3.1262 \(\int (1-2 x)^2 (2+3 x) (3+5 x)^3 \, dx\)

Optimal. Leaf size=45 \[ \frac{12 (5 x+3)^7}{4375}-\frac{64 (5 x+3)^6}{1875}+\frac{319 (5 x+3)^5}{3125}+\frac{121 (5 x+3)^4}{2500} \]

[Out]

(121*(3 + 5*x)^4)/2500 + (319*(3 + 5*x)^5)/3125 - (64*(3 + 5*x)^6)/1875 + (12*(3
+ 5*x)^7)/4375

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Rubi [A]  time = 0.0635102, antiderivative size = 45, 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 \[ \frac{12 (5 x+3)^7}{4375}-\frac{64 (5 x+3)^6}{1875}+\frac{319 (5 x+3)^5}{3125}+\frac{121 (5 x+3)^4}{2500} \]

Antiderivative was successfully verified.

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

[Out]

(121*(3 + 5*x)^4)/2500 + (319*(3 + 5*x)^5)/3125 - (64*(3 + 5*x)^6)/1875 + (12*(3
+ 5*x)^7)/4375

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{1500 x^{7}}{7} + \frac{1100 x^{6}}{3} + 19 x^{5} - \frac{1091 x^{4}}{4} - 111 x^{3} + 54 x + 135 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1500*x**7/7 + 1100*x**6/3 + 19*x**5 - 1091*x**4/4 - 111*x**3 + 54*x + 135*Integr
al(x, x)

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Mathematica [A]  time = 0.00167479, size = 42, normalized size = 0.93 \[ \frac{1500 x^7}{7}+\frac{1100 x^6}{3}+19 x^5-\frac{1091 x^4}{4}-111 x^3+\frac{135 x^2}{2}+54 x \]

Antiderivative was successfully verified.

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

[Out]

54*x + (135*x^2)/2 - 111*x^3 - (1091*x^4)/4 + 19*x^5 + (1100*x^6)/3 + (1500*x^7)
/7

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Maple [A]  time = 0.003, size = 35, normalized size = 0.8 \[{\frac{1500\,{x}^{7}}{7}}+{\frac{1100\,{x}^{6}}{3}}+19\,{x}^{5}-{\frac{1091\,{x}^{4}}{4}}-111\,{x}^{3}+{\frac{135\,{x}^{2}}{2}}+54\,x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1500/7*x^7+1100/3*x^6+19*x^5-1091/4*x^4-111*x^3+135/2*x^2+54*x

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Maxima [A]  time = 1.34272, size = 46, normalized size = 1.02 \[ \frac{1500}{7} \, x^{7} + \frac{1100}{3} \, x^{6} + 19 \, x^{5} - \frac{1091}{4} \, x^{4} - 111 \, x^{3} + \frac{135}{2} \, x^{2} + 54 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1500/7*x^7 + 1100/3*x^6 + 19*x^5 - 1091/4*x^4 - 111*x^3 + 135/2*x^2 + 54*x

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Fricas [A]  time = 0.192873, size = 1, normalized size = 0.02 \[ \frac{1500}{7} x^{7} + \frac{1100}{3} x^{6} + 19 x^{5} - \frac{1091}{4} x^{4} - 111 x^{3} + \frac{135}{2} x^{2} + 54 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1500/7*x^7 + 1100/3*x^6 + 19*x^5 - 1091/4*x^4 - 111*x^3 + 135/2*x^2 + 54*x

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Sympy [A]  time = 0.083081, size = 39, normalized size = 0.87 \[ \frac{1500 x^{7}}{7} + \frac{1100 x^{6}}{3} + 19 x^{5} - \frac{1091 x^{4}}{4} - 111 x^{3} + \frac{135 x^{2}}{2} + 54 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1500*x**7/7 + 1100*x**6/3 + 19*x**5 - 1091*x**4/4 - 111*x**3 + 135*x**2/2 + 54*x

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GIAC/XCAS [A]  time = 0.232447, size = 46, normalized size = 1.02 \[ \frac{1500}{7} \, x^{7} + \frac{1100}{3} \, x^{6} + 19 \, x^{5} - \frac{1091}{4} \, x^{4} - 111 \, x^{3} + \frac{135}{2} \, x^{2} + 54 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1500/7*x^7 + 1100/3*x^6 + 19*x^5 - 1091/4*x^4 - 111*x^3 + 135/2*x^2 + 54*x