3.1244 \(\int (1-2 x)^2 (3+5 x)^2 \, dx\)

Optimal. Leaf size=34 \[ -\frac{5}{8} (1-2 x)^5+\frac{55}{16} (1-2 x)^4-\frac{121}{24} (1-2 x)^3 \]

[Out]

(-121*(1 - 2*x)^3)/24 + (55*(1 - 2*x)^4)/16 - (5*(1 - 2*x)^5)/8

_______________________________________________________________________________________

Rubi [A]  time = 0.0331755, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ -\frac{5}{8} (1-2 x)^5+\frac{55}{16} (1-2 x)^4-\frac{121}{24} (1-2 x)^3 \]

Antiderivative was successfully verified.

[In]  Int[(1 - 2*x)^2*(3 + 5*x)^2,x]

[Out]

(-121*(1 - 2*x)^3)/24 + (55*(1 - 2*x)^4)/16 - (5*(1 - 2*x)^5)/8

_______________________________________________________________________________________

Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ 20 x^{5} + 5 x^{4} - \frac{59 x^{3}}{3} + 9 x - 6 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

20*x**5 + 5*x**4 - 59*x**3/3 + 9*x - 6*Integral(x, x)

_______________________________________________________________________________________

Mathematica [A]  time = 0.00114522, size = 26, normalized size = 0.76 \[ 20 x^5+5 x^4-\frac{59 x^3}{3}-3 x^2+9 x \]

Antiderivative was successfully verified.

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

[Out]

9*x - 3*x^2 - (59*x^3)/3 + 5*x^4 + 20*x^5

_______________________________________________________________________________________

Maple [A]  time = 0.002, size = 25, normalized size = 0.7 \[ 20\,{x}^{5}+5\,{x}^{4}-{\frac{59\,{x}^{3}}{3}}-3\,{x}^{2}+9\,x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)^2*(3+5*x)^2,x)

[Out]

20*x^5+5*x^4-59/3*x^3-3*x^2+9*x

_______________________________________________________________________________________

Maxima [A]  time = 1.34856, size = 32, normalized size = 0.94 \[ 20 \, x^{5} + 5 \, x^{4} - \frac{59}{3} \, x^{3} - 3 \, x^{2} + 9 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

20*x^5 + 5*x^4 - 59/3*x^3 - 3*x^2 + 9*x

_______________________________________________________________________________________

Fricas [A]  time = 0.18651, size = 1, normalized size = 0.03 \[ 20 x^{5} + 5 x^{4} - \frac{59}{3} x^{3} - 3 x^{2} + 9 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

20*x^5 + 5*x^4 - 59/3*x^3 - 3*x^2 + 9*x

_______________________________________________________________________________________

Sympy [A]  time = 0.074949, size = 24, normalized size = 0.71 \[ 20 x^{5} + 5 x^{4} - \frac{59 x^{3}}{3} - 3 x^{2} + 9 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

20*x**5 + 5*x**4 - 59*x**3/3 - 3*x**2 + 9*x

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.211842, size = 32, normalized size = 0.94 \[ 20 \, x^{5} + 5 \, x^{4} - \frac{59}{3} \, x^{3} - 3 \, x^{2} + 9 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

20*x^5 + 5*x^4 - 59/3*x^3 - 3*x^2 + 9*x