3.1166 \(\int (1-2 x) (3+5 x)^3 \, dx\)

Optimal. Leaf size=23 \[ \frac{11}{100} (5 x+3)^4-\frac{2}{125} (5 x+3)^5 \]

[Out]

(11*(3 + 5*x)^4)/100 - (2*(3 + 5*x)^5)/125

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Rubi [A]  time = 0.0190751, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{11}{100} (5 x+3)^4-\frac{2}{125} (5 x+3)^5 \]

Antiderivative was successfully verified.

[In]  Int[(1 - 2*x)*(3 + 5*x)^3,x]

[Out]

(11*(3 + 5*x)^4)/100 - (2*(3 + 5*x)^5)/125

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - 50 x^{5} - \frac{325 x^{4}}{4} - 15 x^{3} + 27 x + 81 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-50*x**5 - 325*x**4/4 - 15*x**3 + 27*x + 81*Integral(x, x)

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Mathematica [A]  time = 0.00108122, size = 28, normalized size = 1.22 \[ -50 x^5-\frac{325 x^4}{4}-15 x^3+\frac{81 x^2}{2}+27 x \]

Antiderivative was successfully verified.

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

[Out]

27*x + (81*x^2)/2 - 15*x^3 - (325*x^4)/4 - 50*x^5

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Maple [A]  time = 0.002, size = 25, normalized size = 1.1 \[ -50\,{x}^{5}-{\frac{325\,{x}^{4}}{4}}-15\,{x}^{3}+{\frac{81\,{x}^{2}}{2}}+27\,x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)*(3+5*x)^3,x)

[Out]

-50*x^5-325/4*x^4-15*x^3+81/2*x^2+27*x

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Maxima [A]  time = 1.33659, size = 32, normalized size = 1.39 \[ -50 \, x^{5} - \frac{325}{4} \, x^{4} - 15 \, x^{3} + \frac{81}{2} \, x^{2} + 27 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-50*x^5 - 325/4*x^4 - 15*x^3 + 81/2*x^2 + 27*x

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Fricas [A]  time = 0.181778, size = 1, normalized size = 0.04 \[ -50 x^{5} - \frac{325}{4} x^{4} - 15 x^{3} + \frac{81}{2} x^{2} + 27 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-50*x^5 - 325/4*x^4 - 15*x^3 + 81/2*x^2 + 27*x

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Sympy [A]  time = 0.075128, size = 26, normalized size = 1.13 \[ - 50 x^{5} - \frac{325 x^{4}}{4} - 15 x^{3} + \frac{81 x^{2}}{2} + 27 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)*(3+5*x)**3,x)

[Out]

-50*x**5 - 325*x**4/4 - 15*x**3 + 81*x**2/2 + 27*x

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GIAC/XCAS [A]  time = 0.208966, size = 32, normalized size = 1.39 \[ -50 \, x^{5} - \frac{325}{4} \, x^{4} - 15 \, x^{3} + \frac{81}{2} \, x^{2} + 27 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-50*x^5 - 325/4*x^4 - 15*x^3 + 81/2*x^2 + 27*x