3.1165 \(\int (1-2 x) (2+3 x) (3+5 x)^3 \, dx\)

Optimal. Leaf size=34 \[ -\frac{1}{125} (5 x+3)^6+\frac{31}{625} (5 x+3)^5+\frac{11}{500} (5 x+3)^4 \]

[Out]

(11*(3 + 5*x)^4)/500 + (31*(3 + 5*x)^5)/625 - (3 + 5*x)^6/125

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Rubi [A]  time = 0.0485321, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056 \[ -\frac{1}{125} (5 x+3)^6+\frac{31}{625} (5 x+3)^5+\frac{11}{500} (5 x+3)^4 \]

Antiderivative was successfully verified.

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

[Out]

(11*(3 + 5*x)^4)/500 + (31*(3 + 5*x)^5)/625 - (3 + 5*x)^6/125

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - 125 x^{6} - 295 x^{5} - \frac{785 x^{4}}{4} + 51 x^{3} + 54 x + 243 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-125*x**6 - 295*x**5 - 785*x**4/4 + 51*x**3 + 54*x + 243*Integral(x, x)

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Mathematica [A]  time = 0.00130457, size = 33, normalized size = 0.97 \[ -125 x^6-295 x^5-\frac{785 x^4}{4}+51 x^3+\frac{243 x^2}{2}+54 x \]

Antiderivative was successfully verified.

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

[Out]

54*x + (243*x^2)/2 + 51*x^3 - (785*x^4)/4 - 295*x^5 - 125*x^6

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Maple [A]  time = 0.001, size = 30, normalized size = 0.9 \[ -125\,{x}^{6}-295\,{x}^{5}-{\frac{785\,{x}^{4}}{4}}+51\,{x}^{3}+{\frac{243\,{x}^{2}}{2}}+54\,x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-125*x^6-295*x^5-785/4*x^4+51*x^3+243/2*x^2+54*x

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Maxima [A]  time = 1.32939, size = 39, normalized size = 1.15 \[ -125 \, x^{6} - 295 \, x^{5} - \frac{785}{4} \, x^{4} + 51 \, x^{3} + \frac{243}{2} \, x^{2} + 54 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-125*x^6 - 295*x^5 - 785/4*x^4 + 51*x^3 + 243/2*x^2 + 54*x

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Fricas [A]  time = 0.186001, size = 1, normalized size = 0.03 \[ -125 x^{6} - 295 x^{5} - \frac{785}{4} x^{4} + 51 x^{3} + \frac{243}{2} x^{2} + 54 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-125*x^6 - 295*x^5 - 785/4*x^4 + 51*x^3 + 243/2*x^2 + 54*x

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Sympy [A]  time = 0.08207, size = 31, normalized size = 0.91 \[ - 125 x^{6} - 295 x^{5} - \frac{785 x^{4}}{4} + 51 x^{3} + \frac{243 x^{2}}{2} + 54 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-125*x**6 - 295*x**5 - 785*x**4/4 + 51*x**3 + 243*x**2/2 + 54*x

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GIAC/XCAS [A]  time = 0.206557, size = 39, normalized size = 1.15 \[ -125 \, x^{6} - 295 \, x^{5} - \frac{785}{4} \, x^{4} + 51 \, x^{3} + \frac{243}{2} \, x^{2} + 54 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-125*x^6 - 295*x^5 - 785/4*x^4 + 51*x^3 + 243/2*x^2 + 54*x