3.1242 \(\int (1-2 x)^2 (2+3 x)^2 (3+5 x)^2 \, dx\)

Optimal. Leaf size=56 \[ -\frac{225}{224} (1-2 x)^7+\frac{85}{8} (1-2 x)^6-\frac{3467}{80} (1-2 x)^5+\frac{1309}{16} (1-2 x)^4-\frac{5929}{96} (1-2 x)^3 \]

[Out]

(-5929*(1 - 2*x)^3)/96 + (1309*(1 - 2*x)^4)/16 - (3467*(1 - 2*x)^5)/80 + (85*(1
- 2*x)^6)/8 - (225*(1 - 2*x)^7)/224

_______________________________________________________________________________________

Rubi [A]  time = 0.0781907, 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 \[ -\frac{225}{224} (1-2 x)^7+\frac{85}{8} (1-2 x)^6-\frac{3467}{80} (1-2 x)^5+\frac{1309}{16} (1-2 x)^4-\frac{5929}{96} (1-2 x)^3 \]

Antiderivative was successfully verified.

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

[Out]

(-5929*(1 - 2*x)^3)/96 + (1309*(1 - 2*x)^4)/16 - (3467*(1 - 2*x)^5)/80 + (85*(1
- 2*x)^6)/8 - (225*(1 - 2*x)^7)/224

_______________________________________________________________________________________

Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{900 x^{7}}{7} + 230 x^{6} + \frac{109 x^{5}}{5} - \frac{341 x^{4}}{2} - \frac{227 x^{3}}{3} + 36 x + 84 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

900*x**7/7 + 230*x**6 + 109*x**5/5 - 341*x**4/2 - 227*x**3/3 + 36*x + 84*Integra
l(x, x)

_______________________________________________________________________________________

Mathematica [A]  time = 0.00242195, size = 42, normalized size = 0.75 \[ \frac{900 x^7}{7}+230 x^6+\frac{109 x^5}{5}-\frac{341 x^4}{2}-\frac{227 x^3}{3}+42 x^2+36 x \]

Antiderivative was successfully verified.

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

[Out]

36*x + 42*x^2 - (227*x^3)/3 - (341*x^4)/2 + (109*x^5)/5 + 230*x^6 + (900*x^7)/7

_______________________________________________________________________________________

Maple [A]  time = 0.001, size = 35, normalized size = 0.6 \[{\frac{900\,{x}^{7}}{7}}+230\,{x}^{6}+{\frac{109\,{x}^{5}}{5}}-{\frac{341\,{x}^{4}}{2}}-{\frac{227\,{x}^{3}}{3}}+42\,{x}^{2}+36\,x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

900/7*x^7+230*x^6+109/5*x^5-341/2*x^4-227/3*x^3+42*x^2+36*x

_______________________________________________________________________________________

Maxima [A]  time = 1.33924, size = 46, normalized size = 0.82 \[ \frac{900}{7} \, x^{7} + 230 \, x^{6} + \frac{109}{5} \, x^{5} - \frac{341}{2} \, x^{4} - \frac{227}{3} \, x^{3} + 42 \, x^{2} + 36 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

900/7*x^7 + 230*x^6 + 109/5*x^5 - 341/2*x^4 - 227/3*x^3 + 42*x^2 + 36*x

_______________________________________________________________________________________

Fricas [A]  time = 0.190918, size = 1, normalized size = 0.02 \[ \frac{900}{7} x^{7} + 230 x^{6} + \frac{109}{5} x^{5} - \frac{341}{2} x^{4} - \frac{227}{3} x^{3} + 42 x^{2} + 36 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

900/7*x^7 + 230*x^6 + 109/5*x^5 - 341/2*x^4 - 227/3*x^3 + 42*x^2 + 36*x

_______________________________________________________________________________________

Sympy [A]  time = 0.083823, size = 39, normalized size = 0.7 \[ \frac{900 x^{7}}{7} + 230 x^{6} + \frac{109 x^{5}}{5} - \frac{341 x^{4}}{2} - \frac{227 x^{3}}{3} + 42 x^{2} + 36 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

900*x**7/7 + 230*x**6 + 109*x**5/5 - 341*x**4/2 - 227*x**3/3 + 42*x**2 + 36*x

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.205965, size = 46, normalized size = 0.82 \[ \frac{900}{7} \, x^{7} + 230 \, x^{6} + \frac{109}{5} \, x^{5} - \frac{341}{2} \, x^{4} - \frac{227}{3} \, x^{3} + 42 \, x^{2} + 36 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

900/7*x^7 + 230*x^6 + 109/5*x^5 - 341/2*x^4 - 227/3*x^3 + 42*x^2 + 36*x