3.1222 \(\int (1-2 x)^2 (2+3 x)^5 (3+5 x) \, dx\)

Optimal. Leaf size=45 \[ \frac{20}{729} (3 x+2)^9-\frac{2}{9} (3 x+2)^8+\frac{13}{27} (3 x+2)^7-\frac{49}{486} (3 x+2)^6 \]

[Out]

(-49*(2 + 3*x)^6)/486 + (13*(2 + 3*x)^7)/27 - (2*(2 + 3*x)^8)/9 + (20*(2 + 3*x)^
9)/729

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Rubi [A]  time = 0.0741714, antiderivative size = 45, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ \frac{20}{729} (3 x+2)^9-\frac{2}{9} (3 x+2)^8+\frac{13}{27} (3 x+2)^7-\frac{49}{486} (3 x+2)^6 \]

Antiderivative was successfully verified.

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

[Out]

(-49*(2 + 3*x)^6)/486 + (13*(2 + 3*x)^7)/27 - (2*(2 + 3*x)^8)/9 + (20*(2 + 3*x)^
9)/729

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Rubi in Sympy [A]  time = 10.109, size = 39, normalized size = 0.87 \[ \frac{20 \left (3 x + 2\right )^{9}}{729} - \frac{2 \left (3 x + 2\right )^{8}}{9} + \frac{13 \left (3 x + 2\right )^{7}}{27} - \frac{49 \left (3 x + 2\right )^{6}}{486} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

20*(3*x + 2)**9/729 - 2*(3*x + 2)**8/9 + 13*(3*x + 2)**7/27 - 49*(3*x + 2)**6/48
6

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Mathematica [A]  time = 0.003076, size = 48, normalized size = 1.07 \[ 540 x^9+1782 x^8+1917 x^7+\frac{273 x^6}{2}-1218 x^5-770 x^4+\frac{224 x^3}{3}+248 x^2+96 x \]

Antiderivative was successfully verified.

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

[Out]

96*x + 248*x^2 + (224*x^3)/3 - 770*x^4 - 1218*x^5 + (273*x^6)/2 + 1917*x^7 + 178
2*x^8 + 540*x^9

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Maple [A]  time = 0.001, size = 45, normalized size = 1. \[ 540\,{x}^{9}+1782\,{x}^{8}+1917\,{x}^{7}+{\frac{273\,{x}^{6}}{2}}-1218\,{x}^{5}-770\,{x}^{4}+{\frac{224\,{x}^{3}}{3}}+248\,{x}^{2}+96\,x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

540*x^9+1782*x^8+1917*x^7+273/2*x^6-1218*x^5-770*x^4+224/3*x^3+248*x^2+96*x

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Maxima [A]  time = 1.34146, size = 59, normalized size = 1.31 \[ 540 \, x^{9} + 1782 \, x^{8} + 1917 \, x^{7} + \frac{273}{2} \, x^{6} - 1218 \, x^{5} - 770 \, x^{4} + \frac{224}{3} \, x^{3} + 248 \, x^{2} + 96 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

540*x^9 + 1782*x^8 + 1917*x^7 + 273/2*x^6 - 1218*x^5 - 770*x^4 + 224/3*x^3 + 248
*x^2 + 96*x

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Fricas [A]  time = 0.182299, size = 1, normalized size = 0.02 \[ 540 x^{9} + 1782 x^{8} + 1917 x^{7} + \frac{273}{2} x^{6} - 1218 x^{5} - 770 x^{4} + \frac{224}{3} x^{3} + 248 x^{2} + 96 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

540*x^9 + 1782*x^8 + 1917*x^7 + 273/2*x^6 - 1218*x^5 - 770*x^4 + 224/3*x^3 + 248
*x^2 + 96*x

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Sympy [A]  time = 0.107352, size = 46, normalized size = 1.02 \[ 540 x^{9} + 1782 x^{8} + 1917 x^{7} + \frac{273 x^{6}}{2} - 1218 x^{5} - 770 x^{4} + \frac{224 x^{3}}{3} + 248 x^{2} + 96 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

540*x**9 + 1782*x**8 + 1917*x**7 + 273*x**6/2 - 1218*x**5 - 770*x**4 + 224*x**3/
3 + 248*x**2 + 96*x

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GIAC/XCAS [A]  time = 0.205053, size = 59, normalized size = 1.31 \[ 540 \, x^{9} + 1782 \, x^{8} + 1917 \, x^{7} + \frac{273}{2} \, x^{6} - 1218 \, x^{5} - 770 \, x^{4} + \frac{224}{3} \, x^{3} + 248 \, x^{2} + 96 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

540*x^9 + 1782*x^8 + 1917*x^7 + 273/2*x^6 - 1218*x^5 - 770*x^4 + 224/3*x^3 + 248
*x^2 + 96*x