2+864 x \]

Antiderivative was successfully verified.

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

[Out]

864*x + 4536*x^2 + 12480*x^3 + 16570*x^4 - 1810*x^5 - (90143*x^6)/2 - (547767*x^
7)/7 - (544185*x^8)/8 - 31275*x^9 - 6075*x^10

_______________________________________________________________________________________

Maple [A]  time = 0.002, size = 50, normalized size = 0.9 \[ -6075\,{x}^{10}-31275\,{x}^{9}-{\frac{544185\,{x}^{8}}{8}}-{\frac{547767\,{x}^{7}}{7}}-{\frac{90143\,{x}^{6}}{2}}-1810\,{x}^{5}+16570\,{x}^{4}+12480\,{x}^{3}+4536\,{x}^{2}+864\,x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-6075*x^10-31275*x^9-544185/8*x^8-547767/7*x^7-90143/2*x^6-1810*x^5+16570*x^4+12
480*x^3+4536*x^2+864*x

_______________________________________________________________________________________

Maxima [A]  time = 1.34777, size = 66, normalized size = 1.18 \[ -6075 \, x^{10} - 31275 \, x^{9} - \frac{544185}{8} \, x^{8} - \frac{547767}{7} \, x^{7} - \frac{90143}{2} \, x^{6} - 1810 \, x^{5} + 16570 \, x^{4} + 12480 \, x^{3} + 4536 \, x^{2} + 864 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-6075*x^10 - 31275*x^9 - 544185/8*x^8 - 547767/7*x^7 - 90143/2*x^6 - 1810*x^5 +
16570*x^4 + 12480*x^3 + 4536*x^2 + 864*x

_______________________________________________________________________________________

Fricas [A]  time = 0.181873, size = 1, normalized size = 0.02 \[ -6075 x^{10} - 31275 x^{9} - \frac{544185}{8} x^{8} - \frac{547767}{7} x^{7} - \frac{90143}{2} x^{6} - 1810 x^{5} + 16570 x^{4} + 12480 x^{3} + 4536 x^{2} + 864 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-6075*x^10 - 31275*x^9 - 544185/8*x^8 - 547767/7*x^7 - 90143/2*x^6 - 1810*x^5 +
16570*x^4 + 12480*x^3 + 4536*x^2 + 864*x

_______________________________________________________________________________________

Sympy [A]  time = 0.104689, size = 53, normalized size = 0.95 \[ - 6075 x^{10} - 31275 x^{9} - \frac{544185 x^{8}}{8} - \frac{547767 x^{7}}{7} - \frac{90143 x^{6}}{2} - 1810 x^{5} + 16570 x^{4} + 12480 x^{3} + 4536 x^{2} + 864 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-6075*x**10 - 31275*x**9 - 544185*x**8/8 - 547767*x**7/7 - 90143*x**6/2 - 1810*x
**5 + 16570*x**4 + 12480*x**3 + 4536*x**2 + 864*x

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.207967, size = 66, normalized size = 1.18 \[ -6075 \, x^{10} - 31275 \, x^{9} - \frac{544185}{8} \, x^{8} - \frac{547767}{7} \, x^{7} - \frac{90143}{2} \, x^{6} - 1810 \, x^{5} + 16570 \, x^{4} + 12480 \, x^{3} + 4536 \, x^{2} + 864 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-6075*x^10 - 31275*x^9 - 544185/8*x^8 - 547767/7*x^7 - 90143/2*x^6 - 1810*x^5 +
16570*x^4 + 12480*x^3 + 4536*x^2 + 864*x