3.1127 \(\int (1-2 x) (2+3 x)^7 (3+5 x) \, dx\)

Optimal. Leaf size=34 \[ -\frac{1}{27} (3 x+2)^{10}+\frac{37}{243} (3 x+2)^9-\frac{7}{216} (3 x+2)^8 \]

[Out]

(-7*(2 + 3*x)^8)/216 + (37*(2 + 3*x)^9)/243 - (2 + 3*x)^10/27

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Rubi [A]  time = 0.063133, 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 \[ -\frac{1}{27} (3 x+2)^{10}+\frac{37}{243} (3 x+2)^9-\frac{7}{216} (3 x+2)^8 \]

Antiderivative was successfully verified.

[In]  Int[(1 - 2*x)*(2 + 3*x)^7*(3 + 5*x),x]

[Out]

(-7*(2 + 3*x)^8)/216 + (37*(2 + 3*x)^9)/243 - (2 + 3*x)^10/27

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Rubi in Sympy [A]  time = 9.56443, size = 27, normalized size = 0.79 \[ - \frac{\left (3 x + 2\right )^{10}}{27} + \frac{37 \left (3 x + 2\right )^{9}}{243} - \frac{7 \left (3 x + 2\right )^{8}}{216} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)*(2+3*x)**7*(3+5*x),x)

[Out]

-(3*x + 2)**10/27 + 37*(3*x + 2)**9/243 - 7*(3*x + 2)**8/216

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Mathematica [A]  time = 0.00292368, size = 53, normalized size = 1.56 \[ -2187 x^{10}-11583 x^9-\frac{207765 x^8}{8}-30942 x^7-18774 x^6-1512 x^5+6468 x^4+\frac{15520 x^3}{3}+1952 x^2+384 x \]

Antiderivative was successfully verified.

[In]  Integrate[(1 - 2*x)*(2 + 3*x)^7*(3 + 5*x),x]

[Out]

384*x + 1952*x^2 + (15520*x^3)/3 + 6468*x^4 - 1512*x^5 - 18774*x^6 - 30942*x^7 -
(207765*x^8)/8 - 11583*x^9 - 2187*x^10

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Maple [A]  time = 0.002, size = 50, normalized size = 1.5 \[ -2187\,{x}^{10}-11583\,{x}^{9}-{\frac{207765\,{x}^{8}}{8}}-30942\,{x}^{7}-18774\,{x}^{6}-1512\,{x}^{5}+6468\,{x}^{4}+{\frac{15520\,{x}^{3}}{3}}+1952\,{x}^{2}+384\,x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)*(2+3*x)^7*(3+5*x),x)

[Out]

-2187*x^10-11583*x^9-207765/8*x^8-30942*x^7-18774*x^6-1512*x^5+6468*x^4+15520/3*
x^3+1952*x^2+384*x

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Maxima [A]  time = 1.32898, size = 66, normalized size = 1.94 \[ -2187 \, x^{10} - 11583 \, x^{9} - \frac{207765}{8} \, x^{8} - 30942 \, x^{7} - 18774 \, x^{6} - 1512 \, x^{5} + 6468 \, x^{4} + \frac{15520}{3} \, x^{3} + 1952 \, x^{2} + 384 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)*(3*x + 2)^7*(2*x - 1),x, algorithm="maxima")

[Out]

-2187*x^10 - 11583*x^9 - 207765/8*x^8 - 30942*x^7 - 18774*x^6 - 1512*x^5 + 6468*
x^4 + 15520/3*x^3 + 1952*x^2 + 384*x

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Fricas [A]  time = 0.182515, size = 1, normalized size = 0.03 \[ -2187 x^{10} - 11583 x^{9} - \frac{207765}{8} x^{8} - 30942 x^{7} - 18774 x^{6} - 1512 x^{5} + 6468 x^{4} + \frac{15520}{3} x^{3} + 1952 x^{2} + 384 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)*(3*x + 2)^7*(2*x - 1),x, algorithm="fricas")

[Out]

-2187*x^10 - 11583*x^9 - 207765/8*x^8 - 30942*x^7 - 18774*x^6 - 1512*x^5 + 6468*
x^4 + 15520/3*x^3 + 1952*x^2 + 384*x

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Sympy [A]  time = 0.099542, size = 51, normalized size = 1.5 \[ - 2187 x^{10} - 11583 x^{9} - \frac{207765 x^{8}}{8} - 30942 x^{7} - 18774 x^{6} - 1512 x^{5} + 6468 x^{4} + \frac{15520 x^{3}}{3} + 1952 x^{2} + 384 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)*(2+3*x)**7*(3+5*x),x)

[Out]

-2187*x**10 - 11583*x**9 - 207765*x**8/8 - 30942*x**7 - 18774*x**6 - 1512*x**5 +
6468*x**4 + 15520*x**3/3 + 1952*x**2 + 384*x

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GIAC/XCAS [A]  time = 0.222854, size = 66, normalized size = 1.94 \[ -2187 \, x^{10} - 11583 \, x^{9} - \frac{207765}{8} \, x^{8} - 30942 \, x^{7} - 18774 \, x^{6} - 1512 \, x^{5} + 6468 \, x^{4} + \frac{15520}{3} \, x^{3} + 1952 \, x^{2} + 384 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)*(3*x + 2)^7*(2*x - 1),x, algorithm="giac")

[Out]

-2187*x^10 - 11583*x^9 - 207765/8*x^8 - 30942*x^7 - 18774*x^6 - 1512*x^5 + 6468*
x^4 + 15520/3*x^3 + 1952*x^2 + 384*x