3.1219 \(\int (1-2 x)^2 (2+3 x)^8 (3+5 x) \, dx\)

Optimal. Leaf size=45 \[ \frac{5}{243} (3 x+2)^{12}-\frac{16}{99} (3 x+2)^{11}+\frac{91}{270} (3 x+2)^{10}-\frac{49}{729} (3 x+2)^9 \]

[Out]

(-49*(2 + 3*x)^9)/729 + (91*(2 + 3*x)^10)/270 - (16*(2 + 3*x)^11)/99 + (5*(2 + 3
*x)^12)/243

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Rubi [A]  time = 0.0858559, 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 \[ \frac{5}{243} (3 x+2)^{12}-\frac{16}{99} (3 x+2)^{11}+\frac{91}{270} (3 x+2)^{10}-\frac{49}{729} (3 x+2)^9 \]

Antiderivative was successfully verified.

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

[Out]

(-49*(2 + 3*x)^9)/729 + (91*(2 + 3*x)^10)/270 - (16*(2 + 3*x)^11)/99 + (5*(2 + 3
*x)^12)/243

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Rubi in Sympy [A]  time = 12.1375, size = 39, normalized size = 0.87 \[ \frac{5 \left (3 x + 2\right )^{12}}{243} - \frac{16 \left (3 x + 2\right )^{11}}{99} + \frac{91 \left (3 x + 2\right )^{10}}{270} - \frac{49 \left (3 x + 2\right )^{9}}{729} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

5*(3*x + 2)**12/243 - 16*(3*x + 2)**11/99 + 91*(3*x + 2)**10/270 - 49*(3*x + 2)*
*9/729

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Mathematica [A]  time = 0.0042225, size = 67, normalized size = 1.49 \[ 10935 x^{12}+\frac{647352 x^{11}}{11}+\frac{1307097 x^{10}}{10}+144315 x^9+59616 x^8-39312 x^7-62160 x^6-\frac{134112 x^5}{5}+3200 x^4+\frac{24832 x^3}{3}+3712 x^2+768 x \]

Antiderivative was successfully verified.

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

[Out]

768*x + 3712*x^2 + (24832*x^3)/3 + 3200*x^4 - (134112*x^5)/5 - 62160*x^6 - 39312
*x^7 + 59616*x^8 + 144315*x^9 + (1307097*x^10)/10 + (647352*x^11)/11 + 10935*x^1
2

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Maple [A]  time = 0.001, size = 60, normalized size = 1.3 \[ 10935\,{x}^{12}+{\frac{647352\,{x}^{11}}{11}}+{\frac{1307097\,{x}^{10}}{10}}+144315\,{x}^{9}+59616\,{x}^{8}-39312\,{x}^{7}-62160\,{x}^{6}-{\frac{134112\,{x}^{5}}{5}}+3200\,{x}^{4}+{\frac{24832\,{x}^{3}}{3}}+3712\,{x}^{2}+768\,x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

10935*x^12+647352/11*x^11+1307097/10*x^10+144315*x^9+59616*x^8-39312*x^7-62160*x
^6-134112/5*x^5+3200*x^4+24832/3*x^3+3712*x^2+768*x

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Maxima [A]  time = 1.32532, size = 80, normalized size = 1.78 \[ 10935 \, x^{12} + \frac{647352}{11} \, x^{11} + \frac{1307097}{10} \, x^{10} + 144315 \, x^{9} + 59616 \, x^{8} - 39312 \, x^{7} - 62160 \, x^{6} - \frac{134112}{5} \, x^{5} + 3200 \, x^{4} + \frac{24832}{3} \, x^{3} + 3712 \, x^{2} + 768 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

10935*x^12 + 647352/11*x^11 + 1307097/10*x^10 + 144315*x^9 + 59616*x^8 - 39312*x
^7 - 62160*x^6 - 134112/5*x^5 + 3200*x^4 + 24832/3*x^3 + 3712*x^2 + 768*x

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Fricas [A]  time = 0.191651, size = 1, normalized size = 0.02 \[ 10935 x^{12} + \frac{647352}{11} x^{11} + \frac{1307097}{10} x^{10} + 144315 x^{9} + 59616 x^{8} - 39312 x^{7} - 62160 x^{6} - \frac{134112}{5} x^{5} + 3200 x^{4} + \frac{24832}{3} x^{3} + 3712 x^{2} + 768 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

10935*x^12 + 647352/11*x^11 + 1307097/10*x^10 + 144315*x^9 + 59616*x^8 - 39312*x
^7 - 62160*x^6 - 134112/5*x^5 + 3200*x^4 + 24832/3*x^3 + 3712*x^2 + 768*x

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Sympy [A]  time = 0.116835, size = 65, normalized size = 1.44 \[ 10935 x^{12} + \frac{647352 x^{11}}{11} + \frac{1307097 x^{10}}{10} + 144315 x^{9} + 59616 x^{8} - 39312 x^{7} - 62160 x^{6} - \frac{134112 x^{5}}{5} + 3200 x^{4} + \frac{24832 x^{3}}{3} + 3712 x^{2} + 768 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

10935*x**12 + 647352*x**11/11 + 1307097*x**10/10 + 144315*x**9 + 59616*x**8 - 39
312*x**7 - 62160*x**6 - 134112*x**5/5 + 3200*x**4 + 24832*x**3/3 + 3712*x**2 + 7
68*x

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GIAC/XCAS [A]  time = 0.203871, size = 80, normalized size = 1.78 \[ 10935 \, x^{12} + \frac{647352}{11} \, x^{11} + \frac{1307097}{10} \, x^{10} + 144315 \, x^{9} + 59616 \, x^{8} - 39312 \, x^{7} - 62160 \, x^{6} - \frac{134112}{5} \, x^{5} + 3200 \, x^{4} + \frac{24832}{3} \, x^{3} + 3712 \, x^{2} + 768 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

10935*x^12 + 647352/11*x^11 + 1307097/10*x^10 + 144315*x^9 + 59616*x^8 - 39312*x
^7 - 62160*x^6 - 134112/5*x^5 + 3200*x^4 + 24832/3*x^3 + 3712*x^2 + 768*x