3.1226 \(\int (1-2 x)^2 (2+3 x) (3+5 x) \, dx\)

Optimal. Leaf size=34 \[ -\frac{3}{8} (1-2 x)^5+\frac{17}{8} (1-2 x)^4-\frac{77}{24} (1-2 x)^3 \]

[Out]

(-77*(1 - 2*x)^3)/24 + (17*(1 - 2*x)^4)/8 - (3*(1 - 2*x)^5)/8

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Rubi [A]  time = 0.0463489, 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 \[ -\frac{3}{8} (1-2 x)^5+\frac{17}{8} (1-2 x)^4-\frac{77}{24} (1-2 x)^3 \]

Antiderivative was successfully verified.

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

[Out]

(-77*(1 - 2*x)^3)/24 + (17*(1 - 2*x)^4)/8 - (3*(1 - 2*x)^5)/8

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ 12 x^{5} + 4 x^{4} - \frac{37 x^{3}}{3} + 6 x - 5 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

12*x**5 + 4*x**4 - 37*x**3/3 + 6*x - 5*Integral(x, x)

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Mathematica [A]  time = 0.00136345, size = 28, normalized size = 0.82 \[ 12 x^5+4 x^4-\frac{37 x^3}{3}-\frac{5 x^2}{2}+6 x \]

Antiderivative was successfully verified.

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

[Out]

6*x - (5*x^2)/2 - (37*x^3)/3 + 4*x^4 + 12*x^5

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Maple [A]  time = 0.003, size = 25, normalized size = 0.7 \[ 12\,{x}^{5}+4\,{x}^{4}-{\frac{37\,{x}^{3}}{3}}-{\frac{5\,{x}^{2}}{2}}+6\,x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

12*x^5+4*x^4-37/3*x^3-5/2*x^2+6*x

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Maxima [A]  time = 1.32101, size = 32, normalized size = 0.94 \[ 12 \, x^{5} + 4 \, x^{4} - \frac{37}{3} \, x^{3} - \frac{5}{2} \, x^{2} + 6 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

12*x^5 + 4*x^4 - 37/3*x^3 - 5/2*x^2 + 6*x

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Fricas [A]  time = 0.195971, size = 1, normalized size = 0.03 \[ 12 x^{5} + 4 x^{4} - \frac{37}{3} x^{3} - \frac{5}{2} x^{2} + 6 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

12*x^5 + 4*x^4 - 37/3*x^3 - 5/2*x^2 + 6*x

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Sympy [A]  time = 0.070317, size = 26, normalized size = 0.76 \[ 12 x^{5} + 4 x^{4} - \frac{37 x^{3}}{3} - \frac{5 x^{2}}{2} + 6 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

12*x**5 + 4*x**4 - 37*x**3/3 - 5*x**2/2 + 6*x

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GIAC/XCAS [A]  time = 0.205351, size = 32, normalized size = 0.94 \[ 12 \, x^{5} + 4 \, x^{4} - \frac{37}{3} \, x^{3} - \frac{5}{2} \, x^{2} + 6 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

12*x^5 + 4*x^4 - 37/3*x^3 - 5/2*x^2 + 6*x