3.1144 \(\int (1-2 x) (2+3 x)^5 (3+5 x)^2 \, dx\)

Optimal. Leaf size=45 \[ -\frac{50}{729} (3 x+2)^9+\frac{65}{216} (3 x+2)^8-\frac{8}{63} (3 x+2)^7+\frac{7}{486} (3 x+2)^6 \]

[Out]

(7*(2 + 3*x)^6)/486 - (8*(2 + 3*x)^7)/63 + (65*(2 + 3*x)^8)/216 - (50*(2 + 3*x)^
9)/729

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Rubi [A]  time = 0.0715466, 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 \[ -\frac{50}{729} (3 x+2)^9+\frac{65}{216} (3 x+2)^8-\frac{8}{63} (3 x+2)^7+\frac{7}{486} (3 x+2)^6 \]

Antiderivative was successfully verified.

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

[Out]

(7*(2 + 3*x)^6)/486 - (8*(2 + 3*x)^7)/63 + (65*(2 + 3*x)^8)/216 - (50*(2 + 3*x)^
9)/729

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Rubi in Sympy [A]  time = 10.3294, size = 39, normalized size = 0.87 \[ - \frac{50 \left (3 x + 2\right )^{9}}{729} + \frac{65 \left (3 x + 2\right )^{8}}{216} - \frac{8 \left (3 x + 2\right )^{7}}{63} + \frac{7 \left (3 x + 2\right )^{6}}{486} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-50*(3*x + 2)**9/729 + 65*(3*x + 2)**8/216 - 8*(3*x + 2)**7/63 + 7*(3*x + 2)**6/
486

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Mathematica [A]  time = 0.0030904, size = 52, normalized size = 1.16 \[ -1350 x^9-\frac{49005 x^8}{8}-\frac{79434 x^7}{7}-\frac{20631 x^6}{2}-3390 x^5+2090 x^4+\frac{8240 x^3}{3}+1272 x^2+288 x \]

Antiderivative was successfully verified.

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

[Out]

288*x + 1272*x^2 + (8240*x^3)/3 + 2090*x^4 - 3390*x^5 - (20631*x^6)/2 - (79434*x
^7)/7 - (49005*x^8)/8 - 1350*x^9

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Maple [A]  time = 0.003, size = 45, normalized size = 1. \[ -1350\,{x}^{9}-{\frac{49005\,{x}^{8}}{8}}-{\frac{79434\,{x}^{7}}{7}}-{\frac{20631\,{x}^{6}}{2}}-3390\,{x}^{5}+2090\,{x}^{4}+{\frac{8240\,{x}^{3}}{3}}+1272\,{x}^{2}+288\,x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1350*x^9-49005/8*x^8-79434/7*x^7-20631/2*x^6-3390*x^5+2090*x^4+8240/3*x^3+1272*
x^2+288*x

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Maxima [A]  time = 1.34281, size = 59, normalized size = 1.31 \[ -1350 \, x^{9} - \frac{49005}{8} \, x^{8} - \frac{79434}{7} \, x^{7} - \frac{20631}{2} \, x^{6} - 3390 \, x^{5} + 2090 \, x^{4} + \frac{8240}{3} \, x^{3} + 1272 \, x^{2} + 288 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1350*x^9 - 49005/8*x^8 - 79434/7*x^7 - 20631/2*x^6 - 3390*x^5 + 2090*x^4 + 8240
/3*x^3 + 1272*x^2 + 288*x

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Fricas [A]  time = 0.175518, size = 1, normalized size = 0.02 \[ -1350 x^{9} - \frac{49005}{8} x^{8} - \frac{79434}{7} x^{7} - \frac{20631}{2} x^{6} - 3390 x^{5} + 2090 x^{4} + \frac{8240}{3} x^{3} + 1272 x^{2} + 288 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1350*x^9 - 49005/8*x^8 - 79434/7*x^7 - 20631/2*x^6 - 3390*x^5 + 2090*x^4 + 8240
/3*x^3 + 1272*x^2 + 288*x

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Sympy [A]  time = 0.099531, size = 49, normalized size = 1.09 \[ - 1350 x^{9} - \frac{49005 x^{8}}{8} - \frac{79434 x^{7}}{7} - \frac{20631 x^{6}}{2} - 3390 x^{5} + 2090 x^{4} + \frac{8240 x^{3}}{3} + 1272 x^{2} + 288 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1350*x**9 - 49005*x**8/8 - 79434*x**7/7 - 20631*x**6/2 - 3390*x**5 + 2090*x**4
+ 8240*x**3/3 + 1272*x**2 + 288*x

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GIAC/XCAS [A]  time = 0.204876, size = 59, normalized size = 1.31 \[ -1350 \, x^{9} - \frac{49005}{8} \, x^{8} - \frac{79434}{7} \, x^{7} - \frac{20631}{2} \, x^{6} - 3390 \, x^{5} + 2090 \, x^{4} + \frac{8240}{3} \, x^{3} + 1272 \, x^{2} + 288 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1350*x^9 - 49005/8*x^8 - 79434/7*x^7 - 20631/2*x^6 - 3390*x^5 + 2090*x^4 + 8240
/3*x^3 + 1272*x^2 + 288*x