3.1133 \(\int (1-2 x) (2+3 x) (3+5 x) \, dx\)

Optimal. Leaf size=25 \[ -\frac{15 x^4}{2}-\frac{23 x^3}{3}+\frac{7 x^2}{2}+6 x \]

[Out]

6*x + (7*x^2)/2 - (23*x^3)/3 - (15*x^4)/2

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Rubi [A]  time = 0.0293821, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062 \[ -\frac{15 x^4}{2}-\frac{23 x^3}{3}+\frac{7 x^2}{2}+6 x \]

Antiderivative was successfully verified.

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

[Out]

6*x + (7*x^2)/2 - (23*x^3)/3 - (15*x^4)/2

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{15 x^{4}}{2} - \frac{23 x^{3}}{3} + 6 x + 7 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-15*x**4/2 - 23*x**3/3 + 6*x + 7*Integral(x, x)

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Mathematica [A]  time = 0.00173303, size = 25, normalized size = 1. \[ -\frac{15 x^4}{2}-\frac{23 x^3}{3}+\frac{7 x^2}{2}+6 x \]

Antiderivative was successfully verified.

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

[Out]

6*x + (7*x^2)/2 - (23*x^3)/3 - (15*x^4)/2

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Maple [A]  time = 0.001, size = 20, normalized size = 0.8 \[ 6\,x+{\frac{7\,{x}^{2}}{2}}-{\frac{23\,{x}^{3}}{3}}-{\frac{15\,{x}^{4}}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)*(2+3*x)*(3+5*x),x)

[Out]

6*x+7/2*x^2-23/3*x^3-15/2*x^4

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Maxima [A]  time = 1.31914, size = 26, normalized size = 1.04 \[ -\frac{15}{2} \, x^{4} - \frac{23}{3} \, x^{3} + \frac{7}{2} \, x^{2} + 6 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-15/2*x^4 - 23/3*x^3 + 7/2*x^2 + 6*x

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Fricas [A]  time = 0.181969, size = 1, normalized size = 0.04 \[ -\frac{15}{2} x^{4} - \frac{23}{3} x^{3} + \frac{7}{2} x^{2} + 6 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-15/2*x^4 - 23/3*x^3 + 7/2*x^2 + 6*x

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Sympy [A]  time = 0.069099, size = 22, normalized size = 0.88 \[ - \frac{15 x^{4}}{2} - \frac{23 x^{3}}{3} + \frac{7 x^{2}}{2} + 6 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-15*x**4/2 - 23*x**3/3 + 7*x**2/2 + 6*x

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GIAC/XCAS [A]  time = 0.232469, size = 26, normalized size = 1.04 \[ -\frac{15}{2} \, x^{4} - \frac{23}{3} \, x^{3} + \frac{7}{2} \, x^{2} + 6 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-15/2*x^4 - 23/3*x^3 + 7/2*x^2 + 6*x