3.1126 \(\int (1-2 x) (2+3 x)^8 (3+5 x) \, dx\)

Optimal. Leaf size=34 \[ -\frac{10}{297} (3 x+2)^{11}+\frac{37}{270} (3 x+2)^{10}-\frac{7}{243} (3 x+2)^9 \]

[Out]

(-7*(2 + 3*x)^9)/243 + (37*(2 + 3*x)^10)/270 - (10*(2 + 3*x)^11)/297

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Rubi [A]  time = 0.0623976, 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 \[ -\frac{10}{297} (3 x+2)^{11}+\frac{37}{270} (3 x+2)^{10}-\frac{7}{243} (3 x+2)^9 \]

Antiderivative was successfully verified.

[In]  Int[(1 - 2*x)*(2 + 3*x)^8*(3 + 5*x),x]

[Out]

(-7*(2 + 3*x)^9)/243 + (37*(2 + 3*x)^10)/270 - (10*(2 + 3*x)^11)/297

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Rubi in Sympy [A]  time = 10.2435, size = 29, normalized size = 0.85 \[ - \frac{10 \left (3 x + 2\right )^{11}}{297} + \frac{37 \left (3 x + 2\right )^{10}}{270} - \frac{7 \left (3 x + 2\right )^{9}}{243} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)*(2+3*x)**8*(3+5*x),x)

[Out]

-10*(3*x + 2)**11/297 + 37*(3*x + 2)**10/270 - 7*(3*x + 2)**9/243

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Mathematica [A]  time = 0.00372492, size = 62, normalized size = 1.82 \[ -\frac{65610 x^{11}}{11}-\frac{356481 x^{10}}{10}-92421 x^9-133164 x^8-110160 x^7-41328 x^6+\frac{62496 x^5}{5}+24576 x^4+\frac{42752 x^3}{3}+4480 x^2+768 x \]

Antiderivative was successfully verified.

[In]  Integrate[(1 - 2*x)*(2 + 3*x)^8*(3 + 5*x),x]

[Out]

768*x + 4480*x^2 + (42752*x^3)/3 + 24576*x^4 + (62496*x^5)/5 - 41328*x^6 - 11016
0*x^7 - 133164*x^8 - 92421*x^9 - (356481*x^10)/10 - (65610*x^11)/11

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Maple [A]  time = 0.001, size = 55, normalized size = 1.6 \[ -{\frac{65610\,{x}^{11}}{11}}-{\frac{356481\,{x}^{10}}{10}}-92421\,{x}^{9}-133164\,{x}^{8}-110160\,{x}^{7}-41328\,{x}^{6}+{\frac{62496\,{x}^{5}}{5}}+24576\,{x}^{4}+{\frac{42752\,{x}^{3}}{3}}+4480\,{x}^{2}+768\,x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)*(2+3*x)^8*(3+5*x),x)

[Out]

-65610/11*x^11-356481/10*x^10-92421*x^9-133164*x^8-110160*x^7-41328*x^6+62496/5*
x^5+24576*x^4+42752/3*x^3+4480*x^2+768*x

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Maxima [A]  time = 1.33192, size = 73, normalized size = 2.15 \[ -\frac{65610}{11} \, x^{11} - \frac{356481}{10} \, x^{10} - 92421 \, x^{9} - 133164 \, x^{8} - 110160 \, x^{7} - 41328 \, x^{6} + \frac{62496}{5} \, x^{5} + 24576 \, x^{4} + \frac{42752}{3} \, x^{3} + 4480 \, x^{2} + 768 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)*(3*x + 2)^8*(2*x - 1),x, algorithm="maxima")

[Out]

-65610/11*x^11 - 356481/10*x^10 - 92421*x^9 - 133164*x^8 - 110160*x^7 - 41328*x^
6 + 62496/5*x^5 + 24576*x^4 + 42752/3*x^3 + 4480*x^2 + 768*x

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Fricas [A]  time = 0.181232, size = 1, normalized size = 0.03 \[ -\frac{65610}{11} x^{11} - \frac{356481}{10} x^{10} - 92421 x^{9} - 133164 x^{8} - 110160 x^{7} - 41328 x^{6} + \frac{62496}{5} x^{5} + 24576 x^{4} + \frac{42752}{3} x^{3} + 4480 x^{2} + 768 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)*(3*x + 2)^8*(2*x - 1),x, algorithm="fricas")

[Out]

-65610/11*x^11 - 356481/10*x^10 - 92421*x^9 - 133164*x^8 - 110160*x^7 - 41328*x^
6 + 62496/5*x^5 + 24576*x^4 + 42752/3*x^3 + 4480*x^2 + 768*x

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Sympy [A]  time = 0.10408, size = 60, normalized size = 1.76 \[ - \frac{65610 x^{11}}{11} - \frac{356481 x^{10}}{10} - 92421 x^{9} - 133164 x^{8} - 110160 x^{7} - 41328 x^{6} + \frac{62496 x^{5}}{5} + 24576 x^{4} + \frac{42752 x^{3}}{3} + 4480 x^{2} + 768 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)*(2+3*x)**8*(3+5*x),x)

[Out]

-65610*x**11/11 - 356481*x**10/10 - 92421*x**9 - 133164*x**8 - 110160*x**7 - 413
28*x**6 + 62496*x**5/5 + 24576*x**4 + 42752*x**3/3 + 4480*x**2 + 768*x

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GIAC/XCAS [A]  time = 0.229213, size = 73, normalized size = 2.15 \[ -\frac{65610}{11} \, x^{11} - \frac{356481}{10} \, x^{10} - 92421 \, x^{9} - 133164 \, x^{8} - 110160 \, x^{7} - 41328 \, x^{6} + \frac{62496}{5} \, x^{5} + 24576 \, x^{4} + \frac{42752}{3} \, x^{3} + 4480 \, x^{2} + 768 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)*(3*x + 2)^8*(2*x - 1),x, algorithm="giac")

[Out]

-65610/11*x^11 - 356481/10*x^10 - 92421*x^9 - 133164*x^8 - 110160*x^7 - 41328*x^
6 + 62496/5*x^5 + 24576*x^4 + 42752/3*x^3 + 4480*x^2 + 768*x