3.1357 \(\int (1-2 x)^3 (2+3 x)^5 (3+5 x)^3 \, dx\)

Optimal. Leaf size=78 \[ -\frac{250 (3 x+2)^{12}}{6561}+\frac{3700 (3 x+2)^{11}}{8019}-\frac{1439}{729} (3 x+2)^{10}+\frac{66193 (3 x+2)^9}{19683}-\frac{10073 (3 x+2)^8}{5832}+\frac{259}{729} (3 x+2)^7-\frac{343 (3 x+2)^6}{13122} \]

[Out]

(-343*(2 + 3*x)^6)/13122 + (259*(2 + 3*x)^7)/729 - (10073*(2 + 3*x)^8)/5832 + (6
6193*(2 + 3*x)^9)/19683 - (1439*(2 + 3*x)^10)/729 + (3700*(2 + 3*x)^11)/8019 - (
250*(2 + 3*x)^12)/6561

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Rubi [A]  time = 0.113466, antiderivative size = 78, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ -\frac{250 (3 x+2)^{12}}{6561}+\frac{3700 (3 x+2)^{11}}{8019}-\frac{1439}{729} (3 x+2)^{10}+\frac{66193 (3 x+2)^9}{19683}-\frac{10073 (3 x+2)^8}{5832}+\frac{259}{729} (3 x+2)^7-\frac{343 (3 x+2)^6}{13122} \]

Antiderivative was successfully verified.

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

[Out]

(-343*(2 + 3*x)^6)/13122 + (259*(2 + 3*x)^7)/729 - (10073*(2 + 3*x)^8)/5832 + (6
6193*(2 + 3*x)^9)/19683 - (1439*(2 + 3*x)^10)/729 + (3700*(2 + 3*x)^11)/8019 - (
250*(2 + 3*x)^12)/6561

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - 20250 x^{12} - \frac{882900 x^{11}}{11} - 111159 x^{10} - 32867 x^{9} + \frac{565167 x^{8}}{8} + 71107 x^{7} + \frac{10297 x^{6}}{2} - 24882 x^{5} - 11798 x^{4} + 1536 x^{3} + 864 x + 5616 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-20250*x**12 - 882900*x**11/11 - 111159*x**10 - 32867*x**9 + 565167*x**8/8 + 711
07*x**7 + 10297*x**6/2 - 24882*x**5 - 11798*x**4 + 1536*x**3 + 864*x + 5616*Inte
gral(x, x)

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Mathematica [A]  time = 0.00410826, size = 65, normalized size = 0.83 \[ -20250 x^{12}-\frac{882900 x^{11}}{11}-111159 x^{10}-32867 x^9+\frac{565167 x^8}{8}+71107 x^7+\frac{10297 x^6}{2}-24882 x^5-11798 x^4+1536 x^3+2808 x^2+864 x \]

Antiderivative was successfully verified.

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

[Out]

864*x + 2808*x^2 + 1536*x^3 - 11798*x^4 - 24882*x^5 + (10297*x^6)/2 + 71107*x^7
+ (565167*x^8)/8 - 32867*x^9 - 111159*x^10 - (882900*x^11)/11 - 20250*x^12

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Maple [A]  time = 0.003, size = 60, normalized size = 0.8 \[ -20250\,{x}^{12}-{\frac{882900\,{x}^{11}}{11}}-111159\,{x}^{10}-32867\,{x}^{9}+{\frac{565167\,{x}^{8}}{8}}+71107\,{x}^{7}+{\frac{10297\,{x}^{6}}{2}}-24882\,{x}^{5}-11798\,{x}^{4}+1536\,{x}^{3}+2808\,{x}^{2}+864\,x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-20250*x^12-882900/11*x^11-111159*x^10-32867*x^9+565167/8*x^8+71107*x^7+10297/2*
x^6-24882*x^5-11798*x^4+1536*x^3+2808*x^2+864*x

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Maxima [A]  time = 1.34458, size = 80, normalized size = 1.03 \[ -20250 \, x^{12} - \frac{882900}{11} \, x^{11} - 111159 \, x^{10} - 32867 \, x^{9} + \frac{565167}{8} \, x^{8} + 71107 \, x^{7} + \frac{10297}{2} \, x^{6} - 24882 \, x^{5} - 11798 \, x^{4} + 1536 \, x^{3} + 2808 \, x^{2} + 864 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-20250*x^12 - 882900/11*x^11 - 111159*x^10 - 32867*x^9 + 565167/8*x^8 + 71107*x^
7 + 10297/2*x^6 - 24882*x^5 - 11798*x^4 + 1536*x^3 + 2808*x^2 + 864*x

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Fricas [A]  time = 0.181945, size = 1, normalized size = 0.01 \[ -20250 x^{12} - \frac{882900}{11} x^{11} - 111159 x^{10} - 32867 x^{9} + \frac{565167}{8} x^{8} + 71107 x^{7} + \frac{10297}{2} x^{6} - 24882 x^{5} - 11798 x^{4} + 1536 x^{3} + 2808 x^{2} + 864 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-20250*x^12 - 882900/11*x^11 - 111159*x^10 - 32867*x^9 + 565167/8*x^8 + 71107*x^
7 + 10297/2*x^6 - 24882*x^5 - 11798*x^4 + 1536*x^3 + 2808*x^2 + 864*x

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Sympy [A]  time = 0.117523, size = 63, normalized size = 0.81 \[ - 20250 x^{12} - \frac{882900 x^{11}}{11} - 111159 x^{10} - 32867 x^{9} + \frac{565167 x^{8}}{8} + 71107 x^{7} + \frac{10297 x^{6}}{2} - 24882 x^{5} - 11798 x^{4} + 1536 x^{3} + 2808 x^{2} + 864 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-20250*x**12 - 882900*x**11/11 - 111159*x**10 - 32867*x**9 + 565167*x**8/8 + 711
07*x**7 + 10297*x**6/2 - 24882*x**5 - 11798*x**4 + 1536*x**3 + 2808*x**2 + 864*x

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GIAC/XCAS [A]  time = 0.218856, size = 80, normalized size = 1.03 \[ -20250 \, x^{12} - \frac{882900}{11} \, x^{11} - 111159 \, x^{10} - 32867 \, x^{9} + \frac{565167}{8} \, x^{8} + 71107 \, x^{7} + \frac{10297}{2} \, x^{6} - 24882 \, x^{5} - 11798 \, x^{4} + 1536 \, x^{3} + 2808 \, x^{2} + 864 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-20250*x^12 - 882900/11*x^11 - 111159*x^10 - 32867*x^9 + 565167/8*x^8 + 71107*x^
7 + 10297/2*x^6 - 24882*x^5 - 11798*x^4 + 1536*x^3 + 2808*x^2 + 864*x