3.1148 \(\int (1-2 x) (2+3 x) (3+5 x)^2 \, dx\)

Optimal. Leaf size=34 \[ -\frac{6}{625} (5 x+3)^5+\frac{31}{500} (5 x+3)^4+\frac{11}{375} (5 x+3)^3 \]

[Out]

(11*(3 + 5*x)^3)/375 + (31*(3 + 5*x)^4)/500 - (6*(3 + 5*x)^5)/625

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Rubi [A]  time = 0.0453745, 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 \[ -\frac{6}{625} (5 x+3)^5+\frac{31}{500} (5 x+3)^4+\frac{11}{375} (5 x+3)^3 \]

Antiderivative was successfully verified.

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

[Out]

(11*(3 + 5*x)^3)/375 + (31*(3 + 5*x)^4)/500 - (6*(3 + 5*x)^5)/625

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - 30 x^{5} - \frac{205 x^{4}}{4} - \frac{34 x^{3}}{3} + 18 x + 51 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-30*x**5 - 205*x**4/4 - 34*x**3/3 + 18*x + 51*Integral(x, x)

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Mathematica [A]  time = 0.00115994, size = 30, normalized size = 0.88 \[ -30 x^5-\frac{205 x^4}{4}-\frac{34 x^3}{3}+\frac{51 x^2}{2}+18 x \]

Antiderivative was successfully verified.

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

[Out]

18*x + (51*x^2)/2 - (34*x^3)/3 - (205*x^4)/4 - 30*x^5

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Maple [A]  time = 0.001, size = 25, normalized size = 0.7 \[ -30\,{x}^{5}-{\frac{205\,{x}^{4}}{4}}-{\frac{34\,{x}^{3}}{3}}+{\frac{51\,{x}^{2}}{2}}+18\,x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-30*x^5-205/4*x^4-34/3*x^3+51/2*x^2+18*x

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Maxima [A]  time = 1.34727, size = 32, normalized size = 0.94 \[ -30 \, x^{5} - \frac{205}{4} \, x^{4} - \frac{34}{3} \, x^{3} + \frac{51}{2} \, x^{2} + 18 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-30*x^5 - 205/4*x^4 - 34/3*x^3 + 51/2*x^2 + 18*x

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Fricas [A]  time = 0.183548, size = 1, normalized size = 0.03 \[ -30 x^{5} - \frac{205}{4} x^{4} - \frac{34}{3} x^{3} + \frac{51}{2} x^{2} + 18 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-30*x^5 - 205/4*x^4 - 34/3*x^3 + 51/2*x^2 + 18*x

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Sympy [A]  time = 0.066773, size = 27, normalized size = 0.79 \[ - 30 x^{5} - \frac{205 x^{4}}{4} - \frac{34 x^{3}}{3} + \frac{51 x^{2}}{2} + 18 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-30*x**5 - 205*x**4/4 - 34*x**3/3 + 51*x**2/2 + 18*x

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GIAC/XCAS [A]  time = 0.206903, size = 32, normalized size = 0.94 \[ -30 \, x^{5} - \frac{205}{4} \, x^{4} - \frac{34}{3} \, x^{3} + \frac{51}{2} \, x^{2} + 18 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-30*x^5 - 205/4*x^4 - 34/3*x^3 + 51/2*x^2 + 18*x