3.1263 \(\int (1-2 x)^2 (3+5 x)^3 \, dx\)

Optimal. Leaf size=34 \[ \frac{2}{375} (5 x+3)^6-\frac{44}{625} (5 x+3)^5+\frac{121}{500} (5 x+3)^4 \]

[Out]

(121*(3 + 5*x)^4)/500 - (44*(3 + 5*x)^5)/625 + (2*(3 + 5*x)^6)/375

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Rubi [A]  time = 0.0368185, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ \frac{2}{375} (5 x+3)^6-\frac{44}{625} (5 x+3)^5+\frac{121}{500} (5 x+3)^4 \]

Antiderivative was successfully verified.

[In]  Int[(1 - 2*x)^2*(3 + 5*x)^3,x]

[Out]

(121*(3 + 5*x)^4)/500 - (44*(3 + 5*x)^5)/625 + (2*(3 + 5*x)^6)/375

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{250 x^{6}}{3} + 80 x^{5} - \frac{235 x^{4}}{4} - 69 x^{3} + 27 x + 27 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

250*x**6/3 + 80*x**5 - 235*x**4/4 - 69*x**3 + 27*x + 27*Integral(x, x)

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Mathematica [A]  time = 0.00132313, size = 35, normalized size = 1.03 \[ \frac{250 x^6}{3}+80 x^5-\frac{235 x^4}{4}-69 x^3+\frac{27 x^2}{2}+27 x \]

Antiderivative was successfully verified.

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

[Out]

27*x + (27*x^2)/2 - 69*x^3 - (235*x^4)/4 + 80*x^5 + (250*x^6)/3

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Maple [A]  time = 0.003, size = 30, normalized size = 0.9 \[{\frac{250\,{x}^{6}}{3}}+80\,{x}^{5}-{\frac{235\,{x}^{4}}{4}}-69\,{x}^{3}+{\frac{27\,{x}^{2}}{2}}+27\,x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)^2*(3+5*x)^3,x)

[Out]

250/3*x^6+80*x^5-235/4*x^4-69*x^3+27/2*x^2+27*x

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Maxima [A]  time = 1.33278, size = 39, normalized size = 1.15 \[ \frac{250}{3} \, x^{6} + 80 \, x^{5} - \frac{235}{4} \, x^{4} - 69 \, x^{3} + \frac{27}{2} \, x^{2} + 27 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

250/3*x^6 + 80*x^5 - 235/4*x^4 - 69*x^3 + 27/2*x^2 + 27*x

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Fricas [A]  time = 0.187849, size = 1, normalized size = 0.03 \[ \frac{250}{3} x^{6} + 80 x^{5} - \frac{235}{4} x^{4} - 69 x^{3} + \frac{27}{2} x^{2} + 27 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

250/3*x^6 + 80*x^5 - 235/4*x^4 - 69*x^3 + 27/2*x^2 + 27*x

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Sympy [A]  time = 0.084692, size = 32, normalized size = 0.94 \[ \frac{250 x^{6}}{3} + 80 x^{5} - \frac{235 x^{4}}{4} - 69 x^{3} + \frac{27 x^{2}}{2} + 27 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

250*x**6/3 + 80*x**5 - 235*x**4/4 - 69*x**3 + 27*x**2/2 + 27*x

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GIAC/XCAS [A]  time = 0.224801, size = 39, normalized size = 1.15 \[ \frac{250}{3} \, x^{6} + 80 \, x^{5} - \frac{235}{4} \, x^{4} - 69 \, x^{3} + \frac{27}{2} \, x^{2} + 27 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

250/3*x^6 + 80*x^5 - 235/4*x^4 - 69*x^3 + 27/2*x^2 + 27*x